OINTARlO

COLLEGE OF PHARNIACY

A-A GERRARD ST. E. TORONTO,

ONTARIO

COLLEGE OF PHARMACY

44 GERRARD ST. E. TORONTO,

REFRACTION

HOW TO REFRACT

THORINGTON

REFf

ut

INC!'

BY THE SAME AUTHOR.

Rctinoscopy (The Shadow Test) in the Determination of Refraction at One Meter Distance witli tlie Plane Mirror. 38 Illustrations, a number of which are in Colors. Third Edition, ///^Z /?<'afl^. Cloth, net, $i.co

From The Medical Record, Ne7v York.

"It presents a clear, terse, and thorough exposition of an objective method of determining refraction errors which is de- servedly increasing in popularity. In our opinion the author is amply justified in declaring that its great value in nystagmus, young children, amblyopia, aphakia, and in examining illiterates and the feeble minded, cannot be overestimated, and we agree with him in reminding those who attempt retinoscopy. fail, and ridicule it, that the fault is behind and not in front of the mirror. The book is well printed and usefully illustrated."

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M^M:

M^

lift: '

mmu

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REFRACTION

AND

HOW TO REFRACT

INCLUDING SECTIONS ON OPTICS, RETINOSCOPY, THE FITTING OF SPECTACLES AND EYE-GLASSES, ETC.

r,

BY

JAMES THORINGTON, A.M., M.D.,

ADJUNCT PROFESSOR OF OPHTHALMOLOGY IN THE PHILADELPHIA POLYCLINIC AND COLLEGE FOR GRADUATES IN MEDICINE ; ASSISTANT SURGEON AT WILLS' EYE HOSPITAL ; ASSOCIATE MEMBER OF THE AMERICAN OPHTH ALMOLOGICAL SOCIETY; FELLOW OF THE COLLEGE OF PHYSICIANS OF PHILADELPHIA; MEMBER OF THE AMERICAN MEDICAL ASSOCIATION ; OPHTHALMOLOGIST TO THE ELVVYN AND THE VINE- LAND TRAINING SCHOOLS FOR FEEBLE-MINDED CHILDREN ; RESIDENT PHYSICIAN AND SURGEON PANAMA RAILROAD CO. AT COLON (aSPINWALL), isthmus OF PANAMA, 1882-1889, ETC.

TWO HUNDRED ILLUSTRATIONS

THIRTEEN OF WHICH ARE COLORED

ONTARIO

COLLEGE OF PHARMACY

44 GERRARD ST. E.

TORONTO, PHILADELPHL\ P. BLAKISTON'S SON & CO.

IOI2 W.\LNUT STREET 1900

BY THE SAME AUTHOR.

Retinoscopy (The Shadow Test) in the Determination of Refraction at One Meter Distance witli the Plane Mirror. 38 Illustrations, a number of which are in Colors. Third Edition. Jus^ /^eady. Cloth, net, fi.co

From The Medical Record, New York.

" It presents a clear, terse, and thorough exposition of an objective method of determining refraction errors which is de- servedly increasing in popularity. In our opinion the author is amply justified in declaring that its great value in nystagmus, young children, amblyopia, aphakia, and in examining illiterates and the feeble minded, cannot he overestimated, and we agree with him in reminding those who attempt retinoscopy, fail, and ridicule it, that the fault is behind and not in front of the mirror. The book is well printed and usefully illustrated."

o

REFRACTION

AND

HOW TO REFRACT

INCLUDING SECTIONS ON OPTICS, RETINOSCOPY, THE FITTING OF SPECTACLES AND EYE-GLASSES, ETC.

BY

n

JAMES THORINGTON, A.M., M.D.,

ADJUNCT PROFESSOR OF OPHTHALMOLOGY IN THE PHILADELPHIA POLYCLINIC AND COLLEGE

FOR GRADUATES IN MEDICINE ; ASSISTANT SURGEON AT WILLS* EYE HOSPITAL ; ASSOCIATE

MEMBER OF THE AMERICAN OPHTHALMOLOGICAL SOCIETY ; FELLOW OF THE

COLLEGE OF PHYSICIANS OP PHILADELPHIA; MEMBER OF THE AMERICAN

MEDICAL ASSOCIATION ; OPHTHALMOLOGIST TO THE ELWYN AND THE VINE-

^ ^k LAND TRAINING SCHOOLS FOR FEEBLE-MINDED CHILDREN ; RESIDENT

.nS

PHYSICIAN AND SURGEON PANAMA RAILROAD CO. AT COLON (aSPINWALL), ISTHMUS OF PANAMA, 1882-1889, ETC.

TWO HUNDRED ILLUSTRATIONS

THIRTEEN OF WHICH ARE COLORED

ONTAt-iiO

COLLEGE OF PHARMACY

44 GERRARD ST. E.

TORONTO, PHILADELPHL\ P. BLAKISTON'S SON & CO.

IOI2 WALNUT STREET 1900

Copyright, 1S99, by P. Blakiston's Son & Co.

WM. F. FELL & CO.,

Electrotvpers and Printers, 1220-24 sansom street, philadelphia.

PREFACE.

This book has been written at the request of the many students who have attended the author's lectures on " Refraction " at the Philadelphia Polyclinic; and while it is intended for all beginners in the study of Ophthalmology, yet it is especially for those practitioners and students who may have a limited knowledge of mathematics and who can not readily appreciate the classic treatise of Bonders.

In the preparation of the manuscript and in arranging these pages the writer has planned to be systematic and practi- cal, so that the student, starting with the consideration of rays of light, is gradually brought to a full understanding of optics ; and following this, he is taught the standard eye, and then is given a description of ametropic eyes, with a differential diagnosis of each, until finally he is told how to place lenses in front of ametropic eyes to make them equal to the standard condition.

By being dogmatic rather than ambiguous, with occa- sional repetitions to avoid frequent references, and by simple explanations and a definite statement of facts, the writer has aimed to make the text more concise and comprehensive than if encumbered with lengthy mathematic formulas or with any discussion of disputed points.

The chapter on Retinoscopy embraces descriptions of that method of refracting, both with the plane and with the concave mirror ; but no matter how carefully expressed, the

VI PREFACE.

Student will frequently confuse the two, and he is therefore referred to the author's manual on " Retinoscopy with the Plane Mirror."

Of the two hundred illustrations used to elucidate this work, nearly all are newly made, and were drawn or photo- graphed by the author. Those in colors, on page 145, and the diagrams of astigmatic eyes, as also several others, are original.

The author desires to tender his thanks to Dr. H. Murphy, of Philadelphia, and to Dr. J. Ellis Jennings, of St. Louis, Mo., for many valuable suggestions.

120 S. i8th St., Philadelphia, Pa.

November, i8gg.

CONTENTS.

CHAPTER I.

PAGE

Optics, 9

CHAPTER II. The Eye. — The Standard Eye. — The Cardinal Points. — Vis- ual Angle. — Minimum Visual Angle. — Standard Acute- ness of Vision. — Size of Retinal Image. — Accommodation. — Mechanism of Accommodation. — Far and Near Points. — Determination of Distant Vision and Near Point. — Amplitude of Accommodation.- — Convergence. — Angle Gamma. — Angle Alpha, 58

CHAPTER III. Ophthalmoscope. — Direct and Indirect Methods, 86

CHAPTER IV. Emmetropia. — Hyperopia. — Myopia, loi

CHAPTER V. Astigmatism, or Curvature Ametropia. — Tests for Astigma- tism, 120

CHAPTER VI. Retinoscopy, 154

CHAPTER VII. Muscles, 172

CHAPTER VIII. Cycloplegics. — Cycloplegia. — AsTHENoriA. — Examination of

THE Eyes, 200

vii

Vin CONTENTS.

CHAPTER IX. How TO Refract, 220

CHAPTER X. Applied Refraction, 233

CHAPTER XI. Presbyopia. — Aphakia. — Anisometropia. — Spectacles, .... 260

CHAPTER XII. Lenses, Spectacles, and Eye-glass Frames. — How to Take Measurements for Them and How They Should be Fitted, 285

INDEX, 295

LIST OF ILLUSTRATIONS.

FIG. _ PAGE

1. Reflection, 12

2. Reflection from Plane Minor, 12

3. Lateral Inversion, 13

4. Reflection from Concave Minor, 14

5. Erect Image P'ormed by Concave Mirror, 15

6. Inverted Image Formed by Concave Mirror, 16

7. Image Fonned by Convex Mirror, 17

8. Perpendicular to Plane Surfaces, 18

9. Refraction, 18

10. Critical Angle, 19

II and 12. Angle of Refraction, 20

13. Density, 20

14. Index of Refraction, 21

15. Maximum Deviation, 22

16. Minimum Deviation, 22

17. Angle of Deviation, 23

18. Displacement, 24

19. Centrad, 24

20. Prism Diopter, 24

21. Neutralization of Prisms, 25

22. Correction of Diplopia, 28

23. 24, and 25. Convex Lenses, 29

26, 27, and 28. Concave Lenses, 30

29. Peripheral Refraction Through a Convex Lens, 30

30. Peripheral Refraction Through a Concave Lens, 30

31. Parallel Rays Passing Through a Convex Lens, 31

32. Parallel Rays Passing Through a Concave Lens, 32

^^. Conjugate Foci, 33

34. Ordinary Foci, 34

35. Negative Focus, 35

36. Secondaiy Axes, 35

37. Optic Center, 36

38. Inverted Image Formed by a Convex Lens, . . 37

39. Erect Magnified Image Formed by a Convex Lens, 39

40. Image Formed by a Concave Lens, 39

41 and 42. Cylindric Lenses, 43

43. Cylinder Axis, 43

44. Parallel Rays Passing Through a Convex Cylinder, 43

45. Parallel Rays Passing Through a Concave Cylinder, 44

46. Trial-case, 45

X LIST OF ILLUSTRATIONS.

FIG. PAGE

47 and 48. Trial-frames, 46 and 47

49. Combining Sphere and Cylinder, 49

50, 51, and 52. Finding Optic Center of a Lens, 54

53 and 54. Finding Cylinder-axis, 55

54, 55, and 56. Action of a Cylinder, 55 and 56

57. Standard Eye, 59

58. Angle of View, 60

59 and 60. Size of Retinal Image, 61

61. Minimum Visual Angle, 62

62 and 63. Five-minute Angle, . . 63

64. Retinal Image in the Standard and Ametropic Eyes, 64

65. Crystalline Lens at Rest and Accommodating, 67

66. Accommodation, 68

67. Hyperopic Eye at Rest, 70

68. Myopic Eye at Rest, 71

69. Randall's Test-letters, 73

70. Wallace Test-letters, 74

71. Illiterate Card, 74

72. Gould's Test-letters, 75

73. Gothic Type for Testing Near Point, 79

74. Block Letters for Testing the Near Point, . . 80

75. Meter Angle of Convergence, 82

76. Angle Gamma, 83

77. Positive Angle Gamma, 84

78. Negative Angle Gamma, 85

79. Loring Ophthalmoscope, 87

80. Direct Ophthalmoscopy, 88

81. Emmetropia with the Ophthalmoscope, 94

82. Hyperopia with the Ophthalmoscope, 95

83. Myopia with the Ophthalmoscope, 96

84. Indirect Ophthalmoscopy, 98

85. Condensing Lens, 98

86. Emmetropia, loi

87. Emmetropic and Ametropic Eyes 23 mm. Long, 102

88. Hyperopic Eye at Rest, 105

89. Hyperopic Eye Refracted, 105

90. Parallel Rays Entering a Myopic Eye IIO

91. Myopic Eye at Rest, Ill

92. Myopic Eye Refracted, ill

93. Astigmatic Lens, 121

94. Simple Hyperopic Astigmatism, 124

95. Simple Myopic Astigmatism, 125

96. Compound Hyperopic Astigmatism, 125

97. Compound Myopic Astigmatism, 126

98 and 99. Mixed Astigmatism, 127

ICXD. Symmetric Astigmati.sm, 128

loi. Asymmetric Astigmatism, 128

102. Astigmatism with the Rule, 129

103. Astigmatism Against the Rule, 129

104. Placido's Disc, I33

105. Stenopeic Slit, 133

106. Green's Astigmatic Chart, 135

LIST OF ILLUSTRATIONS.

FIG. _ PAGE

107. Astigmatic Clock-dial, 136

108. Astigmatic Clock-dial in Black, 137

109. Author's Pointed Line Test, 139

1 10. Perforated Disc, 140

111. Pray' s Letters, 140

112. Scheiner's Disc, 141

113. Scheiner's Disc in Hyperopia, 141

114. Scheiner's Disc in Myopia, 142

115 and 116. Cobalt-blue Glass, 143

117. Refrangibility of Cobalt-blue Glass, 144

118 to 129, inclusive. The Diagnosis of the Different Forms of Ametro- pia with Cobalt-blue Glass, 145

130. Thomson's Ametrometer, 147

131 and 132. Ophthalmometer, 148 and 149

133 and 134. Mires or Targets, 150

135. Indirect Ophthalmoscopy, 153

136. Author's Schematic Eye, 154

137. Point of Reversal, . 155

138 and 139. Author's Mirror with Folding Handle, 156

140. Author's Iris Diaphragm Chimney, 157

141. Position of Light and Mirror, 158

142. High Myopia as Seen with the Concave Minor, 159

143. Hyperopia as Seen with the Concave Mirror, 159

144 and 145. Rate of Movement of Retinal Illumination in Hyperopia

and Myopia, 162 and 163

146. Retinal Illumination in Emmetropia, 164

147. Band of Light, 167

148. Axonometer, 168

149. Scissor Movement, 170

150. Positive Aberration, 171

151. Negative Aberration, 171

152. Homonymous Diplopia, 173

153. Heteronymous Diplopia, 174

154 and 155. Maddox Rods, 182

156. Rotary Prism of Risley, 183

157. Phorometer, 184

158. Strabismometer, I94

159. Angle of Deviation in Strabismus, 195

160. Monocular Blinder, 197

161. Aphakia, 267

162 and 163. Franklin Bifocals, 273

164. Merck's Bifocals, 273

165 to 171, inclusive. Cement Bifocals, 274 and 275

172 and 173. Acromatic Bifocals, 275

174 and 175. Solid Bifocals, 276

176 to 180, inclusive. Half Lenses, 277

181. Toric Lenses, 278

182 to 191. inclusive. Different Sizes and Shaped Lenses, . . 283 and 286

192. Measuring Interpupillary Distance, 289

193 and 194. Fitting of Spectacle Bridge, 290

195. Measurement of Bridge, 291

196. Measurement for Spectacles, 292

XU LIST OF ILLUSTRATIONS.

FIG.

197. Measurement for Eye-glasses, 29

198. Distance Frames

PAGE

2

293

199. Near Frames, 293

200. Measurement for Guards, 293

REFRACTION

HOW TO REFRACT.

CHAPTER I.

OPTICS.

Optics (from the Greek Zr^ropM, meaning "to see") is that branch of physical science which treats of the nature and properties of hght.

Catoptrics (from the Greek xdruirrfjir^, meaning " a mir- ror") and dioptrics (from the Greek <5£'""/'<'v, meaning " to see through ") are subdivisions of optics ; the former treating of incident and reflected rays, and the latter of the refraction of light passing through different media, such as air, water, glass, etc., but especially through lenses.

Light. — Light may be defined as that form of energy W'hich, acting upon the organs of sight, renders visible the objects from which it proceeds. This form of energy is propagated in waves in all directions from a luminous body, and with a velocity in a vacuum of about 186,000 miles a second. In the study of a luminous body, such as a candle-, lamp-, or gas-flame, the substance itself must not be con- sidered as a single source of radiation, but as a collection of minute points, from every one of which waves proceed in all directions and cross one another as they diverge from their respective points. The intensity of light decreases

9

10 REFRACTION AND HOW TO REFRACT.

as the square of the distance from the hght increases : for example, if an object is twice as far from a luminous body as another of the same size, it will receive one-fourth as much light as the latter.

Ray. — Ray (from " radius ") is used in optics in prefer- ence to wave, and means the smallest subdivision of light traveling in a straight line. Rays of light are considered as incident, emergent, reflected, refracted, divergent, par- allel, and convergent.

Incident Rays. — Rays of light are said to be incident when they strike the surface of an object.

Emergent Rays. — Rays of light are emergent when they have passed through a transparent substance.

Reflected Rays. — Rays of light are reflected when they rebound from a polished surface.

Refracted Rays. — A ray of light undergoes refraction when it is deviated from its course in passing through any transparent substance.

Divergent Rays. — Rays of light proceed divergently from any luminous substance, but, in the study of refrac- tion, only those which proceed from a point closer than six meters are spoken of as divergent.

Parallel Rays. — The greater the distance of an)- lumin- ous point, the more nearly do its rays approach to paral- lelism ; this is evident in a study of rays coming from such distant sources as the sun, moon, and stars. For all prac- tical purposes in the study of refraction, ra}-s of light which proceed from a distance of six meters or more are spoken of as parallel, although this is not an absolute fact, as ra)-s of light at this distance still maintain a slight anunnit of di\-er- gcnce. If the pupil of the emmetropic e)'e is represented by a circular opening four millimeters in diameter, then rays of light from a luminous point at si.x meters (6000

OPTICS. 1 1

mm.) will have a divergence of -q^\-q to enter such a pupil.

Convergent Rays. — Convergent rays are the result of reflection from a concave mirror or refraction through a convex lens.

A Beam. — This is a collection or series of parallel rays.

A Pencil. — A pencil of light is a collection of conver- gent or divergent rays. Convergent ra}'s are those which tend to a common point, whereas divergent rays are those which proceed from a point and continually separate as they proceed. This point is called the radiant point.

A Focus. — This is the point of a convergent or diver- gent pencil ; the center of a circle ; the point to which converging rays are directed.

A Positive or Real Focus. — This is the point /o ivJiich rays are directed after passing through a convex lens or after reflection from a concave mirror.

A Negative or Virtual Focus. — This is the point from which rays appear to diverge after passing through a con- cave lens, or after reflection from a convex mirror, or after refraction through a convex lens w4ien the light or object is closer to the lens than its principal focus, or after reflection from a concave mirror when the light or object is closer to the mirror than its principal focus.

The principal phenomena of light are absorption, reflec- tion, and refraction.

Absorption. — Rays of light from the sun falling upon the green grass are partly absorbed and partly reflected. The grass absorbs some of the ra)'s and sends back or reflects only those rays which together produce the effect of green. A piece of red glass owes its color to the fact that it only transmits that portion of the light's rays whose combined effect upon the retina is that of red. The relative

12

REFRACTION AND HOW TO REFRACT.

proportion of absorption and reflection of rays of light greatly depends upon the quality of the surface — whether light colored or polished, or dark colored or rough.

Reflection. — From the Latin rcflcctcrc, " to rebound." This is the sending back of rays of light by the surface on which they fall into the medium through which they came. While most of the rays falling upon the surface of a trans- parent substance pass through it, with or without change in their direction, yet some of the rays are reflected, and it is by these reflected rays that surfaces are made visible.

Fig. 2.

A substance that could transmit or absorb all the rays of light coming to it (if such a substance existed) would be invisible. Reflection, therefore, always accompanies refrac- tion, and, if one of these disappear, the other will disappear also.

Laws of Reflection. — (i) The angle of reflection is equal to tlic angle of incidence. (2) The reflected and in- cident rays arc in the same plane with the perpentiicular to the surface. (See Fig. i.)

If A B represent a polished surface and I the incident ray, tlien P D I is the angle of incidence ; R being the re-

OPTICS.

13

fleeted ray, then P D R, equal to it, is the angle of reflection. I D, P D, and R D lie in the same plane.

A reflecting surface is usually a polished surface (a mirror), and may be plane, concave, or convex.

Reflection from a Plane Mirror. — Rays of light are reflected from a plane mirror in the same direction in which they fall upon it : if parallel, convergent, or divergent be- fore reflection, then they are parallel, convergent, or diver- gent after reflection. An object placed in front of a plane mirror appears just as far back in the mirror as the object is in front of it. (See Fig. 2.)

A B represents a plane mirror with E F, rays from the extremes of the object I, reflected from the mirror A B, and meet- ing at the observer's eye as if they came from the object I in the mirror. (See Visual Angle, p. 60.) The apparent dis- tance of the object I from the observer is equal to the combined length of the incident and reflected rays.

The appearance of an image in a plane mirror is not exactly the same as that of the object facing the mirror ; it undergoes what is known as lateral inversion. This is best understood by holding a printed page in front of a plane mirror, when the words or letters will read from right to left. (See Fig. 3.) An observer facing a plane mirror and raising his right hand, his image apparently raises the left hand.

Tilting a plane mirror gives an object the appearance of

R

r^

E F

^ 3

LEG

03J

T ON

HOIT

Fig. 3. — Lateral Inversion.

14

REFRACTION AND HOW TO REFRACT.

moving in the same direction to that in which the mirror is tilted.

Spheric Mirrors. — A spheric mirror is a portion of a reflecting spheric surface ; its center of curvature is therefore the center of the sphere of which it is a part. Spheric mir- rors are of two kinds — concave and convex.

Reflection from a Concave Mirror (Fig. 4). — Parallel rays are reflected from a concave mirror, and are brought to a focus in front of it. This point is called the principal focus (P.F.). The principal axis of a concave mirror is a straight line drawn from the center of the mirror to the

Fig. 4.

center of curvature (i-i), and a secondary axis (2', 2', 2' , 2') is any other straight line passing from the mirror to the center of curvature (C.C). Rays which diverge from any point beyond the principal focus are reflected con- vergently (G J). Rays which diverge from any point closer than the principal focus are reflected divergently (V V).

Images Formed by a Concave Mirror. — To find the positi(Mi of an image as formed by a concave mirror, two rays may be used : one drawn from a given point on the object to the mirror, and parallel to its principal axis, and reflected through the principal focus (P.P., P'igs. 5 and 6); the other, the secondary axis, from the same point, passing

OPTICS.

15

through the center of curvature. The place where the secondary axis and the reflected ray or their projections in- tersect gives the position of the image. Unhke the plane mirror, which produces images at all times and at all dis- tances, the concave mirror produces either an erect, virtual, and enlarged image, as an object is placed closer than its principal focus, or an enlarged inverted image if the object is between the principal focus and the center of curvature.

By withdrawing the mirror in the former instance the erect image increases slightly in size, and in the latter the inverted image diminishes in size. At the principal focus there is no imacfe formed.

Fig. 5.

Figure 5 shows an erect, virtual, and enlarged image of A R which is closer to the mirror than the principal focus. Parallel rays from A and R are reflected to the principal focus, P.F. Lines drawn from the center of curvature through A and R to the mirror are secondary axes ; these lines and those reflected to the principal focus do not inter- sect in front of the mirror, but if projected, will meet at a and ;- behind the mirror, forming a magnified image of A R. If the mirror is withdrawn from the object, the erect magnified imag-e would increase in size, but at the principal focus no image would be formed, as the rays would be reflected parallel.

i6

REFRACTION AND HOW TO REFRACT.

Figure 6 shows a real inverted image of A R at ^ r ; A R situated beyond the principal focus. Lines drawn from A and R through C.C. are secondary axes. Parallel rays from A and R converge and cross at the principal focus (P.F.).

Where D P and F E intersect the secondary axes, the in- verted image a r of A R is situated. When the object, as in this instance, is situated beyond the center of curvature, the image is smaller than the object. As the image and object are conjugate to each other, they are interchange- able, and in such a case the image would be larger than the object and inverted. This is always true when the

Fig. 6.

object is situated between the center of curvature and the principal focus. When an object is situated at the center of curvature, its image is equally distant and of the same size, but inverted.

Tilting a concave mirror gives an object placed inside of its principal focus the appearance of moving as the mirror is tilted ; but if the object is situated beyond the principal focus, the object appears to move in the opposite direction.

Reflection from a Convex Mirror. — All rays are re- flected divergently from a convex mirror, and parallel ra)\s diverge as if they came from the principal focus situated behind the mirror at a distance equal to one-halt its radius

OPTICS.

17

of curvature. The principal focus of a convex mirror is therefore negative. The foci of convex mirrors are virtual.

Images Formed by a Convex Mirror. — These are always virtual, erect, and smaller than the object. The closer the object, the larger the image ; and the more distant the object, the smaller the image. Tilting a convex mirror, the object does not change position.

In figure 7 parallel rays from the object A R are reflected from the mirror as if they came from the principal focus situ- ated at one-half the distance of the center of curvature, C.C. Lines drawn from the extremes of the object to C.C. are

L;

^.. — t:^''^'

r'"'

c _— — — ^-

'

-^~-p-p.------J

k-c-

..1^ _:

/ '

\

Fig. 7.

secondary axes, and the image is situated at the point of intersection of the secondary axes and the rays from the principal focus ; and as these meet behind the mirror, the image is virtual and erect.

Refraction. — From the Latin rcfrangcrc, meaning "to bend back " — /. c, to deviate from a straight course. Refrac- tion may be defined as the deviation which takes place in the direction of rays of light as they pass from one medium into another of different density.*

* As ordinarily understood in ophthalmology, refraction has come to mean the optic condition of an eye in a state of repose or under the physiologic effect of a cycloplegic.

1 8 REFRACTION AND HOW TO REFRACT.

Two laws govern the refraction of rays of light :

1. A ray of Hght passing from a rare into a denser medium is deviated or refracted toward the perpendicular.

2. A ray of light passing from a dense into a rarer medium is deviated or refracted away from the perpen- dicular.

Aside from these laws, there are other facts in regard to rays of light that should have consideration. A ray of light will continue its straight course through any number of different transparent media, no matter what their densities, so long as it forms right angles with the surface

ICE

FLINT GLASS

CROWN

PLATE

Fig. 8.

or surfaces. Such a ray is spoken of as the normal or perpendicular ; such surfaces are plane, the surfaces and perpendicular forming right angles. (See Fig. 8.) In any case of refraction the incident and refracted ra}^s may be supposed to change places.

Figure 9 shows the perpendicular (P P) to a piece of plate glass with plane surfaces. The ray in air incident at O on the surface S 1" is bent in the glass toward the per- pendicular, P P. The dotted line shows the direction the ray would have taken had it not been refracted. As tlic ray in tlie glass comes to the second surface at R, and

OPTICS.

19

passes into a rarer medium, it is deviated from the perpen- dicular, P P. The ray now continues its original direction, but has been deviated from its course ; it has undergone lateral displacement.

Critical Angle or Limiting Angle of Refraction. — This is the angle of incidence which just permits a ray of light in a dense medium to pass out into a rare medium. The size of the critical angle depends upon the index of refrac- tion of different substances. Figure 10 shows an electric light suspended in water. The ray from this light which forms an angle of 48° 35' with the surface of the w^atcr

Fig. 10. — Critical Angle.

will be refracted and pass out of the water, grazing its sur- face ; but those rays which form an angle greater than 48° 35' will not pass out of the water, but will be reflected back into it. The surface separating the two media be- comes a reflecting surface and acts as a plane mirror.

The critical angle for crown glass is 40° 49'.

Index of Refraction. — By this is meant the relative density of a substance or the comparative length of time required for. light to travel a definite distance in different substances. The absolute index of refraction is the density or refractive power of any substance as compared

20

REFRACTION AND HOW TO REFRACT.

with a vacuum. According to the first law of refraction, a ray of Hght passing from a rare into a dense medium is refracted toward the perpendicular ; in other words, the angle of refraction is smaller, under these circumstances, than the angle of incidence. In the study of the compara- tive density of any substance it will be seen that the angle of re- fraction is usually smaller the more dense the substance ; this is well illustrated in figures ii and 12.

The greater the density, the slower the velocity or the mere effort apparently for the wave or ray to pass through the substance. This is illustrated in figure 13, where a ray or wave of light is seen passing at right angles through different media. A ray passes through a vacuum without apparent resistance, but in its course through air it is slightly impeded, so that air has an index of refraction of

rmrf]

Fig. II.

Fig. 12.

Vacuum

Air

Glass Diamond

Fig. 13.

1.00029-]- when compared with a vacuum ; but as this is so slight, air and a vacuum are considered as one for all pur- poses in refraction. To find the inde.x of refraction of any substance as compared with a x-acuum or air, it is neces- sary to divide the sine of the angle of incidence by the sine of the antrle of refraction.

OPTICS.

21

In figure 14 the angle of incidence I C P is the angle formed by the incident ray I with the perpendicular, P P. The angle of refraction R C P is the angle formed by the refracted ray with the perpendicular, P P. Drawing the circle P H P O around the point of incidence C, and then drawing the sines D X and B F, perpen- diculars to the per- pendicular P P, divide the sine D X of the angle of incidence by the sine F B of the angle of refraction to obtain the index of refraction ; in this in- stance, water as com- pared with air. D X equaling 4 and F B equaling 3, then 4 di- vided by 3 will equal

F

I.

C ]

/ Air \

\ Water

3 2 l\^/

_>\T^

p

Fig. 14.

3'

or

1.33 -|-, the index of refraction of water as compared with air. To find the index of refraction of a rare as compared with a dense substance, divide the sine of the angle of refraction by the sine of the angle of incidence — /. c, air as compared with water would be y^, or 0.75.

Indexes of Refraction.

Air, 1.00029

Water, 1. 333

Cornea, ^Zm

Crown glass, 1-5

Flint glass, i-S^

Crystalline lens, nucleus, 1-43

" " intcrniecliatc layer, I.4I

" " cortical layer, 1-39

22

REFRACTION AND HOW TO REFRACT.

A prism is any refracting substance bounded by plane surfaces which intersect each other. The sides of a prism are the incHned surfaces. The apex is where the two plane surfaces meet. The base of the prism is the thickest part of the prism. The refracting angle is the angle at which the sides come together.

Position of a Prism. — When a prism is placed in front of an eye, its position is indicated or described by the direc- tion in which its base is situated : base down means that the thick part of the prism is toward the cheek ; base up means that the thick part of the prism is toward the brow ; base in means that the thick part of the prism is toward the

Fig. 15.

Fig. 16,

nose ; and base out means that the thick part of the prism is toward the temple.

Prismatic Action. — Rays of light passing through a prism are always refracted toward the base of the prism. If an incident ray is perpendicular to the surface of a prism, there will be only one refraction, and that takes place at the point of emergence. The angle of incidence in this instance will equal the angle of the prism, and the maximum deviation takes place, as all the refraction is done at one surface.

In figure i 5 the incident ray (I) is perpendicular to the surface A B, and is not refracted until it comes to the sur-

OPTICS. 23

face A C at E, when it is bent toward the base B C, all the refraction taking place at the surface A C.

If an incident ray forms an angle other than a right angle with the first surface of the prism, then it will be re- fracted twice — as it enters and as it leaves the prism.

In figure 16 X N is the perpendicular to the surface A B. The ray (I) incident at N is refracted toward this perpen- dicular and follows the course N E inside of the prism. On emergence it is refracted from the perpendicular E P of the surface A C, and in the direction of the base of the prism. If the incident ray (I) so falls upon the surface at A B that the refracted ray (N E) is parallel to the base (B C), then the emergent ray is such that the angle of emergence equals the angle of incidence (I N X) ; as in this instance the angles of incidence and of emergence are equal, the deviation, therefore, is at a minimum, or the least possible.

Angle of Deviation (Fig. 17). — This is the angle formed between the directions of the incident and emergent rays, and measures the total deviation. In all prisms of ten degrees p,,^, i7_

or less the angle of deviation is equal

to half the angle of the prism, but in prisms of more than ten degrees the angle of deviation increases.

Summary. — Prisms do not cause rays of light to con- verge or to diverge ; rays that are parallel before refraction are parallel after refraction. Therefore, prisms do not form images ; prisms have no foci.

Effect of a Prism. — An object viewed througli a prism has the appearance of being displaced, and in a direction opposite to the base — /. c, toward the aj^ex.

Ra}'s from the object (X, Fig. 18) strike the prism at C.

24

REFRACTION AND HOW TO REFRACT.

undergo double refraction, and, falling upon the retina of the

eye, are projected back in the direction in which they

were received, and the apparent position of X is changed

to X', azuay from the base of the

prism and totvard the apex.

Numbering of Prisms. — Form- erly, prisms were numbered by their refracting' anorles ; now, howev^er, two other methods are in use : Dennett's method, known as the centrad ; and Prentice's method, known as the prism-diopter.

Dennett's Method (Fig. 19). — The unit, or centrad (ab- breviated V ), is a prism that will deviate a ray of light the y^Q- part of the arc of the radian. This is calculated as follows : As much of the circumference of a circle is taken as will equal the length of its radius of curvature ; this is called the arc of the radian, and equals 57.295 degrees. The arc of the radian is then divided into 100' parts. A

Fig. 18.

Radius Fig. 19.

prism, base down, at the center of curvature that will devi- ate a ray of light downward just yj,y part of the arc of the radian is a one centrad, and cciuals j-,^, |y of 57--95 degrees, or 0.57295 of a degree.

OPTICS.

25

98765432

98765432

0

Ten centrads will deviate a ray of light ten times as much as one centrad, or 10 X 0.57295 = 5.7295 degrees, etc.

Prentice's Method (Fig. 20). — The unit, or prism-diopter (abbreviated P.D.,or A), is a prism that will deflect a ray of light just I cm. for each meter of dis- tance— that is, the y^-g- part of the radius measured on the tan- gent. The deflection always be- ing I cm. for each meter of dis- tance, I P. D. will deviate a ray of light 2 cm. for 2 meters of dis- tance ; 3 cm. for 3 meters, etc. The comparative values of cen- trads and prism-diopters is quite uniform up to 20, but above 20 the centrad is the stronger.

Neutralization of Prisms. — Knowing that rays of light are de- flected by centrads and prism - diopters up to 20, in the ratio of I cm. for each meter of distance, then to find the numeric strength of any prism all that is necessary is to hold the prism over a series of numbered parallel lines, sepa- rated by an interval of i cm. or fraction thereof, and note the

amount of displacement. For example, figure 2 1 shows a series of vertical lines I3 of a cm. apart, and numbered from o to 9 ; an X is placed at the foot of the o line. Holding a prism, base to the right, at a distance of y^ of a meter (as 3

Fig. 21.

26

REFRACTION AND HOW TO REFRACT.

the lines are ^3 of a cm. apart) and looking through the prism at the X on the o line, it will be seen that the X has been displaced to the line to the left corresponding to the number of centrads or prism-diopters in the prism ; in this instance three.

Table Showing the Equivalence of Centrads in Prism-diopters

AND in Degrees of the Refracting Angle (Index of

Refraction 1.54).

Centr

ADS. Prism-diopters.

Refracting Angle.

I

I.

I°.0O

2

2.000I

2°. 12

3

3-0013

3°.i8

4

4.0028

4°-23

5

5 -0045

5°. 28

6

6.0063

6°. 32

7

7.0115

7°-35

8

8.0172

8°.38

9

9.0244

9°-39

10

10.033

10°. 39

II

11.044

11°. 37

12

12.057

12°.34

13

13-074

i3°.29

14

14.092

I4°.23

15

15.114

15°. 16

16

16.138

16°. 08

17

17,164

16°. 98

18

18.196

i7°.85

19

19.230

i8°.68

20

20.270

i9°-45

25

25-55

23°.43

30

30.934

26°. 81

35

36.50

29°. 72

40

42.28

32°. 18

45

48.30

34°. 20

50

54-514

35°-94

60

68.43

38°.3i

70

S4.22

39°- 73

80

102.96

40°. 29

90

126.01

40°. 49

100

155-75

39°- 14

Or a prism ma\' be neutralized by placing another prism

in apposition to it, with their bases opposite, so that in look-

OPTICS. 27

ing through the two prisms at a straight Hne, no matter at what distance, the straight edge will continue to make one straight line through the prisms ; the strength of the neu- tralizing prism will equal the strength of the prism being neutralized.

Uses of Prisms. — i. To detect malingerers who profess monocular blindness so as to obtain damages for supposed injuries, or who wish to escape war service, or those cases of hysteric blindness wishing to create sympathy. This test or use of a prism is known as the diplopia test, and is practised as follows : A seven P. D., base up or down, with a blank are placed in the trial -frame corresponding to the " blind " eye ; nothing is placed in front of the seeing eye ; the trial-frame, thus arm.ed (without the patient seeing what is being done), is placed on the patient's face and he is in- structed to read the card of test-letters on the wall across the room. While he is thus busy reading, and purposely contradicted by the surgeon, so as to get his mind from his condition, the surgeon suddenly removes the blank from the " blind " eye. The patient exclaiming that he sees two cards and two of all the letters proves the deception.

2. Occasionally, to counteract the effects of strabismus, or diplopia due to a paralysis of one or more of the extra- ocular muscles. For example : A patient looking at a point of light focused on the macula (M) of the left eye (L), and the right eye being turned in toward the nose, receives the rays upon the nasal retina, and hence projects the rays outward to the right, giving a false image to the right side ; a prism of sufficient strength is then placed with its base toward the temple (base out) over the right eye, so that the rays from the light may fall upon the macula (M), and the diplopia will be corrected. (See Fig. 22.)

28

REFRACTION AND HOW TO REFRACT.

3. To test the strength of the extra-ocular muscles : A patient looking with both eyes at a distant point of light is made to see one light just above another by placing a 3 P. D., base down or up, before either eye, and if a 2^ P. D. did not produce diplopia when similarly placed, the strength of his vertical recti is then represented by 2j4 P. D. The strength of the prism placed base in which.

Fig. 22.

if increased, would produce diplopia is the strength of the externi ; and the strength of the prism or prisms placed base outward which, if increased, would produce diplopia is the strength of the interni.

4. For exercise of weak muscles. (See p. 185.) Lenses. — A lens is a portion of transparent substance (usually of glass) having one or both surfaces curved. There are two kinds of lenses — spheric and cylindric.

OPTICS. 29

Spheric Lenses. — Abbreviated S. or sph. Spheric lenses are so named because their curved surfaces are sec- tions of spheres. A spheric lens is one which refracts rays of light equally in all meridians or planes. Spheric lenses are of two kinds — convex and concave.

A convex spheric lens is thick at the center and thin at the edge, (Figs. 23, 24, 25.) The following are synony- mous terms for a convex lens : (i) Plus ; (2) positive ; (3) collective ; (4) magnifying. A convex lens is denoted by the sign of plus ( + ).

Varieties or Kinds of Convex Lenses. —

1. Planoconvex, meaning one surface flat and the other convex. It is a section of a

sphere. (See Fig. 23.)

2. Biconvex, also called con- vexoconvex or bispheric, for the reason that it is equal to two planoconvex lenses with their plane surfaces together. (Fig.

-4-j Fig. 23. Fig. 24. Fig. 25.

3. Concavoconvcx. This lens

has one surface concave and the other convex, the convex surface having the shortest radius of curvature. (Fig. 25.) The following are synonymous terms for a concavocon- vcx lens : (i) Periscopic ; (2) convex meniscus ; (3) con- verging meniscus (meniscus meaning a small moon). (See Fig. 25.) A periscopic lens enlarges the field of vision, and is of especial service in presbyopia.

A Concave Spheric Lens. — Such a lens is thick at the edge and thin at the center. (Figs. 26, 27, 28.) The fol- lowing are synonymous terms for a concave lens : ( i ) Minus ; (2) negative ; (3) dispersive ; (4) minifying. A concave lens is denoted by the sign of minus ( — ).

30

REFRACTION AND HOW TO REFRACT.

Varieties or Kinds of Concave Lenses. —

1. Plajioconcave, meaning one surface flat and the other concave. (Fig. 26.)

2. Biconcave, also called concavoconcave or biconcave

spheric, for the reason that it is equal to two planoconcave lenses with their plane surfaces to- gether. (Fig. 27.)

3. Convcxoco7icave. This lens has one surface convex and the other concave, the concave sur- face having the shortest radius of curvature. (Fig. 28.) The following are synonymous terms for a concavoconvex lens : (i) Concave meniscus ; (2) diverging meniscus ; (3) peri- scopic.

Fig. 26. Fig. 27. Fig. 28.

Fiu. 29.

Fig. 30.

A spheric lens may be considered as made up of a scries of prisms which gradually increase in strength from the center to the periphery, no matter whether tlie lens be con- cave or convex.

OPTICS.

31

In the convex sphere the bases of the prisms are toward the center of the lens, whereas in the concave the bases of the prisms are toward the edge. (See Figs. 29, 30.)

Knowing that a prism refracts rays of hght toward its base, it may be stated as a rule that every lens bends rays of light more sharply as the periphery is approached — /. c, at the periphery the strongest prismatic effect takes place.

Lens Action. — As a ray of light will travel in a straight line so long as it continues to form right angles with sur- faces, then the ray A in figure 3 i passes through the bicon- vex lens unrefracted, or without any deviation from its course whatsoever, for at its points of entrance and emer-

FiG. 31.

gence the surfaces of the lens are plane to each other. This ray is called the axial ray, and the line joining the centers of curvature of the two surfaces is called the principal axis. The axis of a planoconvex or planoconcave lens is the line drawn through the center of curvature perpendicular to the plane surface.

The ray B in figure 31, though parallel to the ray A, forms a small angle of incidence, and must, therefore, be refracted toward the perpendicular to the surfaces of the lens, and, passing through the lens, will meet the axial ray at P.F". The rays C, D, and E, also parallel to A and B, form progressively larger angles with the surface of the lens,

A-^

32 REFRACTION AND HOW TO REFRACT.

and finally meet the axial ray at P.F. It will be seen at once that the rays all meet at P.F., showing the progres- sively stronger prismatic action that takes place as the per- iphery of the lens is approached.

In figure t,2 we have similar rays, A, B, C, D, and E,

passing through a con- cave lens. The axial ray A passes through the cen- ters of curvature unre- fracted, but the ra3^s B, C, D, and E are progres- sively refracted more and Fig. 32. more as the periphery is

approached. The ray E in each instance is refracted the most.

T/w action of a cotn'cx lens is similar to that of a concave mirror, a)id the action of a concave lens is similar to tJiat of a convex mirror.

Principal Focus. — The principal focus of a lens may be defined (i) as the point where parallel rays, after refrac- tion, come together on the axial ray ; or (2) as the shortest focus ; or (3) as the focal point for parallel rays.

Focal Length. — This is the distance measured from the optic center to the principal focus. The principal focus of an equally biconvex or biconcave lens of crown glass is situated at about the center of curvature for either surface of the lens. A lens, therefore, has two principal foci, an anterior and a posterior, according to the direction from which the parallel rays come, or as to which radium of cur- vature is referred to. iMgure 31 shows parallel raws, B, C, D, and E, pas.sing through a convex lens and coming to a focus on the axial ray (A) at P.F. ; and as the path of a ray passing from one point to another is the same, no

OPTICS. 33

matter what its direction, then if a point of hght be placed at the principal focus of a lens, its rays will be parallel after passing back through the lens. This is equivalent to what takes place in the standard or emmetropic eye. An eye, in other words, which has its fovea situated just at the princi- pal focus of its dioptric media, such an eye in a state of rest receives parallel rays exactly at a focus upon its fovea, and therefore is in a condition to project parallel rays outward. Conjugate Foci. — Conjugate meaning "yoked to- gether." The point from which rays of light diverge (called the radiant) and the point to which they converge (called the focus) are conjugate foci or points. For in- stance, in figure 33 the rays diverging from A and passing

Fig. ^i.

through the lens converge to the point B ; then the points A and B are conjugate foci. They are interchangeable, for if rays diverged from B, they would follow the same path back again and meet at A. The path of the ray C C is the same whether it passes from A to B or from B to A : there is no difference. It is by the affinity of these points for each other, with respect to their positions, that they are called conjugate.

The conjugate foci are equal when the point of diver- gence is at twice the distance of the principal focus. The equivalent to conjugate foci is found in the long or myopic eye ; an eye, in other words, which has its fovea situated further back than the principal focus of its dioptric media, the result being that rays of Hght from the fovea of such an

34 REFRACTION AND HOW TO REFRACT.

eye would be projected convergently after passing out of the eye, and would meet at some point inside of infinity. In other words, only rays which have diverged from some point inside of six meters will focus upon the fovea of this long eye. The fovea of the myopic eye represents a con- jugate focus. A myopic eye is in a condition to receive divergent rays of light at a focus on its retina and to emit convergent rays.

Ordinary Foci. — When rays of light diverge from some point inside of infinity (six meters) they will be brought to a focus at some point on the other side of a convex lens, beyond its principal focus ; this point is called an ordinary focus. A lens may have many foci, but only two principal

Fig. 34.

foci. The further away from a lens the divergent rays pro- ceed, the nearer to the principal focus on the other side of the lens will they converge. As the divergent rays are brought closer to the lens they reach a point where they will not focus, but will pass parallel after refraction. This point is the principal focus. (See Fig. 34.) A lens, there- fore, has as many foci as there are imaginary points on the axial ray between the principal focus and infinity.

When rays of light diverge from some point closer to a lens than its principal focus, they do not converge, but, after refraction, continue di\'ergenll\' ; their focus now is negative or virtual, and is found by projecting these diver- gent rays back upon themselves to a point on the same

OPTICS.

35 (See

side of the lens from which they appeared to come.

Fig- 35-)

This is the equivalent of what takes place in a short or hyperopic eye, an eye which has its macula closer to its dioptric media than its principal focus. In a state of rest

——-P.P.

Fig. 35.

the fovea of such an eye would project outward divergent rays, and would only be in a position to receive convergent rays of light at a focus upon its fovea.

Secondary Axes. — In the study of the direction of a ray of light passing through a dense medium with plane sur-

FlG. 36.

faces, it was found that it underwent lateral displacement (see Fig. 9), and so in lenses there is a place where ra}-s undergo lateral displacement. Figure 36 shows a convex lens of considerable thickness, and on each side is drawn a radius of curvature (C C). The ray indicated by the arrow

36 REFRACTION AND HOW TO REFRACT,

passed through the two surfaces, has undergone lateral displacement, but continues in its original direction ; such rays are called secondary rays or axes. The incident ray is projected toward N^ in the lens on the axial ray, and the emergent ray, if projected backward, would meet the axial ray at N'^. These points on the axial ray are such that a ray directed to one before refraction, is directed to the other after refraction. The points N^ and N^ are spoken of as nodal points. Every lens, therefore, has two nodal points, but in thin lenses the deviation of the second- ary rays is so slight that, for all practical purposes, only

Fig. 37.

one nodal point is recognized. It is spoken of as the optic center.

Optic Center. — This term is used synonymously with nodal point, and is the point where the secondary rays (s.(7. in F"ig. 37) cross the axial ray. It is not always the geo- metric center. Rays of light crossing the optic center in thin lenses are not considered as undergoing refraction. (See

i^'^S- 37)

Action of Concave Lenses. — Rays of light passing through a concave lens, no matter from what distance, are always refracted div^ergently, and its focus is, therefore, always negative or virtual, and is found by projecting tliese

OPTICS.

37

divergent rays backward in the direction from which they came until they meet at a point on the axial ray. The principal focus and conjugate foci of concave lenses are found in the same way as in convex lenses. (See Figs. 32, 40.)

Images Formed by Lenses. — An image formed by a lens is composed of foci, each one of which corresponds to a point in the object. Images are of two kinds — real and virtual.

A Real Image. — This is an image formed by the actual meeting of rays ; such images can always be projected on to a screen.

A Virtual Image. — This is one that is formed by the prolongation backward of rays of light to a point.

Fig. 38.

To find the position and size of an image it is necessary to obtain the conjugate foci of the extremes of the object, as the image of an object is equal to the sum of its inter- mediate points. Only two rays are required for this pur- pose, one parallel to the axial ray, and one secondary ray passing through the optic center ; the image of the extreme point of the object will be located at the point of inter- section of these rays. In figure 38 A B is an object in front of a convex lens, o is the optic center and P. F. the principal focus. A ray drawn from A parallel to the axial ray o, and a secondary ray from the same point drawn

38 REFRACTION AND HOW TO REFRACT.

through the optic center, will give at their point of inter- section the conjugate focus of the luminous point A, which will be at A'. In the same way the conjugate focus of B and points intermediate in the object may be obtained. A' B' is a real inverted image of A B ; the size of the image of A B depends upon the distance of the object from the lens. The relative sizes of image and object are as their respective distances from the optic center of the lens. For example, an object ten millimeters high, three meters (3000 mm.) from the optic center of a lens, and its image situated sixty millimeters from the lens : the image will be -gll^ or Jq- of the size of the object ; the image will be ^L- of ten millimeters (the height of the object)— namely, 3- of a millimeter high.

As conjugate foci are interchangeable, then in figure 38 if A' B' was the object, the image A B would be the image of A' B', and, therefore, smaller than the object.

Three facts should be borne in mind in the study of real images formed by a convex lens :

1. The object and image are interchangeable.

2. The object and the real image are on opposite sides of the lens, and,

3. As the rays which pass through the optic center cross each other at this point, the real image must be in- verted.

Rays of light from an object situated at the distance of the principal focus would proceed parallel after refraction, and no image of the object would be obtained.

If an object is situated just beyond the principal focus, tlicn the image would be larger than the object, real and inverted. (See Fig. 38, reversing image for object.)

If an object is situated at twice the distance of the prin- cipal focus, then its image would be of the same size, real,

OPTICS.

39

inverted, and at a corresponding distance, as these conju- gate foci are equal.

If an object is situated at a greater distance than twice the principal focus, and nearer than infinity, its image will be real, inverted, and smaller than the object.

Fig. 39.

Rays of light from an object situated closer to a lens than its principal focus would be divergent after refraction, and could only meet by being projected backward ; the image would, therefore, be larger than the object, erect, and

R A"

A

^^^A

^ — -4^^::C"

/____

__________

---'■'''R^^^^^^

r''^^^^-^ — — ^

R

-^^"^^~~-r'

Fig. 40.

virtual. Such an image is only seen by looking through the lens ; the lens in this instance being a magnifying glass. (Fig. 39.)

Images Formed by Concave Lenses. — These images are always erect, virtual, and smaller than the object. (Sec Fig. 40.) A concave lens is, therefore, a minifying lens.

40 REFRACTION AND HOW TO REFRACT.

Parallel rays from the extremes of the object A R form the divergent ray A' and R' after refraction. Secondary rays pass through the optic center o unrefracted, A" and R". At the points of intersection where these rays meet after being projected backward, the image of A R is found, erect, virtual, and diminished in size. This image is only seen by looking through the lens.

Numeration of Lenses. — Formerly, lenses were num- bered according to their radii of curvature in Paris inches (27.07 mm,). The unit was a lens that focused parallel rays of light at about the distance of one English inch (25.4 mm.) from its optic center.

As lenses for purposes of refraction were never so strong as the unit, they were numbered by fractions, thus showing their relative strength as compared to this unit ; for instance, a lens that was one-fourth the strength of the unit was expressed by the fraction i^, or a lens that was one- sixteenth the strength of the unit was expressed as Jg, etc., the denominator of the fraction indicating the focal length of the lens in Paris inches.

There are three objections to this nomenclature : (i) The difference in length of the inch in different countries ; (2) the inconvenience of adding two or more lenses num- bered in fractions with different denominators — yi^ + ^ _|- _!_; (3) the want of uniform intervals between num- bers.

In the new nomenclature, and the one that is now quite universal, known as the metric or dioptric system (diopter, abbreviated D.), a lens has been taken as the unit which has its principal focus at one meter distance (39.37 English inches), commonly recognized as 40 inches.

Len.ses in the dioptric system arc numbered according to their refractive power and not according to their radii of

OPTICS. 41

curvature. The strength or refractive power of a dioptric lens is, therefore, the inverse of its focal distance. To find the focal distance of any dioptric lens in inches or centi- meters, the number of diopters expressed must be divided into the unit of 40 inches or 100 cm. For example, a 2 D. lens has a focal distance of 40 -^ 2 equals 20 inches ; or 100 cm. -^ 2 equals 50 cm. A +4 D. has a focal distance of 40 -^ 4 equals 10 inches or 100 h- 4 equals 25 cm. Lenses that have a refractive power less than the unit are not expressed in the form of fractions, but in the form of decimals ; for example, a lens which is only one-fourth, one- half, or three-fourths the strength of the unit is written 0.25, 0.50, 0.75, respectively, and their focal distances are found in the same way as in dealing with units : 0.25 D. has a focal distance of 40 h- 0.25 or 100 -^ 0.25, equaling 160 inches or 400 cm. ; 0.50 D. has a focal length of 40 -^ 0.50 or 100 -^ 0.50, equaling 80 inches or 200 cm. ; 0.75 D. has a focal length of 40 -=- 0.75 inches or 100 ^ 0.75 equaling 53 inches or 133 cm. Unfortunately, 0.25 D., 0.50 D., and 0.75 D. are frequently spoken of as twenty- five, fifty, and seventy-five, which occasionally leads to confusion in the consideration of the strength and focal dis- tance. The student should learn as soon as possible to change the old nomenclature into the new, as he will have to make these changes in reading other text-books.

To change the old " focal length " or inch system of numbering lenses into diopters, divide the unit (40 in.) by the denominator of the fraction, and the result will be an approximation in diopters ; for example, yV equals f | equals 4 D.; Jq equals f||- equals 2 D. The following table, from Landolt, gives the equivalents in the old and new systems :

42

REFRACTION AND HOW TO REFRACT,

OLD SYSTEM.

NEW

SYSTEM.

I.

II.

III

IV.

V.

VI.

VII.

VIII.

No.

No.

No.

of the

Focal

Focal

of the

Focal

Focal

Corres-

Lens,

Distance

Distance

Equiva-

Lens,

Distance

Distance

ponding

Old

in English

in Milli-

lent in

New

in Milli-

in English

of the Old

System.

Inches.

meters.

Diopters.

System.

meters.

Inches.

System.

72

67.9

1 7 -'4

0.58

0.25

4000

157 48

166.94

60

56.6

1437

0.695

0.5

2000

7874

8346

48

45-3

1 150

0.87

075

1333

52-5

5563

42

39-6

1005

0.99

I

lOUO

39 37

41-73

36

34

863

I 16

■•25

800

3' 5

33 39

30

28.3

718

I 39

1-5

666

26.22

2779

24 ■

22.6

574

1.74

1-75

571

22.48

23-83

20

18.8

477

2.09

2

500

19.69

20.87

18

17

431

2.31

2.25

444

1748

1853

16

15

H

2.6

2-5

400

15-75

16.69

15

14. 1

358

2.79

3

333

13 '7

13-9

14

13.2

335

2.98

3-5

286

II 26

11.94

13

12.2

312

3.20

4

250

9.84

10.43

12

II. 2

287

3-48

4 5

222

8.74

926

II

10.3

261

382

5

200

7.87

8-35

10

9-4

239

4.18

5-5

182

7 16

76

9

8.5

216

4-63

6

166

654

693

8

7-5

190

5-2.S

7

143

563

5 97

7 ,

6.6

167

5-96

8

125

492

5.22

6J^

6.13

155

6.42

9

111

4-37

4-63

6

5-6

142

7.0

10

100

3-94

4 17

5%

5 2

132

7-57

11

91

3-58

3«.

5

4.7

119

8.4

12

83

3-27

3-46

^^.

42

106

9-4

13

77

3-03

3.21

4

3-8

96

10 4

14

71

2.8

2.q6

3^

3-3

84

11.9

15

67

2.64

2.8

3K

3-1

79

12.7

16

62

244

2.59

3

2.8

71

14.0

17

59

2.32

2.46

23/i

2.6

66

I5-I

18

55

2 17

2.29

2^

2.36

60

17.7

20

50

1.97

2.09

25i

2.1

53

18.7

2

1.88

48

20.94

Cylindric Lenses. — Abbreviated cyl., c, or C. A cylin- dric lens, usuall}' called a " cylinder," receives its name from being a segment of a cylinder parallel to its axis. (See Fig. 41.) Occasionally cylinders are made with both sur- faces curved, and are then equivalent to two planocylinders with their j^lane surfaces together. A cyliiidi-r i/iay be defined as a /ens wJneJi refraets rays of lii^ht opposite to its axis. This definition should be carefully borne in mind in contradistinction to a spheric lens, which refracts ra\'s of light equally in all meridians. A cj'liiulric lens has no one

OPTICS.

43

common focus or focal point, but a line of foci, which is parallel to its axis.

Axis of a Cylinder. — That meridian of a cylindric lens which is parallel to the axis of the original cylinder of

Fig. 41.

Fig. 42.

Fig. 43.

which it is a part is spoken of as the axis, and is indicated on the lens of the trial -case by a short diamond scratch on the lens at its periphery, or by having a small portion of

Fig. 44.

its surface corresponding to the axis ground at the edges, or it may be marked in both ways. (See Fig. 43.) Cylin- ders are of two kinds — convex and concave. (Figs. 41, 42.) Cylinder Action. — A convex cylinder converges parallel

44

REFRACTION AND HOW TO REFRACT,

F-c:

FiG. 45.

rays of light so that after refraction they are brought into a straight hne which corresponds to the axis of the cyHn- der ; for instance, a +5 cyl. will converge parallel rays so that they come together in a straight line at the dis- tance of eight inches, or twenty centimeters, and this straight line will be parallel to the axis of the cylinder. (Fig. 44.)

A concave cylin- der diverges ra)'s of light opposite to its axis, as if they had diverged from a straight line on the opposite side of the lens. (Fig. 45.)

Spherocylinders. — A spherocylinder is a combination of a sphere and a cylinder, and is therefore a lens which has one surface ground with a spheric curve and the other sur- face cylindric. A spherocylinder lens is also spoken of as an astigmatic lens. (See Fig. 93.) A spherocylinder lens is one which has two focal planes. Spherocylinders have different curves : the spheric curve may be convex, with the cylinder surface convex ; or the spheric surface may be concave, with the cylinder surface concave ; or the spheric surface may be convex, with the c}'Iinder surface concave ; or the spheric surfece may be concave, with the c}'linder surface convex.

The Trial-case (see Fig. 46). — This case contains pairs of plus and minus spheres and pairs of plus and minus cylinders; also prisms numbered from 34 or 'i to 20 A. The spheres are numbered in intervals of 0.12 up to 2 S.; and from 2 S. up to 5 S. the interval is 0.25 S.; and from 5 S. to 8 S. the interval is 0.50 S.; and from 8 S. to 22 S.

OPTICS.

45

the interval is i S. The cylinders have similar intervals, but seldom go higher than 6 or 8 cyl.

The trial-case also contains a trial-frame, which is used to place lenses in front of the patient's eyes. (See Fig. 47.) The eye-pieces of such a frame are numbered on the periphery in degrees of half a circle, so that the axis of a cylinder can be seen during refraction. The left of the

Fig. 46.

horizontal line in each eye-piece is recognized as the start- ing-place, or zero (o), and the degrees are marked from left to right on the laivcr /la/f, counting around to the horizontal meridian, which at the right hand is numbered 180; this horizontal meridian is, therefore, spoken of as horizontal, zero (o), or 180 degrees. The meridian midway between zero and 180 is spoken of as vertical, or 90 degrees. In some countries the meridians are differently num-

46

REFRACTION AND HOW TO REFRACT.

berecl (see Fig. 48) ; for example, the vertical meridian is called zero, and the degrees are marked on each side of zero up to 90 degrees. Only the upper half of the eye-piece is thus numbered, so that when a cylinder has the upper end of its axis inclined toward the nose, the record would be so many degrees of inclination to the nasal side ; or if the upper end of the cylinder was inclined toward the temple, the record would be so many degrees to the temporal side. For example, in the right eye 1 5 degrees nasal would

Fic;. 47.

mean axis 75 on the ordinary trial-frame, and 15 degrees temporal would mean 105 degrees.

The trial-case also contains other accessories, such as blanks or blinders, a stenopeic slit, pin-hole disc, etc., all of which are referred to in the text.

Combination of Lenses. — The sign of combination is ^.

Combining Spheres. — Any number of spheric lenses placed with their optic centers over each other, and sur-

OPTICS.

47

faces together, will equal one lens the value of their sum : for example, +2 S. 3 -f- 1 S. ^ +3 S. will equal -f 6 S.; or a — 2 S. :3 ^ — i S. :^ — 3 S. will equal a — 6 S.

If a plus and minus sphere, each of the same strength, be placed with their optic centers together, the refraction will be nothing, for the one will neutralize the effect of the other ; for instance, +4 S. and — 4 S. will be equivalent to a piece of plane glass, as the — 4 S. will diverge rays of light as much as the +4 S. will converge them, and the result

Fig. 48.

is, rays of light parallel before refraction are parallel after passing through such a combination. If, however, a plus and a minus sphere of different strengths are placed together, the value of the resulting lens will equal their difference, in favor of the higher number; for instance, +4 S. and — 2 S. will equal a +2 5., the — 2 S. neutralizing 2 S. of the + 4 S., leaving +2 S.

Combining Cylindric Lenses. — Any number of c)lin- dric lenses placed together, with their axes in the Si7;j/c

48 REFRACTION AND HOW TO REFRACT.

meridian, are equal to a cylinder the value of their sum ; for example : +2 cyl. axis 90 degrees and -f 3 cyl. axis 90 degrees will equal a -f 5 cyl. axis 90 degrees ; or — 2 cyl. axis 180 degrees and — 3 cyl. axis 180 degrees will equal a — 5 cyl. axis 180 degrees ; or — 2 cyl. axis 180 degrees and +1 cyl. axis 180 degrees will equal a — i cyl. axis 180 degrees.

As a cylinder refracts rays of light only in the meridian opposite to its axis, this opposite meridian or axis can always be found by the following simple rule :

" Add po ivJicn the given axis is po or less than po, and stdytract po zvhen the given axis is more than po."

For example : + 3 cyl. axis 90 refracts rays of light in the 180 degree meridian (90-1-90= 180); or -f 3 cyl. axis 75 refracts rays of light in the 165 meridian (75 -[-90 = 165). A — 3 cyl. axis 135 refracts ra)'s of light in the 45 meridian (135 less 90 = 45). A — 2 cyl. axis 180 re- fracts rays of light in the 90 meridian (180 less 90 = 90).

Combining two cylinders of the same strength and same denomination, with their axes at right angles to each other, will equal a sphere of the same strength and same denomination. For instance, +3 c)l. axis 90 and +3 cyl. axis 180, placed together, will equal a -|-3 S. — /. e., the +3 cyl. at axis 90 will converge parallel rays in the 180 meridian, while the +3 cyl. axis 180 will converge parallel rays in the 90 meridian, producing a principal focus ; therefore any sphere is also equal to two c}-linders of its same strength and same denomination with tlieir axes at riglit angles to each other.

Combining cylinders of different strength, but of the same denomination, with their axes at right angles to each other, such a combination will equal a sphere and a cylinder of the same denomination. I'or example :

OPTICS.

49

-\-2 cyl. axis 75 O +3 cyl. axis 165 will equal +2 S. O -(-I cyl. axis 165. The +2 cyl. axis 75 takes +2 of the 4-3 cyl. axis 165 and makes a +2 S., leaving -f- 1 cyl. axis at 165 ; the result is then +2 S. O +1 cyl. axis 165.

Or ^3.50 cyl. axis 15 O — 4.50 cyl. axis 105, will equal — 3.50 S. O — i cyl. axis 105. The — 3.50 axis 15 takes — 3.50 of the — 4.50 and makes a — 3.50 S., leaving — i cyl. axis 165 ; this — i cyl. axis 105 is now joined to the — 3.50 sphere, making — 3.50 S. O — i cyl. axis 105.

Combining a sphere and a cylinder of the same strength, but of differ- ent denomination, will equal a cylinder of the opposite sign and opposite axis from the cylinder given. For example : -(- 1 sphere O — i cyl. axis 180 will equal + I cyl. axis 90. The + I S. equals two -\~ i cylinders, one at axis 90 and one at axis 180, and the — I cyl. at axis 180 is neutralized by the -f i c}'l. at the same axis, leaving

the + I cyl. axis 90. This may be better understood by the diagram (Fig. 49).

Or — 3 S. O +3 cyl. axis 90 equals — 3 cyl. axis 180. The — 3 S. is equal to two — 3 cylinders, one at axis 90 and one at axis 1 80 ; the one at axis 90 is neutralized by the +3 cyl. at the same axis, leaving — 3 C}-1. axis 180.

Combining a Sphere with a Weaker Cylinder of Dif- ferent Denomination. — Such a combinati(in should be 5

+ 1.00

Fig. 49.

50 REFRACTION AND HOW TO REFRACT.

changed to its simplest form of expression, and will equal a sphere of the same denomination, of the v^alue of their difference, combined with a cylinder of the same strength as the cylinder given, but of opposite sign and axis. For example: +4 S. O — i cyl. axis 180. The minus one cylinder is refracting in the 90 degree meridian, therefore it reduces the strength of the +4 S. in this axis, making it a plus 3. The horizontal or 180 meridian of the plus 4 has not been altered, but still remains +4, and the result is there is plus 3 in the vertical meridian and plus 4 in the horizontal meridian, equaling, therefore, +3 S. O + 1 cyl. axis 90.

The following rule will be of service in making this change, and, in fact, this rule will apply in any instance where the sphere and cylinder are of different denomina- tion, no matter what their respective strengths may be :

Rule. — Subtract the less from the greater, and to the result prefix the sign of the greater ; combine zviih this the same strength cylinder, using the opposite sign and opposite axis. Example : +2.25 S. O — 0.75 cyl. axis 75 degrees ; sub- tracting the less from the greater ( — 0.75 from -)-2.2 5), and prefixing the sign of the greater ( + ), will leave +1.50 S. ; and combining with this the same strength cylinder (0.75), with opposite sign and axis (+ and 165), will be -I-0.75 cyl. axis 165. Result, +1.50 S. O +0.75 c}-l. axis 165.

Combining a Sphere and Cylinder of the Same De- nomination.— This is recognized as the minimum or simplest form of expression, and is seldom changed. For example : — 2 S. O — 6 cyl. axis 180 is considered as the thinnest lens and the one with the least weight that can be made by such a combination. It may be changed, how- ever, by the rever.se of the rule above given, and will equal — 8 S. O -f- 6 cyl. axis 90.

OPTICS. 5 I

Combining Two Cylinders of Different Denominations with Opposite Axes. — Commonly called cross cylinders. Such combinations can be written in three ways :

1. +Cyl. 3 — cyl. axes opposite.

2. -|- Sphere 3 — cyl. (cylinder stronger than sphere).

3. — Sphere -(-cyl. (cyhnder stronger than sphere).

For exainple : ^i.oo cyl. axis 180 ;3 +2- 50 cyl. axis 90 may be changed to one of the following :

— 1. 00 S. 3 +3- 50 cyl. axis 90; or — -I-2.50 S. 3 — 3-50 cyl. axis 180.

The first formula shows that the vertical meridian must always be — i and the horizontal or 1 80 meridian must always be +2.50, and with this clearly in mind, the second and third formulas will be understood. In the second formula ( — i.oo S. O +3.50 cyl. axis 90) the +3.50 cyl. is only equal to +2.50, as it has i D. neutralized by — i of the — I sphere. In the third formula (4-2.50 S. O — 3.50 cyl. axis 180) the — 3.50 cylinder is only equal to — I.OO cylinder, as it has — 2.50 neutralized by +2.50 of the sphere.

/;/ any splicrocylindcr combination the meridian in which the axis of the cylinder lies has the strength of one lens, and the meridian opposite to the axis of the cylinder has the com- bined values of sphere and cylinder — /. r., — i.oo S. O + 3.50 cyl. axis 90 means — i.oo on the axis (90) of the cylinder and opposite to the axis ; therefore at 180 it equals + 2.50 (—1 and +3.50).

Cross cylinders in themselves are seldom ordered in a prescription, preference being given to a spheroc}'linder combination. When to order a plus sphere with a minus cylinder, and when to order a minus sphere with a plus cylinder, depends upon the individual lenses. For example :

52 REFRACTION AND HOW TO REFRACT.

-|-0. 50 cyl. axis 90 O — 5.00 cyl. axis 180 equals +0.50 S. O — 5.50 cyl. axis 180 or — 5 S. O +5- 50 cyl. axis 90.

Preference would be given to the plus sphere combina- tion, on account of thinness and lesser weight of the lens. The following formula, — i cyl. axis 180 degrees 3 -|- 3 cyl. axis 90 degrees, equals — i.oo S. 3: +4 cyl. axis 90, or +3 S. 3 — 4 cyl. axis 180, and for similar reasons preference would be given to the nii)ius sphere combination. Whichever combination makes the thinnest and li<ihtest weight glass is the one to be ordered, as a rule.

The student should practise these combinations at the trial-case, and be able at a glance to change one formula into another without diagram or rule.

Prescription Writing. — In writing prescriptions for lenses the. right eye is indicated by one of three signs — R, Rt, or O. D., the latter from the Latin for right eye, Ociilus Dexter. The left eye is also indicated in one of three ways — L, Lt., or O. S., the latter from the Latin for left eye, Oculus Sinister.

A prescription may call for any one of the following :

-(-Sphere, written -f 4 D. or -(-4.00 D. S. or -j-4 S. or -{4 sph. — Sphere, written — 2 D. or — 2.00 D. S. or — 2 S. or — 2 sph. -[-Cylinder, written -(-4.00 D. C. or -(-4 C. or -(-4 cyl. (axis as indicated). . — Cylinder, written — 2.00 D. C. or — 2 C. or — 2 cyl. (axis as indicated). -[-Sphere and -f cylinder, written -(-2.00 S. 3 -h2.cx3 cyl. axis 90 degrees. — .Sphere and — cylinder, written — 2.00 S. 3 — 2.00 cyl. axis 180 degrees. -(-Sphere and — cylinder (cylinder stronger than sphere), -(-2.00 S. 3" — 300

cyl. axis 180 degrees. — Sphere and -(-cylinder (cylinder stronger than sphere), — 2.00 S. 3 4 3-00

cyl. axis 90 degrees.

A plus c)'lindcr and minus cylinder may be prescribed, and, if so, their axes mu.st be at right angles to each other. An occasional exception to this may be found in irrcgul.ir astigmatism. Or a prism with its base indicated max- be

OPTICS.

53

added in any one of the foregoing formulas ; for example : — 2 S. O — 2.00 cyl. axis i8o O 2 A base in ; or the direc- tion of the base may be abbreviated as follows : B. I., meaning base in ; B. O., meaning base out ; B. U., meaning base up ; and B. D., meaning base down.

Prescriptions are never written for two spheres.

Prescriptions are never written for two cylinders at the same axis.

Prescriptions are never written for two cylinders at axes other than those at right angles to each other, except, as just noted, in irregular astigmatism.

For obvious reasons prescriptions are never written for a sphere and two cylinders.

Recognition of Lenses.

A convex sphere is thick at the center and thin at the edge. It has the power of converging rays of light ; hence, if strong, it is a burning glass. Objects viewed through a convex lens as it is moved before the eye, from left to right and right to left or up and down, appear to move in an opposite direction to that in which the lens is moved. The weaker the lens, the slower the object appears to move ; and the stronger the lens, the faster the apparent movement of the object. A convex lens being a magnifier, has the effect of making objects appear larger and closer w hen it is moved away from the observer's eye ; or if brought toward the eye, objects already enlarged appear smaller and more distant.

To Find the Optic Center of a Convex Lens. — Look- ing at a perpendicular straight line and passing a convex lens before the eye from left to right has the effect of displacing toward the right edge of the lens that portion of the line seen through the lens (see Fig. 50). and as the lens is slowly moved still further to the right, the displaced

54

REFRACTION AND HOW TO REFRACT.

portion of the line will finall}' coincide with the original straight line, making one continuous line through the lens. (See Fig. 51.) Marking this straight line on the surface of the lens, and then turning the lens to the opposite meridian and repeating the examina- tion, and marking the lens as before, the optic center will be in the lens beneath the point of intersection of the two lines. (See Fig. 52.)

A concave sphere is thick at the edge and thin at the center, and has the power of causing rays of light to diverge. When moved before the eye from left to right and right to left or up and down, objects appear to move in the same direc- tion as that in which the lens is moved.

A concave lens being a minifier, makes ob'ects appear

Fig. 50.

Fig. 51.

Fig. 52.

smaller and more distant as the glass is moved away from the eye, and if brought closer to the eye, makes objects apparently small appear somewhat larger and nearer.

OPTICS.

55

Looking at a straight edge or line through a concave sphere, and passing the lens from left to right, the portion of the line seen through the lens appears displaced toward the center of the lens (see Fig. 53), and as the lens is still further moved to the right, the displaced portion of the line finally coincides with the original straight edge, as in figure 5 I.

The optic center of a concave lens is found in the same way as the center of a convex lens.

A Convex Cylinder. — When a convex cylinder is moved

Fig. 5:

Fig. 54.

in front of the eye in the direction of its axis, objects looked at do not change their positions ; but when the lens is moved in the direction opposite to its axis, the movement of the object is the same as that of a convex sphere. Look- ing at a straight edge through a convex cylinder, and rotating it, has the effect of displacing away from its axis that portion of the straight edge seen through the lens. (See Fig. 54.)

A Concave Cylinder. — When a concave cjlinder is moved in front of the e)e in the direction of its axis, ob-

56

REFRACTION AND HOW TO REFRACT.

jects looked at do not change their positions ; but when the lens is moved in the direction opposite to its axis, the movement of the object is the same as that of a concave sphere. Looking at a straight line through a concave cylinder, and rotating it, has the effect of displacing toward its axis that portion of the straight line seen through the lens. (See Fig. 55.) A circle viewed through a strong con- cave cylinder appears as an oval with its long diameter cor- responding to its axis. (See Fig. 56.) A circle viewed through a strong convex cylinder appears as an oval with its long diameter opposite to its axis. In place of using a

Fig. 55.

Fig. 56.

Straight line or straight edge to find the optic center of a sphere or axis of a cylinder, two lines at right angles may be substituted (see Fig. 52) or a protractor may be used.

A Prism. — Objects viewed through a prism are dis- placed toward its apex, and that portion of a straight line seen through the prism never coincides with the straight line.

Neutralization of Lenses. — Ha\ing determined from the foregoing description what the character of an indi- vidual lens may be, then to neutralize its effect or find out its strength a lens of opposite character is taken from the

OPTICS.

57

trial-case and held in apposition to it, and the two lenses are moved in front of the eye as a distant object is observed. That lens or combination of lenses which stops all apparent movement of the object is the correct neu- tralizing lens. Spherocylindric lenses are neutralized by finding out what sphere will correct one meridian and what sphere will correct or neutralize the opposite meridian ; for example, if a mi" us 2 S. stops all movement in one meridian and minus 3 S. stops all movement in the other meridian, then the lens being neutralized will be plus 2 S. combined with a plus i cylinder. Or after a sphere cor- rects one meridian, a cylinder may be combined until the other meridian is neutralized.

CHAPTER 11.

THE EYE. — THE STANDARD EYE. — THE CARDINAL POINTS.— VISUAL ANGLE.— MINIMUM VISUAL AN- GLE,—STANDARD ACUTENESS OF VISION.— SIZE OF RETINAL IMAGE.— ACCOMMODATION.— MECHANISM OF ACCOMMODATION.— FAR AND NEAR POINTS.— DETERMINATION OF DISTANT VISION AND NEAR POINT.— AMPLITUDE OF ACCOMMODATION. — CON- VERGENCE.—ANGLE GAMMA.— ANGLE ALPHA.

The Eye. — While the eye is considered as the organ of vision, yet its function is to form upon its retina an inverted image of any object looked at ; and if the retinal image is distinct, the object will appear distinct ; if the retinal image is blurred, the object will appear blurred. By means of the optic nerve and tract the retinal impression or image is placed in communication with the brain, which interprets the image and completes the visual act.

The Standard Eye. — For purposes of exact calcula- tions it has been found necessary to project a standard or schematic eye, whose nodal point (optic center) shall be seven millimeters back of the anterior surface of the cor- nea and fifteen millimeters from the fovea (Helmholtz). Allowing one millimeter for the thickness of the choroid and sclera, such an eye would have an anteroposterior measurement of about twenty -three millimeters. Parallel rays of light passing into such an eye in a state of rest would focus on the macula.

Cardinal Points (Fig. 57). — Images formed upon the retina are the result of refraction by three refracting sur- faces and three refracting media. The refracting surfaces

58

CARDINAL POINTS. ^g

are the anterior surface of the cornea and the anterior and posterior surfaces of the crystalline lens. The refractin*'- media are the cornea (and aqueous humor forming a convex lens), the crystalline lens, and the vitreous humor. These refracting surfaces and media represent a compound dioptric system, centered upon the optic or principal axis — /. c, a line drawn from the pole of the cornea to a point between the nerve and fovea.

On the principal axis, therefore, are situated the anterior and posterior principal foci, the anterior and posterior nodal

Fig. 57.

points, and the anterior and posterior principal points The anterior principal focus is situated upon the optic axis 13.745+ m"i- ill front of the corneal apex. The pos- terior principal focus is situated 15.61-)- mm. back of the posterior surface of the lens. The nodal points are situ- ated about 7 mm. back of the cornea, and correspond approximately to the optic center of this compound re- fracting system ; and as they are so close together, they are considered as one for all purposes in the study of the for- mation of images. The first or anterior principal point is

6o REFRACTION AND HOW TO REFRACT.

situiited 1.75 mm. back of the anterior corneal surface, and the second or posterior principal point is situated 2. 10 mm. behind the anterior surface of the cornea. The principal points are so closely situated that they are considered as one. The anterior focal distance equals 15.49-I- mm. and the posterior focal distance equals 20.71-]- mm.

The Visual Angle, or Angle of View. — The visual angle is the angle formed by rays of light from the extremes of an object passing to the nodal point of the eye ; or the visual angle may be defined as the angle which the object subtends at the nodal point of the compound refracting system of the eye. Rays of light from the extremes of an object

Fig. 58.

directed to the nodal point of the eye pass through unre- fracted, and continuing their straight course, fall upon the retina, forming an inverted image of the object. (See Fig.

58.)

The size of the retinal image depends upon the size and the distance of the object from the nodal point of the eye. Objects, therefore, which are seen under the same visual angle must have the same sized retinal image. (See Fig.

59-)

If the arrows i, 2, 3, and 4 represented a child, a man, a tree, and a church, respectively (some distance apart), they would form the same sized retinal images, and if the eye were guided alone by the size of the retinal image, it would

MINIMUM VISUAT. ANGLE.

6i

judge erroneously ; but, by experience, distance and com- parison of size are brous^ht into consideration.

If, however, arrows 2, 3, and 4 are placed at the side of arrow i, then their resulting images would increase in size according to the size of their respective visual angles. (See Fig. 60.)

The nearer an object to the eye, the larger the visual

Fig. 59.

angle and retinal image ; the further away an object from the eye, the smaller the visual angle and retinal image. An ob- ject, to retain the same sized visual angle, must, therefore, be made larger the further it is removed from the eye ; this is demonstrated in figure 59, where arrow i, to be seen

Fig. 60.

under the same visual angle which it has at present, would have to be as large as arrow 4, at the distance of arrow 4. Minimum Visual Angle. — This is the smallest visual angle in which a standard eye can still recognize an object and give it a name ; this angle is also spoken of as the

62 REFRACTION AND HOW TO REFRACT.

limiting angle of vision. In figure 6i, for example, the letter D at a distance of six meters is recognized as the letter D : it is plainly seen ; but if placed beyond six meters, it would form a smaller visual angle, and could not with certainty be called D.

To be seen at a distance of twelve meters and still occupy this same visual angle, D would have to be made twice as large — /. c, the size of F; and to be seen at twenty-four meters, it would have to be four times its pres- ent size, or the size of P. Thus, while the letter D, seen clearly at six meters, would have to be made proportion- ately larger as it is removed from the eye, then to occupy

Fig. 6i.

the same visual angle it would have to be made smaller if brought closer to the eye and kept within this limiting angle. In figure 6i D, F, and P can be seen closer to the eye than their respective distances call for ; but the pur- pose is to find the greatest distance from the eye at which they can be seen, as this represents the maximum acuteness of vision, or maximum sharpness of sight.

Standard Acuteness of Vision. — As it was necessary for purposes of calculation to have a standard or emmetropic eye, so it is essential to have a standard acuteness of vision which will be consistent with the staiulartl or cinmetroj)ic eye, and thus have some method of recortling numerically any departure from this standard visual condition.

SIZE OF RETINAL IMAGES.

63

Fig. 62.

m

Fig. 63.

The standard acuteness of vision is the power of the eye to distinguish letters and characters occupying an angle of five minutes. Every letter is, therefore, so proportioned that it will measure just five minutes in the vertical and hori- zontal meridians, and be reducible to twenty-five parts or squares, each measuring one minute vertically and horizontally.* (See Fig. 62.)

Figure 63 shows the letter F drawn in a five- minute square, and each stroke of the letter, and space betAveen the strokes, measuring just one minute in width. As twice the tangent of half the angle of five minutes is ex- pressed by the decimal .001425, then to calculate the size of any letter or character which should be seen clearly and dis- tinctly by the standard eye at a certain definite distance, it is necessary to multiply the distance in millimeters by this tangent of the angle of five minutes. Letters or characters made on this scale are called standard letters. For ex- ample, letters to be seen under an angle of five minutes at a distance of one meter (1000 mm.) would have to be 1.425 mm. square (1000 X .001425). At six meters (6000 X .001425) := 8.5 mm., etc.

Size of Retinal Images. — The size of the retinal image depends upon two factors — the size of the object itself and its distance from the nodal point. In the standard eye it has been stated that the nodal point was 7 mm. back of the cornea and 15 mm. in front of the retina; then an object 8.5 mm. square situated 6000 mm. in front of the

* There are two letters in the alphabet which are exceptions to this nile, L and O. L can be seen under an angle of two minutes and O can be seen under an angle of three minutes.

64 REFRACTION AND HOW TO REFRACT.

eye would have a retinal image g^f u of 8.5, or 0.02 -f mm., and this is the size of the retinal image in a standard eye, looking at a standard letter at six meters' distance. A good rule for finding the size of the retinal image is to multiply the height of the object by the nodal distance and divide by the distance. In other words, the size of the retinal image is to the size of the object as their respective dis- tances from the nodal point.

Refraction in ophthalmology has most to do with eyes whose measurements are not according to the standard or emmetropic condition, and which have their retinas closer to or further from the nodal point than 15 mm. (spoken of

as ametropic). The M retinal images in such eyes will be smaller in the former and larger in the latter. (See Fig. 64.) Fig. 64. Accommodation.

— This may be de- scribed as the power of the eye to focus rays of light upon its retina for different distances at different times. In other words, the eye can not focus rays of light upon its retina from different points at one and the same time. For example, the point of a pencil held six inches in front of the eye is not seen clearly (is hazy) as the eye looks at a printed page thirteen inches beyond ; and, vice versa, the printed page is not seen distinctly if the point of the pencil is looked at. In the study of convex lenses it was noticed that when an object was brought closer than infinity, the focus of the lens was correspondingly lengthened ; and so, in the photographer's camera, to keep the focus on the ground-glass (m- sensiti\'e plate as the object is brought toward the camera, it is

THE MECHANISM OF ACCOMMODATION. 65

necessary to push the lens forward b}- means of the accor- dion phiits ; but the human eye does not lengthen or shorten in this way. Normally, the eyeball is inextensible, and to accomplish this same purpose the ciliary muscle must contract, causing the crystalline lens to become more convex, and thus keep the rays of light entering the eye at a focus upon the fovea.

The Mechanism of Accommodation. — To appreciate this, it is necessary to understand something of the anatomy of the ciliary body, of which the ciliary muscle is a part. The ciliary body is circular in form and occupies a small (3 mm.) area in the eye, just beneath the sclera, at its cor- neal junction. (See ¥ig. 57.) In section the ciliary bod}' is triangular in shape, the base of the triangle measuring about 0.8 mm. and facing toward the anterior chamber, the apex of the triangle extending backward beneath the sclerotic. The ciliary body lies in apposition to the sclera, but has only a very minute attachment to it, at the sclerocorneal junction, called the ligamentum annulare, or pectinatum. That portion of the ciliary body lying next to the hyaloid membrane of the vitreous humor is composed of folds, known as the ciliary processes, seventy or more in number.

A portion of the ciliary body is composed of muscular fibers disposed in flat bundles, which interlace with cacli other, forming a sort of plexus, and called the ciliary mus- cle. This muscle, by the character of its fibers, has been subdivided into three parts : (i) Meridional ; (2) radiating ; and (3) circular or sphincter fibers. The meridional are the longest, lie next to the sclerotic in lamellze, parallel with it, and pass back to join the choroid coat of the eye, forming what is known as the tensor choroideai, or muscle of Briicke or Bowman. The radiating fibers are fan-shaped, few in number, and scattered through the ciliar}' bod\'. 6

66 REFRACTION AND HOW TO REFRACT.

The circular or sphincter fibers — also called annular — are sometimes referred to as the muscle of Muller, or com- pressor lentis, and are the most important fibers in the consideration of accommodation ; they form a sphincter ring concentric with the equator of the lens. Attached to the ciliary body, well forward on its inner side, near the base of the triangle, is the ligament of the lens (zonule of Zinn), and it in turn sends fibers to the anterior and poste- rior capsule of the lens. This ligament of the lens occu- pies an interval of about o. 5 mm. between the ciliary body and the periphery of the lens, and is a constant factor in all conditions of the healthy eye.

During the act of accommodation the following changes take place in the eye :

1. The ciliary muscle contracts.

2. The ciliary muscle (sphincter), by contracting, makes a smaller circle.

3. The tensor choroideae draws slightly upon the choroid (compressing somewhat the vitreous body), and these two sets of fibers, sphincter and meridional, acting together, relax the ligament of the lens, with the result that —

4. The lens fibers, no longer held in check, become re- laxed, and by their own inherent quality (elasticity) allow the lens to become more convex, especially on its anterior surface.

5. The anterior surface of the lens being made more convex, approaches the cornea.

6. The posterior surface of the lens becomes slightly more convex, but retains its position at the pole.

7. The lens axis is lengthened, but the equatorial diame- ter diminishes, thus keeping up the uniform interval between the equator of the lens and the ciliary bod}% as previously referred to. The lens dors not increase in volnnie.

FAR POINT. 67

8. The anterior chamber becomes shghtly shallower at the center and deeper in the peripher)'.

9. That portion of the iris resting upon the anterior cap- sule of the lens is pushed forward, espe- cially at its pupillary edge.

10. The iris contracts, producing a smaller pupil ; but it must be remembered that contraction of the iris is not an essen- tial condition in accommodation. The shape of the cornea is not changed during contraction of the ciliary muscle.

The following table shows the compara- tive measurements of a lens at rest and during the height of accommodation in a healthy emmetropic eye of ten years. The dotted lines in figure 65 indicate the changes in the shape of the lens at the height of accommodation.

At Rest. Radius of curvature of anterior surface of lens,

" " posterior " " Distance from anterior surface of cornea to ante- rior surface of lens,

Anteroposterior diameter, on axis,

Distance from anterior surface of cornea to poste- rior surface of lens, 7-- " 7-2 "

E(|uatorial diameter, 8.7 " 8.2 "

Far Point. — Latin, piiiictimi rciiiofimi ; abbreviated p. r. or r. The far point ma\' be defined as the greatest distance at which an eye has maximum sharpness of sight, or the most remote jx^int at which the e\'e, in a state of rest, has maximum acuity of vision. Infinity (sign of infinit}-, y. ) is the far point of an emmetropic e}e.

The standard or emmetropic eye. when looking at distant objects, recei\'es parallel ra)'s of light at a focus upon its

Height of

ACCOMMODATIO.V

10 mm.

6

mm.

6 "

5-5

"

3.6 "

3-2

((

3.6"

4

"

68 REFRACTION AND HOW TO REFRACT.

fovea (F"ig. 66), and also emits parallel rays ; under these conditions the ciliary muscle is not acting, the eye is in a condition of complete repose, of rest, of minimum refrac- tion, and is adapted for its far point.

Near Point. — Latin, pioictum proxiiiiuiii ; abbre\'iatcd p. p. or p. This may be defined as the nearest point at which an eye has maximum sharpness of sight, or the nearest point to the eye at which it has distinct vision, the lens is in the condition of greatest convexity, of maximum refraction.

Amplitude of Accommodation. — This is also called the range * or power t of accommodation, and may be de- fined as the difference between the refraction of the eye in a state of rest (or adapted for its far point) and in a condi- tion of maximum refraction, or adapted for its near point. For example, an emmetropic eye has infinity for its far point, and if lo cm. distance is its near point, then the dif- ference between the lens adapted for infinity and lo cm. will be lo D.,as lo cm. represents the focal length, lo D. In

other words, there is no accom- modation used for infinity, but there is an accommodation of lO D. for the near point, which is the amplitude or power of accommodation. The emme- FiG. 66. tropic c}'e in a state of accom-

modation adds on to the ante- rior surface of its lens what is equivalent to a convex meniscus, h'igure 66 shows an emmetropic eye at rest receiving parallel rays of light at a focus upon its retina,

* Range applies to tlie si)ace between tlie far and near points. I Power applies to the force or .strenglli or dinpters necessary to cliange the refraction from tlie far to the near point.

AMPLITUDE OF ACCOMMODATION. 69

and it also shows the same eye in its niaxinuim state of accommodation for a point 10 cm. distant ; the broken Hne representing what is equivalent to a convex meniscus, added to the anterior surface of its lens.

When the distance of the near point is known in inches or centimeters, the equivalent in diopters is found by divid- ing 40 by the near point in inches, or by dividing 100 by the near point in centimeters. The near point being 10 cm., or 4 inches (10 into 100 or 4 into 40) the amount of accom- modation will be 10 D.

In the study of healthy emmetropic e}'es it has been found that the power of accommodation gradually dimin- ishes as the eye passes from youth to old age. This is the result of one or more changes : the lens fibers lose their elasticity, becoming sclerosed, or the ciliary muscle grows weak, or both of these changes may exist together. Rarely the cornea may flatten. A knowledge of the power of accommodation is absolutely essential, so that any vari- ations from the standard condition maybe noted. The fol- lowing table gives the ages from ten to seventy-five years, respectively, with five-year intervals, and the near point consistent with each, as also the amplitude of accommoda- tion for each period.

A

MPLITUDE

A

MPLITUDE

Year.

Near

Point.

IN

DiOPTKKS.

Year.

Near

Point.

IN

Diopters.

10

7

cm.

14

45

28

cm.

3-5

IS

8.

5 "

12

50

40

2.5

20

10

10

55

55

1-75

25

12

8.5

60

100

I

30

14

7

65

133

0.75

35

18

5-5

70

400

0.25

40

22

4-5

75

00

This table of near points applies only to emmetropic eyes or those eyes which are made emmetropic by the adjust-

70 REFRACTION AND HOW TO REFRACT.

ment of suitable correcting lenses. The table of amplitudes, however, is the same, with a few exceptions, for all eyes of whatever degree or amount of ametropia.

For a better appreciation of the amplitude of accom- modation it is necessary to understand the two forms of eyes already referred to in figure 64.

First, the eye which has its retina closer to its refractive media than the principal focus ; such an eye is spoken of as a short or hyperopic eye. (H in Fig. 64.) (H}-peropia : Greek, uTzsp, over ; and ux/', eye.)

This eye in a state of rest (under the influence of atro- pin) will emit divergent rays of light, and is, therefore, in a

Fig. 67.

condition to receive only convergent rays of light at focus upon its retina. (See Fig. 67.) Parallel rays would not focus upon the retina of such an eye, but, if possible, would focus back of the retina.

Second, the eye that has its retina bej-ond the principal focus of its dioptric media (M in Fig. 64) ; such an e}-e is spoken of as a long or myopic eye (Greek, /wet'^, to close ; (ix/', eye). This eye always emits convergent rays, and is, there- fore, in a state to receive divergent ra}'s of light at a focus upon its retina. (See Fig. 68.) Parallel rays woukl not focus upon the retina of a myopic eye, but in the \itreous in front of the retina.

The Far Point of a Hyperopic Eye. — This nmst neces-

FAR POINT. 71

sarily be negative (see Fig. 67), and is found by projecting the divergent emergent rays backward to the imaginary point behind the retina from which they appear to have diverged. A hyperopic eye, to receive parallel rays of light at a focus upon its retina, must, therefore, accommo- date, and the amount of accommodation thus exerted will remove the near point just that much from the eye as com- pared with an emmetropic eye. For example, according to the table of amplitudes just given, an eye at twenty years has 10 D. of accommodation, but if it uses 2 D. of this to make rays of light parallel, then it only has 8 D. left to accom- modate inside of infinity, with the result that the near point comes to only (8 into 100) 12.5 cm. ; or an eye which is

Fig. 68.

twenty-five years old has an amplitude of accommodation of 8.5 D., and if it has to use 4.5 D. for infinity, it would have (4 into 100) a near point of 25 cm. (10 inches).

The Near Point of a Hyperopic Eye. — From the de- scription just given it will be seen at once that the near point in hyperopic eyes is always further remo\'ed than in the emmetropic eye for a corresponding age, and that the near point depends upon the amount of accommodation that is left after the eye has accommodated for in fin it}'.

The Far Point of a Myopic Eye. — This is always posi- tive and situated some place inside of infinity. It is found by uniting the convergent emergent rays. (See Fig. 68.)

72

REFRACTION AND HOW TO REFRACT.

The far point of a myopic eye is the result of its strong refracting power or the distance of its retina beyond the principal focus of its dioptric media. The retina and far point of a myopic eye are conjugate foci. (See Fig. 68.) The myopic far point is equivalent to just that much refrac- tion in excess of the emmetropic eye. An emmetropic eye under the influence of atropin would require a + 2 S. placed in front of it to make rays of light focus upon its retina from a distance of 50 cm., and ra}'S of light from the retina of this eye with a +2 S. in front of it would focus at 50 cm. This eye, then, equals a myopic e}'e of 2 D. This myopic eye would have a far point of 50 cm. Where the rays of light meet as they come from a m}'opic e)'e in a state of rest is its far point.

The Near Point of a Myopic Eye. — This is always closer than in the emmetropic eye for a corresponding age, and depends upon the distance of its far point. For exam- ple, an eye at twenty-five years has 8.5 D. amplitude of accommodation, but if it has a far point of 70 cm., then its near point will be represented by 8.5 D. and 70 cni., — /. c, 1.5 D., which would equal 10 D., or a near point of 10 cm. The following table gives the comparative near points in an emmetropic eye, a hypcropic eye of 2 D., and a m}'opic eye of 2 D. :

Age.

10

15

20

25

30

35

40

45

50

55

60

65

70

75

Emnietropia, p.p. 2 I). Hyperopia, " 2 D. Myopia, "

7

8.3

6

8.3 10

7

10 125 8.3

12 16 10

M 20 II

iS

28.5

J3

22 40 15-3

28

66 ,8

40 200

55 00

25

100 33

133 36

400 44

00 SO

Determining the Vision. — This may be considered as the method of finding out what an eye can see without any lenses placed in front of it ; in other words, the determina- tion (jf \-ision ma)' be defined as the seeing qualit\' of tlu-

TEST-TVPE OR TEST-LETTERS FOR DISTANT VISION. 73

un refracted eye. The refraction of an eye should never be confounded with the visual quality, as refraction applies to the refractive media ; for ei-cample, an emmetropic eye with a hemorrhage at the fovea would be practically without visual quality, and yet its refraction or refractive condition would be standard. The most acute vision is at the fovea and the region immediately surrounding it, but this sensi- bility diminishes as the fovea is departed from and the per- ipheral portion of the retina approached ; this is due to the fact that the cones are as close as 0.002 mm. at the macula, and not so close or numerous in the forepart of ^m ^m

the eye-ground. V^ tr V^ *

Test-type or Test-let- L 6 A O A L

ters for Distant Vision. —

T^j. ,1 TGYD GYDT

1 o determine the vision we „ „

, , ,1 FAVHU VFHUA

employ cards on which are

,... 1,, DLOECM LE CN D O

engraved test-type or letters c p a r-c e o i, c e o r'l c p a

of various sizes, constructed ^l^LY.MV. :L".7.V/. = ! so that each letter subtends .v;.:;/* ,:•

E C

an angle of five minutes, as Fk;. 69.— Randall's Test-letters. Block . , 1 o II 1 letters in black on cream-colored

suggested by Snellen, and ^^^^^ described on page 63 .

Figure 69 shows such cards of test-letters, reduced in size. The Roman characters just over the top of the letters indi- cate the distance in meters that the letters should be seen by the standard eye, and the little figures at the left of the letters indicate the equivalent distance in English feet. The top letter should be seen at 60 meters, and the bottom letters at 3 meters ; the intervening letters are to be seen at the respective distances indicated. As it is not unusual to find eyes that have a seeing quality better than that obtained 7

74

REFRACTION AND HOW TO REFRACT.

with Snellen's t\'pe constructed on the an^^le of five min- utes, Dr. James Wallace has constructed letters which sub- tend an angle of only four minutes. Such a card is shown in figure 70 and has a large field of usefulness. While test-cards are usually white or cream-colored, with black letters, Gould has white letters constructed on black cards. (See Fig. 71.) As white stimu- ^^ lates the retina and black does not, it

" ^1 will be recognized at once that in one

instance the card, and in the other the letters, produce the retinal stimulation. The white letters seem to stand out from the black card al- most as if they were embossed, giving a clear-cut edge and most soothing effect to the eye under ex- amination, and can be recognized when subtending a much smaller angle than the black letters. To avoid reflection, this card should be hung at an angle.

For aliens who do not know the English letters, and for illiterates, a special card has been made, known as the illiterate or " dummy " card, with characters consisting of lines shaped

like the capital letter " \\," and made to conform to the fivc- niinute angle. As these letters are warioush' placed, the patient is asked to tell, or indicate with his finger or fingers,

-000

-M X Y V

■fl a a H M

-T s o o A n

• Y V T 3 S X X

Fic. 70. — Four Min- ute Letters of Dr. J. Wallace. This card is constructed ]5rincipally for re- flection purposes.

u

3 LU

E UJ 3

E 3 uj m

ui 3 E m m

ui n E Ul 3 E

Fig. 72.

METHOD OF PROCEDURE.

75

the direction in which the prongs of the "E" point: up, down, to the right or left. This ilHterate card (see Fig. 72) is much to be preferred to the German, Hebrew, and "figure" cards occasionally displayed in clinics.

Selection of Test-cards. — The surgeon should have several of these in duplicate with the order of the letters

Fig. 71. — Gould's Test-letters. Gothic letters in white on black cards.

changed (Figs. 67, 71), as patients not infrequently and un- intentionally commit them to memory. Care should be exercised in the selection of test-cards, to see that each letter on the card measures up to the standard square of five minutes, as many of the A's and R's and N's, etc., on the old cards as seen in the shops measure six and so\en minutes horizontally. It is a matter of choice with the

76 REFRACTION AND HOW TO REFRACT.

surgeon whether to use test-cards with the block or Gothic letters. It is well to have both.

Method of Procedure. — The test-card should be hung on the wall with its ^ line five or six inches below the level of the patient's eyes, and illuminated by means of reflected artificial light. This is always a certain quantity, whereas daylight is too variable and not to be depended upon. The patient should be placed with his back toward any bright light, and at a distance of six meters from the card. Sometimes the surgeon's ofifice is not six meters long, and this distance must be obtained by using diagonal corners of the room or by using a plane plate-glass mirror and a specially prepared test-card with reversed letters (see Fig. 70), the card being hung as many meters in front of the mirror as will make six meters when added to the length of the ofifice. While a distance of six meters is always to be preferred, yet if this can not be obtained, the surgeon may use a distance of four meters, but never less than this. Each eye should be tested separately, the fellow-eye being shielded or covered by a card or opaque disc held in front of it or placed in the trial-frame. The eye should never be held shut, and any pressure upon the eyeball must be avoided.

The record of the visual acuity is usually made in the form of fractions, using Arabic or Roman notation ; figures usually indicate feet, and Roman letters usually sig- nify meters, though there is no fi.xed rule for this. How- ever expressed, the numerator indicates the size of the type which the eye reads, at the distance indicated b\- the denominator. For examj)le, if at VI meters the eye read the line of letters marked VI, then tlie record would be This would be the same if the numerator and (knomi- nator were expressed in feet, |[]. If the e}'e, at a distance

THE RECORD OK IIIE VISUAL ACUITY. //

of VI meters, read only tlie letters on the XII line, then the record would be ^j, or |-fi- (feet). If the top letter was the only one recognized at the distance of six meters, then the record would be i^- (meters), or -^^^^^ (feet). If the eye read the VI line, miscalling two letters, then the record could be made in one of three ways and would each indicate the same thing. ? ? (one question mark

for each miscalled letter), or " ^j- partly," would indicate that the eye saw —- , but not each letter correctly. This way of making the record is not so explicit as that with question marks. Or, ^— ; h would mean that the eye saw all of

' VHss ' •'

,4^ and some of the letters of -^ ; but this, too, is not so

VHss VI ' '

definite as the first record and the one recommended.

If the eye can not recognize any letter on the card at the distance of VI meters, then the card should be brought toward the patient, or the patient told to approach the card, until the eye cdiWjnst make out the top letter and no more. If this is seen at IV meters, then the record will be - ; if at one meter, the record would be — , etc. While it has been stated that the visual record is usually made in the form of common fractions, as just described, yet there are some who prefer to make the record in the form of deci- mals ; namely, a vision of — would be i.o, a vision of — - would be O. SO, or a vision of rrrrrr, would be 0.25, or a vision of ^^ would be o. I. Most authorities prefer to make their records in the form of common fractions.

In some instances the eye may not be able to distinguish any letter on the card, no matter how close it may be brought to the eye, and in such a case the vision is tested by holding the outstretched fingers between the patient's eye and a bright light (an open window), and a note is made of the greatest distance at which the eye can count

y8 REFRACTION AND HOW TO REFRACT.

fingers ; if at ten inches, the record would be " fingers counted at ten inches," or whatever the distance may be. This abihty to recognize form is spoken of as " quahtative Hght perception." Eyes that are not able to recognize form may still be able to distinguish light from darkness, and this ability is tested by alternately covering and uncov- ering the eye as it faces a light, or as light is reflected into it from a mirror. If " qualitative light perception " is pres- ent, the vision is recorded L. P., which means "light per- ception," or the record may be made L. & S., which means practically the same thing, " light and shade."

Determining the Near Point. — Having obtained and recorded the distant vision of an unrefracted eye, it is well to also find out and note what is the nearest point to the eye at which small type may be made out ; this is spoken of as determining the near point.

Test-type or Test-letters for Near Vision. — To deter- mine the near point, we employ cards on which are printed or engraved words or sentences, or a series of letters, so that each letter in each word or sentence shall subtend an angle of five minutes, at a given distance from the standard eye ; for instance, letters that are to be seen at one meter and occupy the angle of five minutes, must be 1.425 mm. square ; letters that are to be seen at half a meter distance must be 0.712 mm. square, etc. Most of the "near" cards in the market arc very defective in this respect, and the near types of Jaeger are becoming obsolete, as they are not standard letters, but merely represent the various fonts of printers' type. The writer's card is one of Gothic t)'pe, as shown in figure 73. Another card in block letters is shown in figure 74. Above each series of letters is marked the greatest distance (D) at which the respective letters ma)- be seen ; the.se distances var\- from 0.25 to 2 meters (25 to

TEST-TYPE FOR NEAR VISION.

79

0

z

o

z

z o

1- Q

I

J o

U

o

Ll

J u

DC X

Q.

J

U

D

<

O

u.

z

N

(0

0)

N

(0

0)

N

(0

0)

a

in J

J o

X

o

0 ^

L.

o

D

Q.

I

i 2

O X

Q

<

in O

z

I

Q.

O

a:

^

in

u>

^

in

(0

^

in

(0

D.

J

X

o

X

J

O

o

O

h

J

h

Q.

q: o

z

<

Q.

ir

J

>

J

o

I

o

i ■

(U

n

OJ

fO

OJ

n

<

N

0

z

L.

K

o

J

y

o

a.

I

z

o

o

N

(0

ff>

X

u

(T

J

a:

h

7 X

o

O

Q O

K

z

a

Q

5C

*•

in

(0

a.

o

I

X

z

Q.

J

I

J

z

o

X

o

1-

o

-

nj

n

8o

REFRACTION' AND IIOW TO REFRACT.

0. h «

O O J

ft: » Pi

o > o

t^ CO o>

> O H

•n X tJ tD

M

-• H K >

o W O K

^ in (o

o: s ti

o »^ :3

O O H

»4 Eh O

-• N n

D

H

»^

J

U

h

n

•J

o

k1

>

K

>

H

>

Cs.

00

a>

t^

00

O)

»

K

>

h

Q

H

H

H

K

N

H

O

O

.1 X

O

O

^

in

w

^

in

KD

O

D

»

o

>

u

f^

H

Q

n

X

H

K

H

(i1

•H

CM

CO

r-l

CM

CO

CONVERGENCIi:. 8 1

200 cm.), which are ample ' for all purposes in estimating the near point.

Method of Procedure to Find the Near Point. — The patient is seated so that the light entering the room may come over his shoulder and fall upon the card of test-type held in front of him. The surgeon, to one side of the patient, holds the card in one hand and a meter stick in the other, the eye which is not being tested is covered with a card, and the patient is told to select the smallest type on the card which he can read or spell, and as he continues to do so (aloud), the surgeon gradually approaches the card to the eye until the patient says that the letters commence to grow "hazy" and he can scarcely decipher them; or another way is to hold the card close to the patient's eye and gradually withdraw it until he can just recognize the letters ; when this point is reached, the distance from the eye to the card is measured with the meter stick, and this dis- tance, as also the size of the type which was read, is care- fully recorded. For example, the patient selecting the type marked 0.50 D. and is able to read it as close as 8 cm. and no closer, the record will be "near point equals type 0.50 D. at 8 cm."; or abbreviated, would be "type 0.50 D. = 8 cm."

In some instances the patient may not be able to read any of the near type without the aid of a glass, and if so, it will be necessary to place a plus sphere in front of the eye to assist in finding the near point ; for example, if a + 2 S. was employed, then the record might be " near point equals type 0.50 D. at 12 cm. with -\-2 S.," or " -|-2 S. = type 0.50 D. at 12 cm."

Convergence. — Con, "together," and 7'crgcre, "to turn " ; literally, turning together. This is the power of the internal recti muscles (especially) to turn the eyes toward

82 REFRACTION AND HOW TO REFRACT.

the median line ; to " fix" an object closer than infinity. Standard eyes, when looking at an object at a distance of six meters or more, are not supposed to converge ; the visual lines are spoken of as parallel and the power of con- vergence is in a state of repose. The angle which the visual line makes in turning from infinity ( oo) to a near point is called the angle of convergence, and the angle which is formed at one meter distance by the visual axis with the median line is called the meter angle, or the unit of the angle of convergence. (See i, in Fig. 75.)

If the visual line meets the median plane at J^ of a

Fig. 75.

meter, it has then two-meter angles of convergence ; at ^ of a meter, four-meter angles of convergence, etc. Or five-meter angles means that the eye is converging to a point -5^ of a meter distant.

The size of the meter angle varies ; it is not the same in all individuals ; in fact, the meter angle is smaller in children than in adults, as a rule, on account of the shorter inter- ocular distance. In children this distance is about 50 mm., whereas in atlults it is, on the average, 60 or 64 mm.

While standard eyes, to see a point at one meter distance would converge just one meter angle, they would also accommodate just one diopter ; to sec a point at '3 of a

NEAR POINT. 83

meter they would converge just three meter angles, and at the same time would accommodate three diopters, etc., thus showing how intimately the powers of convergence and accommodation are linked together, though it is possible to converge without accommodation (see Presbyopia) or to accommodate without convergence (paralysis of the in- terni).

Far and Near Points of Convergence. — Just as we have a far and a near point of accommodation, we also have a far and a near point of convergence. The far point of conver- gence is the point to which the visual lines are directed when convergence is at rest, or at a minimum. The near

Fig. 76.

point of convergence is the point to which the visual lines are directed when the eyes are turned inward to their utmost degree.

Infinity, or parallelism, is the position of the visual lines in the standard eyes in a state of rest (K cc, in F"ig. 75). Visual lines that diverge in a state of rest can only meet by being projected backward, and, therefore, meet at an imag- inary point behind the eyes (N, in Fig. 75) ; convergence is then spoken of as negative, or minus ( — ).

If the visual lines meet in a state of rest, then conver- gence is spoken of as positi\c ( • ).

The amplitude of convergence is the distance measured from the far point to the near point of convergence, and is

84

REFRACTION AND IIOW TO REFRACT.

represented by the greatest number of" meter angles of con- vergence which the eyes can exert.

Angle Gamma. — An understanding of what is known as the angle gamma is important, that the observer may understand and appreciate the real or apparent position of the eyes when looking at a near or distant point. Figure 76 shows the line O A (optic axis) and the optic center, or nodal point (N), is situated on this line in the posterior part of the crystalline lens. The line V M is really a secondary axis to this dioptric system of the eye, and unites the object (V) with the fovea centralis at M ; this line is known as the

visual line. The angle formed by the visual line with the optic axis at the nodal point i/un' be con- sidered as the angle gam- ma. *

If the fovea centralis at M was situated on the optic axis at A, then the visual line and optic axis would coincide, and there would not be any angle gamma.

In hyperopia and emme- tropic eyes the outer ex- tremity of the visual line

v.r. »„ hes 15, 7, or, in some in-

r in. 77- -" / >

stances, as much as 10 degrees to the na.sal side of the optic axis (averaging

* This is not a perfectly correct statement, as the real angle gamma ' is the angle formed by the line of fixation V R with the optic axis, R being ihe center of fixation. The angle V N O and the angle V R () being so nearly equal, are, for all intents and purpo.ses, consideretl as the same.

ANGLE ALPHA.

:5

about 5 degrees), and is spoken of as positive, and given the plus sign. In some long myopic eyes, however, the outer extremity of the visual line may lie to the outer side of the optic axis, when it is spoken of as negative, and given the minus sign.

To demonstrate the angle gamma, the patient is told to look at the point of a pencil or pen held in the hand of the surgeon, at about 13 inches distant (A in Figs, jy and 78). If the angle gamma is positive, the eyes will appear divergent to the observer, who looks at the position of the poles of the cornea or centers of the pupils. (See Fig. JJ^)

If the angle gamma is negative, the eyes will appear convergent — that is, they appear to con- verge to a point in front of the pencil. (See Fig. 78.)

The amount of the angle gamma can be measured by using the arc of the perimeter held horizontally, the patient being placed in the same position as when having

his field taken. To do this, while the eye fixes the central point, the surgeon passes a candle-flame along the arc until the catoptric image of the flame is seen at the center of the pupil ; this position of the candle -flame on the arc is noted in degrees, which is the size of the angle gamma.

Fig. 78.

86 REFRACTION AND HOW TO REFRACT.

Angle Alpha. — This is the angle formed by the long axis of the corneal ellipse with the visual axis. In the consideration of this angle it must be remembered that the cornea resembles, in its central area, at least, an ellipsoid of revolution, with the shortest radius usually in the verti- cal meridian. The angle alpha is spoken of as positive when the outer extremity of the long axis of the cornea is to the outer side of the visual line, and negative when it is to the nasal side.

CHAPTER III. OPHTHALMOSCOPE.

Direct and Indirect Method.

Ophthalmoscope. — From oipOaXpAx;, "eye," and gvmt.zIv, " to observe " or " view "; literally, " to view an eye." An instrument used for studying the media and interior of the eye. The pupil of an eye in health appears to an observer as black ; this is due to the fact that the observer's eye does not ordinarily intercept any of the rays of light which return from the eye. Ra>^s of light entering an eye are returned toward their immediate source, and, therefore, if an observer wishes to see into or study the interior of an eye, he must have his own eye in the path of the returning rays. To accomplish this, the observer places a mirror in front of his eye, so that the reflected rays entering the e)'e are returned toward the mirror. There is an infinite variety of these in- struments in the market, but for the general student the modified instrument of Loring appears to meet with most favor. (See Fig. 79.)

This has a concave mirror with a radius of curvature of 40 cm., giving a principal focus, therefore, at 20 cm. The sight-hole is round and about 3^ mm. in diameter, cut through the glass ; this mirror can be tilted to an angle of 25 degrees. As an improvement over such a mirror, and to take its place, the writer would recommend the mirror used on his own ophthalmoscope, which has a radius of curvature of 15 cm.; and the sight-hole, 21/ mm. in diameter, is not cut through the glass, but is made by rcmoxing the quick-

«7

88

REFRACTION AND HOW TO REFRACT.

silver. The glass at the siglit-hole gives additional reflect- ing surface, and at the same time does away with much annoying aberration which results wlien the glass is per- forated.

BACK

Fig. 79.

The small sight-hole is an advantage, also, in looking into small puj)ils. The mirror, oblong in shape, 18 by 33 mm., is secured at the center of its ends, b}' two elevated .screws, to a hollow disc 4^^ cn- i'l diameter, in which is a revolving milled wheel, containing small spheres, each about 6 mm. in diameter. The series of spheres ranges

OrilTIIALMOSCOPE.

89

from — I D, to — 8 D., and irom +1 D. to -f 7 D. The central aperture does not contain a lens, but is left open.

When it is desirable to use any lens stronger than — 8 D. or +7 I^-, there is an additional quadrant, which can be superimposed and turned into place at the sight-hole ; it contains four lenses, — 0.50 D. and — 16 D., also +0.50 D. and ~{- 16 D. With this quadrant and the spheres in the milled wheel, any spheric combination can be made from zero to — 24 D. or to +23 D. An index below the si^jht-hole of the instrument records the strength of lens

Fig. 80.

that may be in use ; minus lenses are usually marked in red and plus lenses in white.

How to Use the Ophthalmoscope. — There are two wa)'s or methods by which the ophthalmoscope may be used — the direct and the indirect.

The Direct Method (see Fig. 80). — Proficicnc}- with the ophthalmoscope docs not come except from long and constant practice, and se\'eral important matters should receive very careful attention before the student attempts to study the interior of an e}'e. 8

90 REFRACTION AND HOW JX) REFRACT.

The Room. — This should be darkened by drawing the shades or closing the blinds ; the darker the room, the better.

The Light. — This should be steady, clear, and bright ; a good lamp is suitable, but an Argand burner gives more intense light, and is to be preferred, especially if it is placed on an extension bracket that can be raised or lowered and is capable of lateral movement.

Position of Light and Patient. — The light should be several inches to one side and back of the patient, and on a level with the patient's ear, so as to illuminate the outer half of the eyelashes of the eye to be examined ; it may even be well to have the tip of the patient's nose illuminated.

The patient should be seated in a comfortable chair (without arms), and is instructed to look straight ahead into vacancy, or at a fixed object if necessary, and is only to change the direction of his vision when told to do so. Under no circumstances should the patient be allowed to look at a light, as this will contract the pupil.

For the beginner, it may be well to dilate the patient's pupil with a solution of cocain or homatropin. The student, however, should learn as soon as possible to see into an eye without the aid of a mydriatic, as many patients seriously object to the slight inconvenience that results from the drugs mentioned.

The Observer. — If the observer has any decided refrac- tive error, he should wear his correcting glasses ; the reason for this will be explained later. The observer should be seated at the side of the patient corresponding to the eye he is to examine. LLxamining the right e)'e, the observer should be on the patient's right ; if the left e)'e, then on the patient's left.

When examining the right eye, the ophthalmosct>j)e is held in the right hand, before the right eye ; and in the left

OPHTHALMOSCOPE. 9 1

hand, and before the left eye, when examining the left eye. The surgeon's eye should be a little higher than the patient's. Patient and observer should keep both eyes open. The one exception to this is when the patient has a squint, when it will be necessary for him to cover the eye not being examined, and in this way the eye under observation will look straight ahead.

The surgeon holds the ophthalmoscope perpendicularly, so that the sight-hole in the mirror is directly opposite to his pupil and close to his eye. The side of the instrument rests on the side of his nose or the upper margin is in the hollow of the brow. The mirror is tilted toward the light. The surgeon's elbow should be at his side, and not form an angle with his body.

With these several details carefully executed, the surgeon begins his examination at a distance of about 25 or 30 cm., never closer ; and at this distance he reflects the light from the mirror into the eye, and observes a " red glare," which occupies the prevdously black pupil. This is called the " reflex," and is due to the reflection from the choroidal coat of the eye. The color of the reflex varies with the size of the pupil, transparency of the media, the refraction, and the amount of pigment in the eye-ground.

Having obtained the " reflex," it will be well for the be- ginner to practise keeping the reflected light upon the pupil by changing his distance, approaching the eye as close as an inch or two ; this must be done slowly, and ]iot with a rush.

What the Observer Sees. — Having learned to keep the light on the pupil, the next thing is to study the transparency of the media — /. c, to find out if there is any interference with the free entrance and exit of the reflected ra\\s, such as would be caused by opacities in the cornea, lens, lens

92 REFRACTION AND HOW TO REFRACT.

capsule, or vitreous ; and, if present, to note their character and exact location, whether on the visual axis or to one side, etc. The next objective points will be mentioned individually, and with the idea of systematizing the study.

The Optic Nerve. — Also called the disc or nerve head or papilla.

Color of the Optic Disc. — This has been described as resembling in color the marrow of a healthy bone, or the pink of a shell, etc. ; yet this is not by any means a true statement or description, as the apparent color of the nerve is controlled in great part by the surrounding eye-ground — whether this is heavily pigmented or but slightly so, or whether there is an absence of pigment, as in the albino. The student should be ready to make allowances for these contrasts.

The shape of the disc varies : it may appear round, oval, or even irregular in outline. Usually it is a vertical oval.

The vessels on the disc which carry the blood to and from the retina are not of the same caliber, nor do they have the same curves and branches in all eyes or in the same pair of eyes. The central artery may be single or double (if it has branched in the nerve before entering the eye), and enters the eye at the nasal side of the center of the disc.

Approximating the central artery on its temporal side is the retinal vein, which may also be double. The relative normal proportion in size between arteries and veins is generally recognized as about two to three. The veins are usually recognized by their larger size and darker color. At or near the center of the disc is often seen a depression, known as the physiologic cup ; this may be shallow or deep ; it may have shelving or abrupt edges ; it may even be funnel-shaped.

OPHTHALMOSCOPE. 93

At the bottom of the cupping is frequently seen a gray stippHng, the membrana cribrosa ; openings in the sclera for the passage of the transparent optic nerve-fibers which go to form the retina. Surrounding the disc proper is often seen a narrow white ring ; this is sclera, and is known as the scleral ring. Just outside of this ring is frequently seen a ring of pigment; this is called the choroidal ring. In many cases the choroidal ring is not complete, the pigment being quite irregular, or possibly there may be just one large mass of pigment to one side of the disc ; this is not patho- logic.

The retinal arteries and veins, while possessing many anomalies, and while occasionally an artery and vein are seen to twine around each other, usually pursue a uniform course up and down from the disc, and are named accord- ingly— /. i\, upper nasal vein and artery ; upper temporal vein and artery ; lower nasal artery and vein ; lower tem- poral artery and vein.

The retina itself, in health being transparent, is not seen. The fovea centralis, occupying the center of the macular region, is about two discs' diameter to the temporal side of the disc and slightly below the horizontal meridian. The fovea is recognized because it is a depression, and its edges give a reflex ; it is very small, and appears as a bright spot one or two mm. in diameter. The " macular region " is the part of the eye-ground immediately surrounding the fovea ; it contains minute capillaries, but it is impossible, in healthy eyes, to recognize them with the ophthalmoscope.

The Choroid. — This is distinguished by the character of its circulation, the vessels being large, numerous, and flat- tened, and without the light streak which characterizes the retinal vessels. Pigment areas between the vessels are also diagnostic of this tunic. The choroidal circulation is best

94

REFRACTION AND HOW TO REFRACT.

studied in the blond or albino, and may be seen in many eyes toward the periphery of the eye-ground.

In the foregoing description of the use of the ophthal- moscope, etc., it is presumed that the instrument has been used without any lens in position, and that the observer's eye and the eye under examination are health}^ emmetropic eyes with the accommodation at rest. Figure 8i shows the position of the light, L, the ophthalmoscope, the examiner's and the examined eye under these conditions.

The divergent rays from the light (L) are reflected con-

FiG. 8i.

vergently from the concave mirror, and focusing in the vitre- ous, they cross and form an area of illumination on the retina at IF. The retina, situated at the principal focus of the dioptric media, naturally projects out from its indi- vidual points rays of light which are parallel as they leave the eye ; some of these pass through the sight-hole of the mirror and meet upon the retina of the observer's emme- tropic eye.

There are two very important points which nuist bo

OI'IIIIIALMOSCOI'E.

95

considered when usinL;' the ophthahiioscope in the direct method : one is the direction which the rays of hght take as they leave the eye under examination, and the other is for the observer to keep his own eye emmetropic ; in other words, the observer wearing his correcting glasses should not accommodate.

Figure 82 shows that rays of light passing out of an eye divergently must be made parallel, so as to focus upon the surgeon's own retina (emmetropic), and to do this it is

Fig. 82. — T B indicate points at the edge of the disc from which rays pass out of the eye divergently in the direction T' B^, T'' W, T^ W, and being received by the observer's eye, are projected backward, forming an erect magnified when image at T^'' B^^. This image is not so large as that seen when looking into a myopic eye. (Fig. 83.)

necessary to turn a plus lens in front of the sight-hole of the ophthalmoscope ; the strength of the convex lens thus employed, other things being normal, is the amount of the refractive error of the eye being examined.

Figure 83 shows rays of light passing out of an ej^e convergently, and to have them parallel, so as to focus upon his own retina (emmetrojjic), it is necessarx^ to turn a concave lens in front of the sight-hole of the ophthalmo-

96

REFRACTION AND HOW TO REFRACT.

scope ; the strength of the concave lens thus employed, other things being normal, is the amount of the refractive error of the eye under examination.

The Observer's Accommodation. — It has already been stated that, when using the ophthalmoscope, the observer should wear any necessary correcting lenses. If the ob- server has a refractive error and does not wear his glasses, he must deduct this amount from the lens used in the ophthalmoscope. If he has two diopters of hyperopia

Fig. 83. — T B indicate points at the edge of the disc from which rays pass out of the eye convergently in the direction T' B', and, being received by the observer's eye, are projected backward, forming an erect magnified image at T" B". This image is much larger than that seen when look- ing into tlie hyj)eropic eye. (Fig. 82.)

himself, and the lens used in the ophthalmoscope is plus four diopters, then the eye under examination has onl)' two diopters. It is not unusual for beginners to see the e)'e- ground (disc) in hyperoj)ic eyes with a strong concave lens ; this is due to the fact that the}' accommodate. Prac- tice will overcome this habit, and it should be mastered as soon as possible. There are .several wa\'S of doing this : one is to begin the examination at a distance of 30 or 40

OPHTHALMOSCOPE. 97

cm. from the eye, with both eyes open, and to gradual 1)' approach tlie eye as close as 3 cm., imagining all the time that one is looking for some remote point ; otherwise, if one begins the examination close to the eye, and imagines he is going to see an object about an inch away, he will most invariably accommodate several diopters, with the result that he turns a strong concav^e lens in front of the sight- hole of the ophthalmoscope to neutralize his accommodation.

This explains how so many beginners diagnose all cases of hyperopia as myopia. An excellent way to learn to relax the accommodation is to practise reading fine print at a distance of about thirteen inches through a pair of plus three lenses, placed before the surgeon's emmetropic eyes. Another good way to learn to relax the accommo- dation is to practise on one of the many schematic eyes found in the shops. (Fig. 136.)

Size of the Image of the Eye-ground (Figs. 82 and 83). — In concluding the subject of the direct method of examination it may be interesting to note the apparent size of the image of the eye-ground, which, it must be remem- bered, is virtual, erect, and enlarged ; in fact, it seems to be at some distance behind the eye, and if the student has paid close attention to the study of images as formed by convex lenses, detailed in chapter i, he need not ha\-e an}' difficulty in appreciating these facts.

The optic disc of an emmetropic eye, as seen through the ophthalmoscope, appears to be about 25 mm. in diam- eter, and about 250 mm. away. The retina of the emme- tropic eye is about i 5 mm. from its nodal point ; then the actual size of the emmetropic disc is -J/^ of 25, or -1. or 1.5 mm. ; then 15 is to 250 as 1.5 is to 25, or 16.6 — the magnification, in other words, when the emmetropic disc is observed, it appears about 16.6 times larger than it actually is. 9

98

REFRACTION AND HOW TO REFRACT.

The Indirect Method (see Fig. 84). — Practising this method, the observer sees a larger part of the eye-ground

Fig. 84.

at one time, but it is not so perfect in detail nor is it mag- nified to the same extent as in the direct method. The observer does not have to get so close to his patient, which is a decided advantage in some clinical cases. Unfortun- ately, as a preliminary step, it is often neces- sary to dilate the pu- pil. In addition to the ophthalmoscope, there is also required a convex lens of known strength and large aperture ; the one which comes in the case with the scope is usual!)- too small and too strong for general use. The writer prefers his plus 13 I), with metal rim and con\-en- ient handle, shown in figure 85 (reduced one-third in size).

Fig. 85.

Ol'H THALMOSCOPE. 99

This is held at about three inches in front of the eye under examination, the observer resting his httle and ring fingers on the temple of the patient. The hght may be over the patient's head, or to the side corresponding to the eye under examination, the patient being instructed to look with both eyes open toward the surgeon's right ear when the right eye is being examined, and toward the surgeon's left ear when the left eye is examined.

With a +4 D. in the ophthalmoscope held close to his eye, the surgeon seats himself in front of the patient at about sixteen inches distant, and reflects the light through the condensing lens into the patient's eye, and then approaches or moves away from the eye until he recog- nizes clearly a retinal vessel or the disc ; he must remem- ber, however, that he is not looking into the eye. but is viewing an aerial image formed between the convex lens and the ophthalmoscope ; this image is not only inverted, but undergoes lateral inversion, so that the right side of the disc becomes the left side of the image, and vice versa ; the upper side of the disc becomes the lower side of the image, and vice versa. As tJic direct method gi%<es an erect, virtual, and enlarged image, the indirect method prodiices an inverted, real, and small image. The principle of the direct method is similar to a simple microscope, and the indirect to a compound microscope.

The size of the image depends upon the refraction of the eye and the distance of the convex lens from the e}'e under examination. In the standard eye this is always the same, no matter how far away from the eye the convex lens is held. To estimate the size of the image in the standard eye, all that is necessary to know is the principal focal dis- tance of the lens employed ; if a +13 D., then the image is formed at 75 mm. (three inches), and remembering that the

lOO REFRACTION AND HOW TO REFRACT,

retina in the eye is i 5 mm. back of the nodal point, the size of the image will be to the size of the disc (if that is what is looked at) as their respective distances, or as 15 is to 75 which equals 5, the magnification.

The purpose of the +4 D. in the scope is to take the place of the eye -piece in the microscope, and, therefore, to magnify the image at the same time it relieves the observer's accommodation. In high myopia the +4 D. may be dis- pensed with.

CHAPTER IV. EMMETROPIA.— HYPEROPIA.— MYOPIA.

Emmetropia. Emmetropia ('-', "in"; iiirpo'^, "measure"; ('^4', "eye ") literally means an eye in measure, or an eye which has reached that stage of development where parallel rays of light will be focused on its retina without any effort of accommodation. As the emmetropic eye is the ophthal- mologist's ideal unit of measurement or goal in refraction, the beginner should know this form of eye thoroughly, so that he may recognize any departure from this standard condition. The emmetropic eye may be described in vari- ous ways, and while these descriptions may appear like repetitions, they are given for purposes of illustration :

1. The standard or schematic eye: Authorities differ somewhat in the exact measurements of a schematic eye, but the one suggested by Helm-

holtz is certainly worthy of careful consideration. (See p. 58.)

2. An emmetropic eye is one which, in a state of rest (without any effort of accom- p^, 35 modation whate\er), receives

parallel rays of light exactly at a focus upon its fovea. (See Fig. 86.)

3. An emmetropic e}'e, therefore, is one which, in state of rest, emits parallel ra}-s of light. (Sec Fig. 86.)

lOI

I02

REFRACTION AND HOW TO REFRACT.

4. An emmetropic e}'e is one whose fovea is situated exactly at the principal focus of its re- fractive system. (See Fig. 86.)

5. An emmetropic eye is one the vision of which, in a state of rest, is adapted for infinity. •

6. An emmetropic eye is one which has its near point consist- ent with its age. (See p. 69.)

7. An emmetropic eye is one which does not develop pres- byopic symptoms until forty- five or fifty years of age. (See p. 261.)

8. An emmetropic eye, in contradistinction to a myopic eye (see p. 1 1 3), is spoken of as a healthy eye, or one which shows the least amount of irri- tation in its choroid and retina.

Because we refer to Helm- holtz's schematic eye as an em- metropic eye, it will not do to say that all eyes that measure just 23 mm. in their antero- posterior diameter are emme- tropic (Fig. 87) ; for while an

I'^ic. 87. — I. Emmetropia. 2. Mvo]iia due to a strong lens. 3. Hyperopia due to a weak lens. 4. Myojiia due to a short radius of curvature of cornea. 5. Hyperopia due to a long radius of curvature of cornea. The anteropos- terior diainelcr of all tlu'sc eyes is just 2 ; Mini.

AMETROPIA. 103

eye may be just 23 mm. in Iciigtli, it may have it.s refractive system stronger or weaker than is consistent v/ith its length, making it, if stronger, a myopic or long eye, and, if weaker, a short or hyperopic eye. An eye, to be emmetropic, therefore, no matter what its length, must have its refractive apparatus of just such strength that, in a state of rest, the principal focus will coincide exactly with the cones at the fovea. (Fig. 86.)

Ametropia.

Ametropia (« priv. ; iiirfxiv, "a measure" ; cl^t?, "sight") literally means "an eye out of measure." An ametropic eye is one which, in a state of rest, does not form a distinct image of distant objects upon its retina. An ametropic e}'e may be defined as one which, in a state of rest, does not focus parallel rays of light upon its fovea. An eye which is not emmetropic is ametropic. There are two forms of ametropia — axial and curvature ametropia.

Axial ametropia is the condition in which the dioptric apparatus refracts equally in all meridians, but the retina of the eye, when at rest, is either closer to, or further away from, the nodal point than the principal focus. (See Figs. 88 and 90.) The refraction is measured on the length of the anteroposterior axis of the eye ; hence its name, axial ametropia.

Curvature ametropia, in contradistinction to axial ame- tropia, is the condition in which the dioptric apparatus does not refract equally in all meridians, and with the result that there is no focusing of all the rays at any one point ; or cun'ature ametropia may be considered as that condition in wliicii parallel rays of light entering an e\'c ha\e two focal planes for two principal meridians at right angles to each other. Curvature ametropia is commonh" spoken of as astigmatism. (See Chap, v.)

I04 REFRACTION AND HOW TO REFRACT.

Varieties of Axial Ametropia. — Axial ametropia is of two forms : one in which the eye has its fovea closer to the dioptric apparatus than its principal focus (see Fig. 88), known as the hyperopic, short, or flat eye ; and the other form of the eye in which the fovea is further away than its principal focus, known as the myopic or long eye. (See Fig. 90.)

Hyperopia.

Hyperopia (J^-if^, "over"; w^, "eye") literally means an eye which does not equal the standard condition, or an eye which is less than the standard measurement. Hyper- opia is often abbreviated H. About twenty per cent, of all eyes have simple hyperopia. The hyperopic eye is spoken of as far-sighted, and the condition as one of far- sightedness. The hyperopic eye may be described in many different ways :

1. The "natural eye," or "the eye of nature."

2. The "short eye." This term is used on account of its fovea lying closer to the dioptric apparatus than the principal focus.

3. Parallel rays of light passing into a hyperopic eye in a state of rest fall upon its retina or fovea before tliey focus. (See Fig. 67.)

4. Rays of light from the fovea of a hyperopic eye in a state of rest pass out divergently (see Fig. 88), and the condition is equivalent to a convex lens refracting ra}'s of light which proceed from a point closer to the lens than its principal focus. (See Fig. 35.)

5. A hyperopic eye is one which, in a state of rest, can only receive convergent rays of light at a focus uptm its fox'ca (I'ig. 88) ; therefore, to repeat : the h)-peropic e}'e, in a state of rest, emits divergent ra)s and receives convergent rays at a focus upon its fovea.

nvpEKoi'iA. 105

6. As convergent rays are not found in nature, and are, therefore, artificial, a hyperopic eye is one which, in a state of rest, requires a convex lens to focus parallel rays of light on its fovea. (See Fig. 89.)

7. A hyperopic eye is one which must accommodate for infinity, and, in fact, for all distances ; in other words, a hyperopic eye in use is in a constant state of accom- modation.

8. A hyperopic eye having to use some of its accommo- dative power for infinity, must, in consequence, have its near point removed beyond that of an emmetropic eye of corresponding age. (Seep. 71.)

9. From the description contained in 3, it follows that

Fig. 88. Y\q. 89.

the far point of a hyperopic eye in a state of rest is negative ( — ), and is found by projecting the divergent rays back- ward to a point behind the retina. (See Fig. 88.)

10. From the description contained in 6, and the descrip- tion of accommodation on page (>(>, it is natural to find the retina and choroid of many hyperopic eyes in a state of irritation.

11. From the description contained in 6 and 7, and on page 262, it fc^Uows that symptoms of prcsb}-opia manifest themselves earlier in hyperopic than in an\- other form ot eyes.

12. From the description contained in 5, — and this may

I06 REFRACTION AND HOW TO REFRACT.

appear like repetition), it follows that a liyperopic eye will accept a plus glass for distant vision. (See Fig. 89.)

13. From 6 it is evident that the circular fibers of the ciliary muscle must become highly developed ; much more so than the longitudinal fibers. Microscopically, a section of the ciliary muscle on this account will bear evidence of the character of the eye from which it came.

Causes of Hyperopia. — It is a well-known fact that the eyes of the new-born are, with comparatively few excep- tions, hyperopic ; such eyes are supposed to grow in their anteroposterior diameter, and at adolescence to reach that stage of development called emmetropia. It is also a well- known fact that this ideal condition of emmetropia is very rarely attained, the length of the eyeball not increasing in proportion to the strength of its refractive system.

Eyes may approximate the emmetropic condition, but very seldom remain so, passing into the condition where the fovea lies beyond the principal focus, becoming what is known as long, or myopic.

A standard eye may be made hyperopic by removing its lens ; the condition following cataract extraction. (See Fig. 161.)

An eye may possibly become hyperopic in old age, from flattening of the lens due to sclerosis of its fibers.

Any disease which will cause a flattening of the cornea in a standard eye will produce hyperopia.

A diminution in the index of refraction of the media of the standard eye will produce hyperopia.

Subdivisions of Hyperopia. — For purposes of study h}'per()j)ia has been classed as :

I. Facultative hyperopia (abbreviated Ilf) is a condi- tion of the eye in which the patient can overcome the error by using his accommodation. It is a condition of early

HVPEKOPIA. 107

life, and is voluntary. The patient can see clearly, with or without a convex glass.

2. Absolute hyperopia (abbreviated Ha.). — This is hy- peropia that can not be overcome by the accommodative effort. It is generally a condition of old age, and is invol- untary ; facultative hyperopia in youth becomes absolute in old age. Old age, in fact, develops every variety of hyperopia. Absolute hyperopia exists whenever the defect is of so high a degree that it can not be overcome by the accommodation or when the accommodative power itself is gone.

3. Relative hyperopia (abbreviated Hr.) is where ac- commodation is assisted in its efforts by the internal recti muscles ; in other words, the eyes squint inward.

4. Manifest hyperopia (abbreviated Hm.) is repre- sented by the strongest convex lens through which an eye can maintain distinct distant vision. Manifest hyperopia, therefore, includes facultative and absolute.

5. Latent hyperopia (abbreviated HI.) is the amount of hyperopia which an eye retains when a plus lens is placed in front of it. Or latent hyperopia is the difference between the manifest h}'peropia and that lens which an eye would select if its accommodation was put at rest with a cycloplegic (atropin). P'or example, an eye accepts a + 1.25 S. as its manifest H., and, when atropin is instilled, w^ould accept +2.75 S. for the same distant vision ; then the difference between the manifest +1.25 S. and +2.75 S. (the total) is +1.50 S., which is the latent h\-per- opia.

6. Total hyperopia (abbreviated Ht.) is the full amount of the h)-peropia ; or is represented by the strongest glass which an eye will accept, and have clear, distinct vision when in a state of rest.

I08 REFRACTION AND HOW TO REFRACT.

Symptoms and Signs of Hyperopia. — These are many and various ; tlic principal one, however, and the one that generally causes the patient to seek relief, is Juadaclic. Headache caused by the eyes is usually frontal, and is denominated " brow ache " ; it may be frontotemporal ; the pain or discomfort starting in or back of the eyes may extend to the occiput or all over the head, and be accom- panied with all kinds of nervous manifestations. The most characteristic distinguishing feature of ocular headache is that it comes on while using the eyes, and gradually grows worse as the use of the eyes is persisted in ; and, likewise, the headache gradually ceases after a few minutes' or hours' rest of the eyes. Vertex headache, or a feeling of weight on the top of the head, has been preempted by the gyne- cologist, and is not usually classed as ocular. The ciliary muscle being the prime factor in causing the headaches, the writer feels justified in calling it the " headache mus- cle." " Sick headaches " are largely due to eye-strain. Various functional disorders, such as dyspepsia, constipa- tion, biliousness, lithemia, chorea, convulsions, epileptoid diseases, hysteria, melancholia, etc., are, according to some few authorities, attributable to this condition. See Asthen- opia, page 211.

Blepharitis marginalis, styes, and conjunctivitis are frequently present, and in truth the hyperopic eye on this account can often be diagno.sed in public outside of the surgeon's office. A feeling as of sand in the eyes, ocular pains or postocular discomfort, a dr\'ncss of the lids, as if they would stick to the eyeballs, are common complaints, and part of the conjunctivitis. Other patients have their eyes filling with tears (epiphora) as soon as they begin reading, etc. A drowsiness or desire to sleej) often comes on after or (iurin<r forced accommodation.

HYPEROPIA. 109

Congestion of the choroid and retina, as evidenced by the ophthahiioscope, often go together with the blepharitis and conjunctivitis.

The patient complains that the print blurs or becomes dim after reading, and this is especially apt to occur by artificial light. When the "blur" comes on, he has to stop and rub his eyes or bathe them ; and then, with additional light, he is able to continue the reading for a short time longer, when the blur again returns and the effort must be given up. Strong light stimulates the accommodation. The " h}'per- opic blur" is nothing more or less than a relaxation of the accommodation.

In children hyperopia sometimes simulates myopia, from the fact that the child in reading holds the print veiy close to the eyes. He does this in order to get a larger retinal image and to relieve his accommodation ; the retinal image is not clear, and the child has to read slowly ; the retinal image is composed mostly of diffusion circles. The child holds the print close to his eyes to avoid using his total accommodation, which he might have to do if he held the print at a respectable distance.

He also calls into play the orbicularis palpebrarum, and narrows the palpebral fissure, looking through a stenopeic slit, as it were. These cases of simulated myopia can be quickly diagnosed by :

1. The narrow palpebral fissure during the act of reading, and reading very slowly, as each letter has to be studied.

2. The fact that very few children have myopia.

3. The comparatively good distant vision, as a rule, w^hich myopes never have, unless the myopia is of ver)^ small amount.

4. The ophthalmoscope.

The beginner in ophthalmology should be on his guard

I lO REFRACTION AND HOW TO REFRACT.

for these "pseudo-myopias," and not be guilty of putting .concave lenses on hyperopic eyes.

Diagnosis of Hyperopia. — This form of ametropia may be recognized in many ways :

1. Blepharitis marginalis, if present, is generally due to hyperopia.

2. Hyperopic eyes are said to be small, and to have small pupils, which facts are generally confirmed ; but myopic eyes sometimes appear small, and have small pupils also.

3. A narrow face and short interpupillary distance are quite indicative of hyperopia, but these indexes are not infallible.

4. A child with one eye turned inward toward the no.se (convergent squint) has hyperopic eyes, as a rule ; the hyperopia generally not being of the same amount in the two eyes, the squinting eye usually being the more hyperopic.

5. It has been authoritatively stated that light-colored irises are seen in hyperopic eyes and dark irises are to be found in myopic eyes, and yet this is not always correct. German students, with their blue irises, will average from 50 per cent, to 60 per cent, of m}'opia.

6. Hyperopic eyes, with few exceptions, have excellent distant vision : often -^, or even better. The student should be on his guard for this, and not imagine, because a patient has ^.' vision, that he is emmetropic ; on the con-

* \ I

trary, hyperopic eyes accommodate for distance, and obtain this acute vision by effort.

7. The patient gives a history of accommodati\e aslhe- n(ipia, with or without headaches coming on during or after the use of the eyes.

8. The distant vision of a li)-peropic eye may remain

MVOPIA. I I I

unchanged or may be improved with the addition of a convex lens, which latter would be impossible in emme- tropia and myopia.

9. The near point of a hyperopic eye without glasses lies beyond that of an emmetropic eye for a corresponding age.

10. A hyperopic eye can see fine print clearly through a convex lens at a greater distance than its principal focus, which would not be the case in any other form of eye.

Other tests for determining hyperopia are with (11) the ophthalmoscope, (12) the retinoscope, (13) Scheiner's test, (14) Thomson's ametrometer, and (15) the cobalt-blue glass test, commonly spoken of as the chromo-aberration test. These tests are described in the text.

Myopia. Myopia {p-uth, "to close"; wip, "eye") means, liter- ally, "to close the eye," and this origin of the name has arisen from the fact that many long eyes (myopic) squint the eyelids together when they endeavor to see beyond their far point. Brachymetropia is another name for the same kind of eye. Myopia is abbreviated M. About 1.5 per cent, of all eyes have simple myopia. The mj^opic eye is spoken of as near- sighted, and the condition as one of near-sightedness. The myopic eye may be described in many different ways :

1. The long eye. The Fig. 90. origin of this name is pure- ly anatomic, the fovea lying beyond the principal focus of the refracting system. (See Fig. 90.)

2. Parallel raj's of light entering a m}-opic eye focus in

112

REFRACTION AND HOW TO REFRACT.

the vitreous humor before they can reach the fov^ea. (See Fig. 90.)

3. Rays of hght from the fovea of a myopic eye pass out of the eye convergently (see Figs. 68 and 91), focusing at

Fig. 91.

some point inside of infinity. The refractive condition of a myopic eye is similar or equivalent to a convex lens refracting rays of light which proceed from some point further away than its principal focus. (See Fig. 33.) The nearer the emergent rays of light focus to the eye (in a state of repose), the longer the eye ; and the further away the emergent rays focus from the eye, the nearer the eye approaches to emmetropia, or normal length.

4. A myopic eye is one which receives rays of light which diverge from some point closer than six meters at a

focus on its fovea and which emits convergent rays. (See Fig. 33, and also description of conjugate foci.)

5. As parallel raj's can not focus on the fo\ea of a myopic eye, it is necessary to give parallel ra\'s entering the eye a certain amount of di\crgence, so as to i)lace the tocus at the fovea ; and to accomplish this, a concave lens must ]:)c used. (Sec V\g. 92.) A myopic eye, therefore, is one

Fig. 92.

MVOl'IA. I I 3

which requires a concave lens to improve distant vision. (See Fi^. 92.)

6. A myopic eye is one whose distant vision is made worse by the addition of a convex lens.

7. A myopic eye is one which does not accommodate for distance.

8. A mj'opic eye having a refracting system stronger than is consistent with its length, or vice versa, greater length than is consistent with its dioptric S}'stem, naturally does not use any accommodation except for points inside of its punctum remotum, and with the result that its ampli- tude of accommodation is used near by ; consequently, a myopic eye is one which has a near point closer than an emmetropic eye of corresponding age. (See p. 72.)

9. From the description contained in 3 it follows that the far point of a myopic eye is positive ( + ).

10. From the description contained in 3 and 7, it also follows that the myopic eye does not develop presbyopic symptoms until late in life.

11. From 6 and 9 it follows that the circular fibers of the ciliary muscle are not used to the same extent in a myopic eye as in the emmetropic and especially in the hyperopic e\'e. Microscopically, a section of a ciliary muscle on this account will bear evidence of the character of the eye from which it came, and have the longitudinal fibers more in evidence. In some very long myopic eyes there may not be any circular fibers recognized.

12. Eyes in which the m}-opia is progressive are spoken of as " sick eyes."

Causes of Myopia. — An\' disease or injur\- which will so alter the refracting sj'stem of an c)-e that parallel rays must focus in front of the fovea will produce the form of eye known as long or mj-opic. This may be brought about

I 14 REFRACTION AND HOW TO REI'RACT.

in different ways : A shortening in the radius of curvature of the cornea, such as comes with conic cornea and staphy- loma of the cornea ; an increase in the refractive power of the lens from swelling, as often precedes cataract, and is spoken of as "false" second sight; cyclitis and irido- cyclitis, which diseases cause a relaxation of the lens ligament, allowing the lens to assume a greater convexity ; or ciliary spasm may produce temporarily the same con- dition.

Technically, however, myopia is quite universally under- stood to mean a permanent elongation of the visual axis of the eye beyond the principal focus of its refracting system.

Heredity is certainly a predisposing factor to myopia, but this does not mean that the babe is necessarily born with long eyes. On the contrary, the eye is very likely hyperopic at birth, and what the child may inherit is weak eye tunics. Such eyes, when placed under strain or what to them is overuse, soon become elongated. This may also be brought about or assisted by poor hygienic surround- ings, poor health, or develop after an attack of typhoid or one of the eruptive fevers.

Three causes for the elongation of eyes have been brought forward by able authorities and expounded as theories, any one of which, or all three, may appear conspicuously in in- dividual cases.

1. Anatomically, the size of the orbit and the broad face give a long interpupillary distance and cause excessive convergence (turning inward of the eyes) when the eyes fix at the near point.

2. Mechanically, when the eyes are far apart and attempt to converge, the external recti muscles press upon the outer side of the globes, flattening the c\es hiter.illy,

MVOPIA. I I 5

with the result that the point of least resistance for the compressed contents of the globes is at the posterior pole of the eye, and here it is that the pressure shows itself, by an elongation of the eye backward in its anteroposterior diameter. This combination of the anatomic and mechanic theories may explain in great part the presence of myopia in the average German student or any broad-faced indi- vidual.

3. The inflammatory theory is that a low grade of inflammation attacks the tunics of the eye, especially at the posterior pole, and is spoken of as macular chor- oiditis ; this is brought about by faulty use of the eyes, in the school or in the home, in a poor light or too glaring a light improperly placed, or by using the eyes with the head bent over the work so that the return circu- lation from the retina and choroid is interfered with. This inflammation or congestion of the tunics of the eye may be primary in itself or secondary to the anatomic and mechanic causes. Be this as it may, the conditions exist, and go to show more and more that myopia is actually acquired and not per se congenital. " The inherited con- genital anomalies of refraction, particularly astigmatism, are responsible for the m)-opic e}-e, by virtue of the pathologic changes they occasion in hard-worked eyes rather than any inherited predisposition to disease." (Risley, "School Hygiene.")

Symptoms and Signs of Myopia. — \\'hile the myope may complain of headache and symptoms of accommodative asthenopia, yet the principal visual complaint will be the inability to see objects distinctly which lie be\ond the far point. The myope's world of clear vision is limited to the distance of the far point, where the rays of light leaving his e}-e come to a focus. ICvery object situated beyond the far

Il6 REFRACTION AND HOW TO REFRACT.

point is blurred and indistinct, and the further the object from the far point, the more indistinct it becomes. The myopic child at school soon ranks high in the class, is fond of study, of books, music, or needlework, according to the sex. The myope, in other words, is usually literary in taste. Myopes avoid out-of-door sports, such as foot-ball, base-ball, golf, etc.

Diagnosis of Myopia. — This form of ametropia may be recognized in various ways :

1. The prominent eyeball. This is not a positive sign of myopia, though this and other signs are mentioned for the reason that they are often present in the myopic condition.

2. The broad face and (3) long interpupillary distance are quite significant of myopia, and yet the broadest face with longest interpupillary distance the writer ever saw was in a hyperopic subject.

4. Divergent squint usually indicates myopia, and this condition is often brought about by an inability to converge, or one eye may be more myopic than its fellow, with the result that the more myopic eye turns out and soon be- comes amblyopic.

5. It has been stated that myopic eyes usuall}- have dark-colored irises, but this is often a fallacy, as is onl)' too evident in the German student with his blue iris.

The foregoing are but signs of mj'opia, and are recog- nized by inspection ; they should be looked for and care- fully estimated, and each given its due consideration. Subjective and objective symptoms are the true tests of myopia, and are as follows :

6. Poor distant vision ; inabilit)- to see numbers on the liouses across the street or on the .same sitle of the street ; history of passing friends without speaking to them. The myope enjoys clo.se work and takes little or no interest in

MVOI'lA. I \y

sports. A history, in other words, that is in keeping with a vision of short range.

7. Good near visibn ; abihty to see the finest print or to thread the finest needle or do the finest embroidery.

8. The near point is closer than that of an emmetropic eye of corresponding age. (See p. 72.)

9. Distant vision is made worse by the addition of a convex lens. The writer prefers to teach the diagnosis of myopia in this way, and not to say that a concave lens will improve distant vision ; of course it will, but he does not want the student to put concave lenses before the eye of the young "pseudo-myope," referred to under Hyperopia.

10. The far point is brought nearer by the addition of a convex lens. Objective methods of determining myopia are by means of the —

11. Ophthalmoscope.

12. Retinoscope.

13. Scheiner's method.

14. Thomson's ametrometer.

15. Chromo-aberration test.

Direct Ophthalmoscopy in Axial Ametropia. — Pro- ficiency in this method only comes by perseverance and long practice. It should not be employed to the exclusion of other and more exact methods. To estimate with the ophthalmoscope which lens is required to give an eye emmetropic vision, three very important facts should receive careful attention :

1. The distance between the surgeon's and patient's eye.

2. The surgeon's and patient's accommodation.

3. The surgeon's own refractive error.

First, the surgeon should have his eye as close to the patient's eye as possible, usually at 13 mm. ; this is the

Il8 REFRACTION AND HOW JO KKFKACT.

anterior principal focus of the eye, and is the distance at which the patient will wear his glasses.

Second, as already explained, the observer's and patient's accommodation should be in repose. The most difficult part for the student to learn is to relax his accommoda- tion. The ambitious student strains his accommodation (ciliary muscle) in his haste, and with the result that he thinks all eyes myopic and all eye-grounds as affected with " retinitis."

T/iird, the surgeon, if not emmetropic, must wear any necessary correcting lenses ; otherwise, the lens in the ophthalmoscope will record his and the patient's error together, and deductions must be made accordingly. For instance, if the surgeon is hyperopic +2 S., and does not wear his glasses, and the ophthalmoscope records the fundus as seen clearly with -|- 5 S., this would mean that the paticMit had -I-3 S. (2 of the 5 S. being the surgeon's error); or if the fundus is seen without any lens in the ophthalmoscope, then the patient's error would be — 2 S. (the surgeon's + 2 S. from o leaving — 2 S.) ; or if the ophthalmoscope showed — 2 S., then the patient's error would be — 4S. ; or if the ophthalmoscope registered +2 S., then the patient would be emmetropic, and this +2 S. is the sur- geon's error.

Rules. — I. When the surgeon and patient are both h)-- peropic or both myopic, the surgeon must subtract his cor- rection from the lens which shows at the sight-hole in the ophthalmoscope.

2. Wiien the surgeon's c)^c is h)-peropic or myopic, and the eye of the patient is the opposite, he nuist aild his- cor- rection to the lens at the sight-hole in Ihe ophthalmoscoi)e.

With the foregoing details clearly in iniiul ami carefully executed, the surgeon selects small \es.scls near the macula

M\(>I'1A. I 19

for his observations. If it is impossible to sec these on account of the small pupil, then he will have to observe the lart^er vessels at the disc (nerve-head, or papilla).

Whenever the vessels in the macular re<^ion are seen clearly with one and the same glass in the ophthalmo- scope, the refractive error can be approximated as one of axial ametropia, and every three diopters, plus or minus, or any multiple of three diopters, represent very closely one millimeter of lengthening or shortening of the anteropos- terior diameter of the eye. For example, any eye that takes a plus 3 S. to make it emmetropic is just i mm. too short ; any eye that takes a minus 3 S. to make it emme- tropic is about I mm. too long. It will be observed, however, under the head of curvature ametropia (astigmatism), that every 6 D. cylinder represents about i mm. in length, as measured on the radius of curvature of the cornea. The following table, from Nettleship, gives the exact equiva- lents in millimeters for axial ametropia :

H I D. = o.3 mm. M i D. = o.3 mm.

2D. = o.5 " 3D.=:0.9 "

6D.= i.7S "

9D.= 2.6 "

I2D.= 3.5 " i8D.= s

Indirect Method. — Sec page 98 for a full description of this method. Slowl}' withdrawing the objective lens, and the disc remaining unchanged in size, signifies emmetropia ; if the disc grows uniformly smaller, it means H., and if it grows uniformly larger, it means M. (See Fig. 135.) This is merely a method of diagnosis, and is never used for definite measurements.

I D.

= 0.3

mm

2D.

= 0.5

3D-

= I

5D.

= 1.5

6D.

= 2

9D.

= 3

12 D.

= 4

CHAPTER V.

ASTIGMATISM, OR CURVATURE AMETRO- PIA.—TESTS FOR ASTIGMATISM.

Astigmatism (from the Greek, a, priv. ; ariyim, " a point"). — Optically, astigmatism may be defined as the re- fractive condition in which rays of light from a point, pass- ing through a lens or series of lenses, do not focus at a point.

In ophthalmology astigmatism is recognized as that con- dition of the refractive system of an eye in which rays of light are not refracted equally in all meridians, and the resulting image of a point becomes an oval, a line, or a circle. (See Fig. 93.)

Or astigmatism is that condition of an eye in wliich there are two principal meridians, of greatest and least ametropia, each having a different focus.

In the standard eye the cornea is represented as a section of a sphere ; anatomically, however, the cornea is generally found to be an ellipsoid of revolution, with its shortest radius of curvature (normally 7.8 mm.) in the vertical meridian.

In the study of astigmatism the meridians of minimum and maximum refraction alone are considered ; tlie\' are spoken of as the principal meridians, and are at right angles to each other.

With very few exceptions most eyes have some degree of astigmatism. The standard or emmetropic e\'e is an extremely rare condition, ant! plain m\-opic e\-es (long e\-es) witJiont 'M\y astigmatism arc almost as rare as the emmctrt^pic

120

ASTIGMATISM.

121

condition ; and while plain h}'peropic eyes are seen, yet statistics show that fully eighty per cent, of hyperopic eyes have astigmatism.

Astigmatism is located in the cornea or lens, or it may be a condition of both structures in one and the same eye. Astigmatism of the lens may increase, diminish, or neutral- ize the corneal astigmatism. Astigmatism, however, is more often a condition of the cornea than of the lens.

Figure 93 shows parallel rays of light passing through an astigmatic lens where the vertical meridian has the

Fig. 93.

shortest radius of curvature, with the result that those rays which pass through the vertical meridian V V come to a focus before those in the horizontal meridian H H', which has the longest radius.

Intercepting the refracted rays at I, 2, 3, 4, 5, and 6, the image would be at i a horizontal oval, at 2 a liorizontal line, at 3 a circle, at 4 a vertical oval, at 5 a vertical line, and at 6 a vertical oval. The space between the points of foci of the two meridians (2 and 5) is known as Sturm's interval. The importance of this space or interval is that

122 REFRACTION AND HOW TO REFRACT.

it represents astigmatism. Sturm's interval is the quantity which must be found in correcting astigmatism.

Causes of Astigmatism. — Most cases of astigmatism are congenital, and some can be traced to heredity. Ac- quired astigmatism may result from conic cornea, cicatrices following ulcers or wounds of the cornea, or be a tempo- rary condition from pressure of a chalazion or other growth ; and, in fact, astigmatism may develop from any disease or injury that will cause a lengthening or shortening or inequality in one or more of the meridians of the cornea or lens. Swelling of the different sectors of the lens will cause astigmatism. The visual line not passing through the center of the cornea is a cause of astigmatism, and astigmatism is the usual result following extraction of the lens. Tenotomy of one or more of the extraocular mus- cles will often change the corneal curvature.

Irregular Lenticular Astigmatism. — This is a normal condition of all clear lenses. It is often infinitesimal in amount, and on this account does not interfere with vision. It is caused by the different sectors of the lens or by the individual lens-fibers themselv^es not being uniform in their refracting power. In this form of astigmatism a light does not appear to have a distinct edge, but, on the contrary, the edge has radiations passing from it, giving the light a stellate appearance. There is no known glass that will correct this variety of astigmatism.

Physiologic Astigmatism. — This is due to lid pressure, or temporarily to extreme pulling or contraction of the extra- ocular muscles. It is a voluntary astigmatism, and therefore not constant. It is not a condition of all ej^es. The writer has demonstrated with the retinoscope and ophthalmometer that the condition can be produced in eyes not otherwise astigmatic. Drawing the lids together in the act of squint-

ASTIGMATISM. 1 23

ing or frowning, the patient can press the cornea from above and below, and give the horizontal meridian of the cornea a longer radius of curvature and the vertical meri- dian a shorter radius ; or with the eye looking into the telescope of the ophthalmometer, no overlapping of the mires is noted, but in some instances when told to open the eye widely and "stare" into the instrument, as much as y^ or 3/^ of a diopter of astigmatism may be recorded.

This "transient" astigmatism should never be corrected with a glass.

Subdivisions of Astigmatism. — In addition to the astigmatisms just described, curvature ametropia has been further considered as :

1. Irregular. 6. Astigmatism against the

2. Regular. rule.

3. Symmetric. 7. Homonymous.

4. Asymmetric. 8. Heteronymous.

5. Astigmatism with the 9. Homologous.

rule. 10. Heterologous.

1. Irregular Astigmatism. — This is usually located in the cornea, and is due primarily to some breach in the continuity of one or more of its meridians ; for example, the vertical meridian may appear regular, but the hori- zontal meridian is not a uniform curve, but is irregular at some point or points. Such meridians can not produce clear retinal images, but, on the contrar}-, the resulting retinal image is hazy or irregular.

2. Regular Astigmatism. ^In this variety the cornea and lens are regular in their curvatures, from the maximum to the minimum radius, and the retinal image can be made clear with correcting glasses.

Before entering upon the study of the various forms of refrular astigmatism, the student's attention is called to two

124 KKFKACTION AND HOW TO REFRACT.

important facts : (^7) That, as a rule, the shortest radius of curvature of the cornea is in the vertical meridian — that is to say, the vertical meridian has a stronger refracting power than the horizontal.

{b) The student should bear in mind that in the measure- ment of curvature ametropia each millimeter of lengthening or shortening of the radius of curvature is equivalent to a 6 D. cylinder. For instance, an eye which requires a -f 6 D. cylinder axis 90 degrees has the horizontal radius of curva- ture about one millimeter longer than the vertical radius ; or an eye that requires a — 6 D. cylinder axis 180 degrees has its vertical radius of curvature about one millimeter shorter than the horizontal. In cixuiii ametropia, however, it was shown that every three diopter sphere represented about one millimeter in length, as measured on the axis.

Varieties of Regular Astigmatism. — There arc five different forms of regular astigmatism : [a) Simple hyperopic. {c) Compound hyperopic.

{p) Simple myopic. {d) Compound myopic.

[e) Mixed astigmatism. {a) Simple Hyperopic Astigmatism. — Abbreviated As. H., or H. As., or Ah. About 5 '^ per cent, of eyes have

this form of refraction. This is a condition where one meridian of the eye is emmetropic, and the meridian at right angles to it is lu'peropic (see Fig. 94) ; the vertical meridian focuses parallel rays on the retina, and the horizontal meridian woiiUi focus back of it. The retinal image of a point is a line, usually horizontal. (See 2, in Fig. 93.) The correcting lens is a plus cylinder with its axis usually at 90 degrees,

ASTIGMATISM.

125

Fig. 95.

or within 45 degrees of 90 degrees. Example, -|-2.oo cylinder axis 90 degrees.

{/?) Simple Myopic Astigmatism. — Abbreviated As. M., or M. As., or Am. This is not a common condition. About I ^ per cent, of all eyes have this form of astigmatism. This is a condition where one meridian of the eye is emme- tropic, and the meridian at right angles to it is myopic (see Fig. 95) ; the horizontal meridian focuses parallel rays on the retina, and the vertical meridian focuses parallel rays in front of the retina (in the vitreous), with the result that they cross before reaching the retina. The retinal image of a point is a line, usually vertical. (See Fig. 93.) The correcting lens is a minus cylinder with its axis at 180 degrees, or within 45 degrees of 180 degrees. Example, — 2.50 cylinder axis 180 degrees.

[c) Compound Hyperopic Astigmatism. — Abbreviated H. As. Co., or Comp. Has., or H + Ah (hyperopia com- bined with astigmatism hyperopic). This condition repre- sents nearly fort)'-four per cent, of all eyes ; it is the most

common of all forms of re- fractions.

The retinal image of a point is an oval ; ne\-er a line and never a circle. (See i, in Fig. 93.)

The correcting lenses are a plus sphere and a plus cylin- ^ +3.00 cylinder axis 90 de- grees. Compound hyperopic astigmatism is a combination of axial ametropia (short eye) and simple hyperopic astig-

der.

¥u.. 96. E.xample, -|-2.oo S.

126 REFRACTION AND HOW TO REFRACT.

matism (curvature ametropia). In this form of astigmatism both meridians have their foci back of the retina — one further back than the other. The retina intercepts the ra)-s before they can focus. Figure 96 shows this condition. Usually the vertical meridian focuses nearer the retina than the horizontal.

(d) Compound Myopic Astigmatism. — Abbreviated M. As. Co., or Comp. Mas., or M.+Am. (myopia combined with astigmatism myopic). This is by far the most com- mon condition of all myopic eyes, and represents about eight per cent, of all eyes.

The retinal image of a point is always an oval ; never a line or a circle. (See 6, in Fig.

93-)

The correcting lenses are a minus sphere and a minus cylin- der. Example, — i sph. O — 2 cylinder axis 180 degrees. A combination of axial ametropia Fit;- 97- (long eye) and simple m}-opic

astigmatism. Figure 97 shows that parallel rays have two points of foci in front of the retina — one further front than the other.

(r) Mixed Astigmatism. — This form of refraction is found in about 6}4 per cent, of all eyes, and is abbreviated in three different waj's :

1. Ah + Am. (astigmatism hypcropic with astigmatism myopic).

2. H+Am. (h)'peroj)ia with astigmatism nu'opic).

3. M+Ah. (myopia with astigmatism hyperopic).

The retinal image of a point is an oval or a circle ; never a line. (See 3 and 4 in l-'ig. 93.)

ASTIGMATISM.

127

The correcting lenses are one of three combinations, and spoken of as crossed cyhnders. Examples :

1. -|-l.oo cyl. axis 90 degrees 3 — --^o cyl. axis 180 degrees.

2. -j-l S. 3 — 3 cyl. axis 180 degrees (cylinder always stronger than the sphere).

3. — 2 S. 3 +3 cyl. axis 90 degrees (cylinder always stronger than the sphere) .

The condition of mixed astigmatism is one of simple hyperopic astigmatism, with simple myopic astigmatism : one meridian focuses parallel rays in front of the retina and the other meridian (at right angles) focuses parallel rays

FiG. 98.

Fig. 99.

back of the retina. Figures 98 and 99 show this arrange- ment.

The remaining subdivisions of astigmatism are merely classifications of the different forms already described, and arise from a study of the axis of shortest radius of curva- ture.

3. Symmetric Astigmatism. — When the combined values, in degrees, of the meridians of shortest or longest radii of curvature in both ej-es equal 180 degrees (no more and no less), then the astigmatism in the two eyes is spoken of as symmetric. For example, if the cylinder in the right eye is at a.xis 75 degrees, and in the left eye at 105 de- grees ; 75 degrees and 105 degrees added together will

128

REFRACTION AND HOW TO REFRACT.

make i8o degrees. (See Fig. loo.) Or if each eye takes a cylinder axis at 90 degrees, they are also symmetric, 90 degrees and 90 degrees making 180 degrees. If both e)'es hav^e axes 180 degrees, they are symmetric also, one meridian being considered as zero (o).

4. Asymmetric astigmatism is the reverse of sym- metric, and is, therefore, the condition where the combined values, in degress, of the cylinder axes do not make 180 degrees. For instance, if the right eye has a cylinder at axis 75 degrees and the left at 120 degrees, then these

180 0

75' 90' 105

Fig. 100. — Illustrating Symmetric Astigmatism.

75 90

Fig. IOI. — Illustrating Asymmetric Astigmatism.

added together would not make 180 degrees, but more than 180 degrees. (See Fig. loi.) Or, if the astigmatism in the right eye was at 35 degrees, and the left at 90 degrees, then these added together would not make 180 degrees.

Symmetric astigmatism generally accompanies a regular physiognomy, the center of each pupil being at an equal distance from the median line of the face. Asymmetric astigmatism usually accompanies an as)-mmctric i)h\'siog- nomy, the center of one pupil being further from the median line of the face than the other.

ASTIGMATISM.

129

Muscular insufficiency, hereafter to be described, is much more common, and, in fact, should be looked for or antici- pated in cases of asynmietric astigmatism.

5 and 6. Astigmatism with the Rule and Astigmatism Against the Rule. — Astii^matism with the rule and asti<^- matisni against the rule refer to the condition already described as that in which the vertical meridian of the eye, as a general rule, has the shortest radius of curvature.

Statistic tables on astigmatism show that most eyes accept a plus cylinder at axis 90 degrees, or within 45

80° 0

Fig. 102. — Illustrating Astigmatism with the rule.

Fig. 103. — Illustrating Astigmatism against the Rule.

degrees (inclusive) either side of 90 degrees (see Fig. 102); or a minus cylinder at axis 180 degrees, or within 45 degrees (inclusi\'e) either side of 180 degrees. For example, if an eye requires a plus cylinder at 45 degrees, or at any axis from 45 degrees up to 135 degrees (inclu- sive), taking axis 90 as the median line, then the astig- matism is