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THE

REFRACTION

OP

THE EYE

A MANUAL FOB STUDENTS

BY

GUSTAVUS HARTRIDGE, F.R.C.S.

SENIOR SURGEON TO THE ROYAL WESTMINSTER OPHTHALMIC HOSPITAL

OPHTHALMIC SURGEON AND LECTURER ON OPHTHALMIC SURGERY TO

THE WESTMINSTER HOSPITAL ; CONSULTING OPHTHALMIC SURGEON

TO ST. Bartholomew's hospital, Chatham, and to st.
George's dispensary, hanoyer square, etc.

WITH ONE HUNDRED AND NINE ILLUSTRATIONS

FOURTEENTH EDITION



PHILADELPHIA
P. BLAKISTON^S SON & CO.

1012, WALNUT STEEET
1907



OPTO



First Edition, Jan., 1884



Second „





1886


Third


»


1888


Fourth „


Nov.,


1889


Fifth „


July,


1891


Sixth „


Oct.,


1892


Seventh „


Sept.,


1894


Eighth


June,


1896


Ninth „


Aug.,


1898


Tenth


March, 1900


Eleventh „


July,


1901


Twelfth „


Oct.,


1903


Thirteenth „


June,


1905


Fourteenth,,


Jan.,


1907



Total 28,000 copies.



PRINTED IN GREAT BRITAIN.



PREFACE QpTO



FOURTEENTH EDITION



#



In preparing tlie f ourteentli edition of ' Refraction
of the Eye ' for publication, tlie original plan of tlie
book has been maintained, and no effort has been
spared to make the work more worthy of the favour
with which it has been received in this country and
abroad.

Although but a short time has elapsed since the
last edition of 3000 was published, the book has
been carefully revised, and alterations made in
accordance with our increasing knowledge of the
subject.

a. H.

12, WiMPOLE Street, W.
January, 1907.



PREFACE



FIRST EDITION



I HAVE endeavoured in the. following pages to state
"briefly and clearly the main facts with which practi-
tioners and students should be acquainted, in order
to enable them to diagnose errors of refraction accu-
rately, and to prescribe suitable glasses for their
correction.

Those who would do this with facility can only
acquire the requisite amount of dexterity by prac-
tically working out a large number of cases of refrac-
tion. No book, or even the knowledge gained by
watching others who are thus employed, can take the
place of this, the practical part of the subject.

To many of my readers the chapter on Optics may
appear unnecessary. I have added it for the benefit
of those whose school education did not include this
subject, since its elementary details so completely
underlie the whole subject of refraction, that every



VI PREFACE

student should understand tliem thoroughly before
passing on to the real subject in hand.

I have found it necessary in several instances to
repeat important matters, and this I have done to
obviate the necessity of continual reference to other
parts of the book, as well as in some cases to impress
the importance of the subject upon the student.

The woodcuts are numerous in proportion to the
size of the work, but I consider that they are a very
great help to the thorough understanding of the
subject.

The old measurements have been purposely omitted
in favour of the almost universally adopted metrical
system. It is confusing to the learner to have two
distinct sets of measurements to deal with, and no
possible good can accrue from perpetuating the old
system of feet a.nd inches.

At the end of the work I have given a list of those
authors to whom I have been indebted for much
valuable information ; and in conclusion, I take this
opportunity of thanking my numerous friends for
their help and suggestions.

G. H.

January, 1884.



CONTENTS



CHAPTER I

PAGE

Optics . . . ... .1

Reflection . . . . .2

Refraction . . . . .6

Formation of Images . . . .17



CHAPTER II

Refraction of the Eye . . . .22

Accommodation . . . .32

Convergence . . . . .41



CHAPTER III

Methods of Determining the Refraction . 53

Acuteness of Yision . . . .55

Sclieiner's Method . . . .64



CHAPTER lY

The Ophthalmoscope . . . .66

The Indirect Method . . . .66

The Direct Method . . . .73



Vlll CONTENTS



CHAPTER Y

PAGE

Retinoscopy . . . . .82



CHAPTER YI

Hypermetropia ..... 117
Aphakia ...... 132



CHAPTER YII
Myopia ...... 134

CHAPTER YIII

Astigmatism ..... 156
Anisometropia ..... 184

CHAPTER IX

Presbyopia . - . . . . 187

Paralysis of the Accommodation . . . 196

Spasm of the Accommodation . . .197

CHAPTER X
Strabismus ..... 200



CONTENTS IX



CHAPTER XI

PAGE

Asthenopia . - . . . . 224

Accommodative .... 226

Muscular ..... 228

Eetinal ..... 234



CHAPTER XII

Spectacles ..... 237

Cases . . . . . . 244

Appendix ..... 259

Regulations fok Army, Navy, &c. . . 261

Test Types ..... 265



LIST OF ILLUSTRATIONS



No.

1. Eeflection by a plane surface

2. Virtual image formed by a plane mirror

3. Reflection by a concave surface

4. Ditto ditto

5. Eeflection by a convex surface

6. Eefraction by a plane surface

7. Eefraction by a prism

8. Ditto ditto .

9. Eefraction by a spherical surface

10. Ditto ditto

11. Formation of convex lenses .

12. Different forms of lenses

13. Eefraction of rays (secondary axes) by a convex lens

14. Eefraction of parallel rays by a convex lens

15. Ditto ditto

16. Properties of a biconvex lens

17. Ditto ditto

18. Properties of a biconcave lens

19. Eefraction of parallel rays by a concave lens

20. Formation of an inverted image

21. Eeal inverted image formed by a convex lens .

22. Virtual image formed by a convex lens

23. Virtual image formed by a concave lens

24. Diagram of eye showing the cardinal points

25. Formation of inverted image on the retina

26. Emmetropic, hypermetropic, and myopic eyeballs

27. Eye represented by a biconvex lens .

28. Formation of visual angle .

29. Diagram of accommodation .

30. Scheiner's method of finding the punctum proximum

31. Amovint of accommodation at different ages

32. Diagram representing the convergence

33. Landolt's ophthalmo-dynamometer

34. Diagi-am of the relative accommodation

35. Angle subtended at nodal point by test type .



LIST OF ILLUSTEATIONS XI

No. PAGE

36. Sclieiner's method ....

37. Image formed in emmetropia by the indirect ophthalmo

seopic method ....

38. Image formed in hypermetropia

39. Image formed in myopia ...

40. Size of the image in emmetropia for different distances

of the objective ....
41 & 42. Decrease of the image in hypermetropia on with
drawing the objective

43. Image formed in emmetropia

44. Image formed in hypermetropia

45. Image formed in myopia

46. Direct ophthalmoscopic examination in emmetropia

47. Estimation of hypermetropia by the ophthahnoscope

48. Estimation of myopia by the ophthalmoscope .

49. Kays coming from the hypermetropic eye

50. Eays coming from the myopic eye

51. Position of light for retinoscopy

52. Light with diaphragm

53. Plane mirror

54. Shadows in retinoscopy

55. Eetinoscopy with the plane mirror

56. Image formed in myopia

57. Image formed in hypermetropia

58. Oblique shadows in astigmatism

59. Cause of oblique shadows

60. Band-like shadows .

61. Band-like shadows .

62. Eecording the astigmatism .

63. Retinoscopy with the concave mirror

64. Shadows with the concave mirror

65. Movements of the shadow with the concave mirror

66. Refraction of a hypermetropic eye

67. Refraction increased by changes in the lens

68. Correction by a biconvex lens

69. Accommodation at different ages in hypermetrope of 3 D

70. Refraction of a myopic eye .

71. Ditto ditto

72. Correction by a biconcave lens



Xll LIST OF ILLUSTEATIONS

No. PAGE

73. Section of a myopic eyeball . . . 139

74. Accommodation at different ages in a myope of 2 D. . 140

75. Size of retinal image in myopia . . . 145

76. Section of cone of light after passing through an astig-

matic cornea. . . . . .159

77. Diffusion patches when the cone is divided at right

angles . , „ . . . . 159

78. Interval of Sturm ^ . . . . 160

79. Simple hypermetropic astigmatism . . . 161

80. Compound hypermetropic astigmatism . . 162

81. Simple myopic astigmatism ... 162

82. Compound myopic astigmatism . . . . 162

83. Mixed astigmatism . . . . 163

84. Astigmatic clock face .... 170

85. Astigmatic fan ..... 171

86. Erect image of a disc seen through an astigmatic cornea. 172

87. Same disc seen by the indirect method . . 172

88. Tweedy's optometer .... 179

89. Diagram of the accommodation . . .188

90. Angle a in emmetropia .... 201

91. Angle a in hypermetropia . . .. . 202

92. Angle a in myopia .... 202

93. Diagram of primary and secondary deviation . . 204

94. Strabismometer ..... 206

95. Method of measuring the angle of the strabismus . 208

96. Diagram representing convergent strabismus . . 210

97. Diagram representing divergent strabismus . . 216

98. Worth's amblyoscope .... 220

99. Stereoscopic slide ..... 222

100. Graefe's test for insufficiency of internal recti miiscles . 232

101. Scale for testing latent deviation at the reading distance. 233

102. Convex and concave glasses acting as prisms . . 234

103. Bifocal lens . . . . .241

104. Bifocal lens . . . . .241

105. Invisible bifocal lens .... 242



Lithographic Plate opposite page 147 ;

1, 2, and 3. Drawn from myopic patients.
4. Copied from Atlas of Wecker and Jaeger.
Test types .... 168, 265



THE REFEACTION OF THE EYE



CHAPTER I

OPTICS

Light is propagated from a luminous point in every
plane and in every direction in straight lines ; these
lines of directions are called rays. Rays travel with
the same rapidity so long as they remain in the same
medium.

The denser the medium^ the less rapidly does the
ray of light pass through it.

Rays of light diverge, and the amount of diverg-
ence is proportionate to the distance of the point
from which they come ; the nearer the source of the
rays, the more they diverge.

When rays proceed from a distant point such as the
sun, it is impossible to show that they are not parallel ;
and in dealing with rays which enter the eye, it will
be sufficiently accurate to assume them to be parallel
when they proceed from a point at a greater distance
than 6 metres.

A ray of light meeting with a body may be absorbed,

1



2 THE REPEACTION OF THE EYE

reflected, or if it is able to pass through this body it
may be refracted.

Reflection

Reflection hy a Plane Surface

Reflection takes place from any polished surface,
and according to two laws.

1st. The angle of reflection is equal to the angle
of incidence.

2nd. The reflected and incident rays are both in
the same plane, which is perpendicular to the reflect-
ing surface.

Fig. 1.




Thus, if A B be the ray incident at b, on the mirror
c D, and B E be the ray reflected, the perpendicular
p B will divide the angle a b e into two equal parts,
the angle a b p is equal to the angle p b e ; while
A B, p B, and e b lie in the same plane.

When reflection takes place from a plane surface,
the image is projected backwards to a distance behind
the mirror equal to the distance of the object in front
of it, the image being of the same size as the object.

Thus in Fig. 2 the image of the candle c is formed
behind the mirror m, at &, a distance behind the



REFLECTION



mirror equal to the distance of the candle in front of
it; an observer's eye placed at e would receive the
rays from c as if they came from c\



Fig. 2.




M. The mirror, c. The candle, c'. The virtual image of the candle.
E. The eye of the observer receiving rays from the mirror.

The image of the candle so formed by a plane mirror
is called a virhial image. ^

Reflection hy a Concave Surface
A concave surface may be looked upon as made up
of a number of planes inclined to each other.

Parallel rays falling on a concave mirror are re-
flected as convergent rays^ which meet on the axis at
a point (f, Fig. 3) called the priiicipal focus, midway
between the mirror and its optical centre c. The dis-
tance of the principal focus from the mirror is called
the focal length of the mirror.



4 THE REFRACTION OF THE EYE

If the luminous point be situated at f, then the
diverging rays would be reflected as parallel to each
other and to the axis.

If the luminous point is at the centre of the con-
cavity of the mirror (c), the rays return along the
same lines, so that the point is its own image.

If the luminous point be at a the focus will be at a,

Fig. 3.




and it is obvious that if the luminous point be moved
to a, its focus will be at a; these two points therefore,
A and a, bear a reciprocal relation to each other, and
are called conjugate foci.

If the luminous point is beyond the centre, its con-
jugate focus is between the principal focus and the
centre.

If the luminous point is betAveen the principal focus
and the centre, then its conjugate is beyond the
centre ; so that the nearer the luminous point ap-
proaches the principal focus, the greater is the dis-
tance at which the reflected rays meet.

If the luminous point be nearer the mirror than the



EEFLECTION 5

principal focus (f), the rays will be reflected as diver-
gent, and will therefore never meet : if, however, we
continue these diverging rays backwards, they will
unite at a point (h) behind the mirror ; this point is
called the virtual focus, and an observer situated in

Fig. 4.




the path of reflected rays will receive them as if they
came from this point.

Thus it follows that —

Concave mirrors produce two kinds of images or
none at all, according to the distance of the object, as
may be seen by looking at one^s self in a concave mirror.
If the mirror is placed nearer than its principal focus,
then one sees an enlarged virtual image, which in-
creases slightly in size as the concave mirror is made
to recede; this image becomes confused and disap-
pears as the principal focus of the mirror is reached :
on moving the mirror still farther away (that is be-
yond its focus) one obtains an enlarged inverted
image, which diminishes as the mirror is still further
withdrawn.



b THE REFRACTION OF THE EYE

Reflection hy a Convex Surface
Parallel rays falling on a convex surface are reflected
as divergent, hence never meet ; but if tlie diverging
rays thus formed are carried backwards by lines,
then an imaginary image is formed Avhich is called
negative, and at a point called the principal focus (r).
Foci of convex mirrors are therefore virtual; and
the image, whatever the position of the object, is
always virtual, erect, and smaller than the object.

Fia. 5.




The radius of the mirror is double the principal
focus.

Refraction

Refraction hy a Plane Surface

A ray of light passing through a transparent me-
dium into another of a different density is refracted,
unless the ray fall perpendicular to the surface sepa-
rating the two media, when it continues its course
without undergoing any refraction (Fig. G, H k).



REFRACTION



A ray is called incident before entering the second
medium, emergent after leaving it.

A ray passing from a rarer to a denser medium is
refracted towards the perpendicular; as shown in
Fig. 6, the ray A b is refracted at b, towards the per-
pendicular p p.

In passing from the denser to the rarer medium
the ray is refracted from the perpendicular; b d is
refracted at c, from p p (Fig. 6).

Fig. 6.




Keflection accompanies refraction, the ray dividing
itself at the point of incidence into a refracted portion
B c, and a reflected portion b e.

The amount of refraction is the same for any
medium at the same obliquity, and is called the index
of refraction; air is taken as the standard, and is
called 1 ; the index of refraction of water is 1*3, that
of glass 1*5. The diamond has almost the highest
refractive power of any transparent substance, and



8 THE REFRACTION OP THE EYE

has an index of refraction of 2'4. The cornea has an
index of refraction of 1"3^ and the lens 1*4.

The refractive power of a transparent substance is
not always in proportion to its density.

If the sides of the medium are parallel_, then all
rays except those perpendicular to the surface which
pass through without altering their course are re-
fracted twice, as at b and c (Fig. 6), and continue in
the same direction after passing through the medium
as they had before entering it.

If the two sides of the refracting medium are not
parallel, as in a prism, the rays cannot be perpen-
dicular to more than one surface at a time.

Therefore every ray falling on a prism must un-
dergo refraction, and the deviation is always towards
the base of the prism.

The relative direction of the rays is unaltered
(Fig. 7).

Fig. 7. Fia. 8.




If D M (Fig. 8) be a ray falling on a prism (a b c) at
M, it is bent towards the base of the prism, assuming
the direction m n; on emergence it is again bent at n;
an observer placed at e would receive the ray as if it
came from k; the angle k h d formed by the two lines



REFEACTION 9

at H is called the angle of deviation, and is about half
the size of the 'principal angle formed at A by the two
sides of the prism.

Refraction by a Spherical Surface.

Parallel rays passing through a spherical surface
separating media of different density do not continue
parallel^ but are refracted, so that they meet at a
point called the principal focus.

If parallel rays k, d, e, fall on A b, a spherical sur-
face separating the media m and n of which n is the
denser; ray d, which strikes the surface of a b at right
angles, passes through without refraction, and is called
the principal axis ; ray K will strike the surface at an
angle, and will therefore be refracted towards the
perpendicular c J, meeting the ray d at P; so also with
ray E, and all rays parallel in medium m. The point
F where these rays meet is the principal focus, and the
Fig. 9.




distance between the principal focus and the curved
surface is spoken of as the principal focal distance.
Rays proceeding from f will be parallel in m after



10 THE EP]FRACT10N OF THE EYE

passing througli the refracting surface. Rays parallel
in medium n will focus at f', which is called the ante-
rior focus.

Had the rays in medium m been more or less diver-
gent^ they would focus on the principal axis at a
greater distance than the principal focus, say at H;
and conversely rays coming from h would focus at G;
these two points are then conjugate foci.

When the divergent rays focus at a point on the
axis twice the distance of the principal focus, then its
conjugate will be at an equal distance on the other
side of the curved surface.

If rays proceed from a point o, nearer the surface
than its principal focus, they will still be divergent
after passing through A b, though less so than before,
and will therefore never meet; by continuing these

Fig. 10.




rays backwards they will meet at L, so that the conju-
gate focus of o will be at l, on the same side as the
focus; and the conjugate focus will in this case be
spoken of as negative.



U



LENSES 11

Refraction hy Lenses

Refraction by lenses is somewhat more complicated.

A lens is an optical contrivance usually made of
glass, and consists of a refracting medium with two
opposite surfaces, one or both of which may be seg-
ments of a sphere; they are then called spherical
lenseSj of which there are six varieties.

Fig. 11.




1. Plano-convex, the segment of one sphere (Fig.

11, B).

2. Biconvex, segments of two spheres (Fig. 11, a).

3. Converging concavo-convex, also called a con-
verging meniscus.

4. Plano-concave.

5. Biconcave.

6. Diverging concavo-convex, called also a diverg-
ing meniscus.

Lenses may be looked upon as made up of a number
of prisms with different refracting angles — convex
lenses, of prisms placed with their bases together;
concave lenses, of prisms with their edges together.

A ray passing from a less refracting medium (as



12 THE EEFEACTION OP THE EYE

air) througli a lens_, is deviated towards the thickest
part, therefore the first three lenses, which are thickest
at the centre, are called converging ; and the others,
which are thickest at the borders, diverging.

Fig. 12.




A line passing through the centre of the lens
(called the optical centre), at right angles to the sur-
faces of the lens, is termed the principal axis, and any
ray passing through that axis is not refracted.

All other rays undergo more or less refraction.

Rays passing through the optical centre of a lens,
but not through the principal axis, suffer slight devia-
tion, but emerge in the same direction as they entered.
These are called secondary axes (Fig. ]3). The
deviation in thin lenses is so slight that they are
usually assumed to pass through in a straight line.

Parallel rays falling on a biconvex lens are ren-
dered convergent ; thus in Fig. 14 the rays A, B, c,
strike the surface of the lens (l) at the points d, e, f;
the centre ray (b) falls on the lens at e perpendicular
to its surface, and therefore passes through in a
straight line ; it also emerges from the lens at right



BICONVEX LENSES 13

angles to its opposite surface^ and so continues its
course without deviation ; but the ray a strikes the
surface of the lens obliquely at d, and as the ray is
passing from one medium (air) to another (glass)
Fig. 13.




Lens with secondaryaxes undergoing slight deviation.

which is of greater density, it is bent towards the
perpendicular of the surface of the lens^ shown by the
dotted line m k ; the ray after deviation passes through
the lenSj striking its opposite surface obliquely at o,

Fig. 14.




and as it leaves the lens^ enters the rarer medium
(air), being deflected from the perpendicular n o ; it



14 THE REFRACTION OF THE EYE

is now directed to h^ where it meets the central ray
B H ; ray c^ after undergoing similar refractions, meets
the other rays at h, and so also all parallel rays falling
on the biconvex lens (l).

Parallel rays, therefore, passing through a convex
lens (l) are brought to a focus at a certain fixed point

Fig. 15.




(a) beyond the lens; this point is the ^principal focus,
and the distance of this focus from the lens is called
the focal length of the lens.

Rays from a luminous point placed at the principal
focus (a) emerge as parallel after passing through the
lens.

Divergent rays from a point (b) outside the princi-
pal focus (f, Fig. 16) meet at a distance beyond (f')
the principal focus on the other side of the lens (l),
and if the distance of the luminous point (b) is equal
to twice the focal length of the lens, the rays will focus
at a point (c) the same distance on the opposite side
of the lens ; rays coming from c would also focus at
B : they are therefore called conjugate foci, for we
can indifferently replace the image (c) by the object
(b), and the object (b) by the image (c).



BICONVEX LENSES 15

If the luminous point (d) be between the lens and
the principal focus (p), then the rays will issue from
the lens divergent^ though less so than before enter-
ing it ; and if we prolong them backwards they will

Fig. 16.




meet at a point (h) further from the lens than the
point D ; H will therefore be the virtual focus of d, and
the conjugate focus of d may be spoken of as negative.

Biconvex lenses have therefore two principal foci,
r and f'^ one on either side^ at an equal distance from
the centre.

In ordinary lenses^ and those in which the radii of
the two surfaces are nearly equal^ the principal focus
closely coincides with the centre of curvature.

We have assumed the luminous point to be situated
on the principal axis; supposing, however, it be to one
side of it as at e (Fig. 17), then the line (e f) passing
through the optical centre (c) of the lens (l) is a
secondary axis, and the focus of the point e will be
found somewhere on this line, say at f, so that what
has been said respecting the focus of a luminous point
on the principal axis (a b) is equally true for points
on a secondary axis, provided ahvays that the inclina-



16 THE REFRACTION OF THE EYE

tion of this secondary axis is not too great, when
the focus will become imperfect on account of the
spherical aberration which will be produced.

Fig. 17.




In biconcave lenses the foci are always virtual,
whatever the distance of the object.

Rays of light parallel to the axis diverge after
refraction, and if their direction be continued back-
ward they will meet at a point termed the principal
focus (Fig. 18, f).

Fig. 18.




Fig. 19 shows the refraction of parallel rays by a
biconcave lens (l) ; the centre ray B strikes the lens
at E perpendicular to its surface, passing through
without refraction, and as it emerges from the oppo-


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