The errors of accommodation and refraction of the eye and their treatment; a handbook for students

Front matter

ERRORS Ol

ACCOMMODATION AND REFRACTION

CLARKE r\ i:

Preface To The Fourth Edition

The first edition of this work was published fifteen years ago based on lectures delivered at the Central London Ophthalmic Hospital and the Medical Graduates' College . I have not altered its character, which is essentially practical, all matter unnecessary for the busy practitioner or overburdened student being omitted.

The whole work has been thoroughly revised and brought up to date, many chapters having been rewritten.

The subject of Eyestrain still occupies the prominent place that is its due.

ERNEST CLARKE.

Chandos Street,

Cavendish Square, W.

February, 191 8.

Contents

CHAPTER PAGE

I. REFRACTION PRISMS LENSES - - - I

II. OPTICAL PROPERTIES OF THE NORMAL EYE - "19

Chapter I Refraction— Prisms— Lenses

Light is propagated in straight lines which diverge from any luminous point in all directions, and these lines of direction are called " luminous rays." The propagation is produced by ether waves which are across the path of light. The velocity of light is, in round numbers, 186,000 miles per second, and is appreciably retarded in passing through a denser medium. Rays of light entering the eye coming from any luminous point at a greater distance than 6 metres may be assumed, for all practical purposes, to be parallel.

Light is absorbed, refracted, or reflected.

Refraction of Light. — A ray of light passing from a rarer into a denser transparent medium, if it be perpendicular to the surface, and the boundaries of the medium be parallel, will pass out of the denser medium in the same straight line (Fig. i, l), the only effect upon it being a retardation. If the ray enter the denser medium other than perpendicularly, or if the boundaries of the medium be not parallel, the ray is bent or refracted.

A simple illustration will explain this.

Explanation of Refraction. — i\s ether waves are at right angles to the path of light, if a beam of light enter

2 TH£ RtFRACTION OF TH£ EYE

a denser medium obliquely, one end of the wave will enter the denser meditim before the other, and consequently be retarded earlier. Let A, B, c, d (Fig. i), be a denser medium, with parallel boundaries, and n, o, p, q, the beam of light.

The wave front will reach Q before it reaches R, and it will at once be retarded ; and as it thus travels more slowly from Q to s than from p to R (which is outside the denser medium), the beam must be swung round so that it is bent or refracted on entering the denser medium.

Fig. I

Across the denser medium the whole wave front is equally affected, so that the beam passes across in a straight line ; and if the sides of the medium be parallel the converse happens, and it is again bent on passing out, the incident and the emergent rays being parallel.

Let this be applied to the case of, for example, a prism where the sides of the denser medium are not parallel. Suppose A, B, c (Fig. 2), to be a triangular strip of velvet pasted on a smooth board, and suppose d to be two small wheels connected by an axle in such a way that each wheel can turn independently of the other. Roll

REFRACTION 3

the wheels up to the velvet triangle; the lower or right wheel will pass on to the velvet at e before the left wheel reaches it, and as the velvet will retard its progress, it will turn now more slowly than the left wheel, so that the pair of wheels will be slewed round towards the base of the triangle. When the left wheel enters on the velvet at /, its progress will be the same as that of the other wheel, and the pair of wheels will cross the velvet now in a straight line ; when it reaches w, the left or upper wheel will leave the velvet earlier, and will consequently travel more rapidly, and will again swing the pair round, so

Fig. 2.

that in the transit across the triangle the pair of wheels have been bent towards the base.

It is in this manner that light behaves; in passing through a prism, it is bent or refracted towards the base. *W|

A ray of light passing obliquely from a less dense into a denser transparent medium is refracted or bent towards the perpendicular, and when passing from a dense to a less dense medium is refracted away from the perpendicular.

Index of Refraction. — The index of refraction of a transparent substance is the number that denotes the refractive power of such substance compared with air, which is taken as the unit i. In Fig. 3, let A c be the incident ray meeting the horizontal surface of water at c, and forming with p p', the perpendicular, an angle A c P ; and let c b be the refracted ray in water bent towards the perpendicular, and forming the angle B c p'.

v^

/O c

W k

Fig. 3.

The sine l m is to the sine n o as 4 to 3, expressed as I, or 1*33, and this is the index of refraction of water.

The following are a few of the indices of refraction useful to the ophthalmologist :

Air . .

I'O

Water

1*33

Cornea

1*33

Aqueous humour

1-3379

Vitreous humour

1-3379

Crystalline lens

1-4

Crown glass

1-5

PRISMS 5

Prisms. — An ophthalmic prism is a wedge-shaped piece of glass having two of its sides, or plane surfaces, intersecting each other at the apex, and separated at the base, which is the thickest part of the prism.

We have already seen that a ray of light entering one of the sides of a prism is refracted or bent towards the base, and the amount of this refraction depends upon —

I. The strength of the prism.

|2. The refractive index of the prism substance.

3. The position at which the light enters the prism.

The Strength of the Prism — The Numbering of Prisms. — ^The power of a prism to deflect or refract light depends on the size of the angle at the apex formed by

Fig.

the two plane surfaces. This is called the refracting angle, and is written with the sign of a degree after the numeral — thus : 4° — which is scratched on the surface of the glass. This is the old, and even up to the present very general, method of numbering prisms.

Maddox has suggested the word " prismetry " to denote the numbering by the deviating angle.

IThe Deviating Angle of a Prism. — In Fig. 4, if a ray, p, enter the prism, instead of passing out at p', it is refracted towards

O THE REFRACTION OF THE EYE

the base b c, and away from the angle b a c, and is again bent towards the base on passing out, and emerges in the direction / (see page 3). The angle p' o f, made by the backward prolongation of / and the forward prolongation of p, is the angle of deviation, and it is equal to about half the angle of refraction.

To indicate that the angle of deviation is implied, a small d is added; thus, prism 4° is approximately equal to prism 2° d.

Angle of Refraction. Angl* of Deviation.

1° 32'

5° 2° 42'

10° 5° 26'

As the metrical system is now universally adopted in ophthalmology. Prentice has suggested the numbering of prisms on the metrical plan, and the prism dioptre is the unit, designated by the sign A after the numeral.

A prism of the strength of i P.D. (i A) is a prism that, at a distance of i metre, apparently displaces an object i centimetre. In Fig. 5, E, being the observer, sees o at o' apparently displaced* i centimetre, the distance between o and the prism

Fig.

b?ing I metre, and the prism i A ; that is, the apparent displacement of an object looked at through a prism is i per cent, of the distance of the prism from the object, multiplied by the prism dioptre.

A prism i A apparently displaces an object 3 metres off, 3 centimetres, and a prism 3 A displaces an object 2 metres off, 6 centimetres, and so on.

Dennett has suggested the centrad as the unit for numbering prisms. The centrad is the hundredth part of a radian, a radian being the angle subtended at the centre of a circle by an arc, which is equal in length to the radius. A prism i centrad, designated i v. deviates a ray of light one-hundredth part of the arc of the radian.

It is interesting to note that the centrad has a relative value to the metre angle, in that half the number of centimetres between the pupils indicates the number of centrads in the metre angle.

This method is not much used, although probably the most scientific.

* Note that the apparent displacement of an object viewed through a prism is always towards the apex.

PRISMS 7

All three methods of numbering prisms are practically identical for weak prisms, and, as it is only weak prisms that an ophthalmologist can use, it matters little what method he adopts.

Table showing the Equivalence of Centrads, Prism Dioptres, and Refracting Angle, of the Six Weakest Prisms. (Index of Refraction, 1*54.)

Centrad. Prism Dioptre. Refracting Angle.

1 I I*

4 4*0028 4*23°

5 5-0045 5-28°

6 6*0063 6*32°

The minimum of deviation occurs when the incident ray crosses the prism parallel to its base; but in thin prisms — and it is thin prisms only that the ophthalmologist uses — this has no practical importance. Hence we can neglect the position of the incident ray.

The Uses of Prisms.—

1. To remove diplopia.

2. To ease the muscles, and so prevent muscle

strain and subsequent diplopia (see page 176) .

3. To exercise weak muscles (see page 182).

4. To test the strength of the external ocular

muscles.

5. To detect malingerers (see page 183).

In trial cases the prisms are usually cut circular, so that they can be used in a trial frame ; the exact position of the base of the prism is usually marked by a line on the glass at right angles to the base.

Rotating Prisms. — If two prisms of equal strength be placed in apposition in such a manner that the base of the one is in contact with the apex of the other, they neutralize each other, and if we rotate them in opposite directions we obtain the effect of an increasingly strong prism.

Risley's Rotary Prism (Fig. 6) is made on this principle. If we place it in one side of a trial frame, both eyes being used, start from zero and gradually turn the button, we can ascertain the strongest prism the eyes can stand without having diplopia, or, if we are deaUng with a case of diplopia, we can ascertain the weakest prism that will procure " fusion " vision.

Fig. 6.

The numbers on the frame indicate the refracting angle in degrees. The instrument can give a total prismatic power of 30°.

i fisms form no images and have no foci.

Fig. 7.

Lenses. — If two prisms are placed with their bases in contact, we have roughly a bi-convex lens (Fig. 7, a), and rays of light passing through it are bent towards the base of the prisms — i.e., the centre of the lens; in other words, they converge. If the prisms have their

LENSES apices in contact, we have a bi-concave lens (Fig. 7, b), and the rays]are]bent towards the bases — i.e., outwards — and diverge.

Spherical Lenses. — Besides the bi-convex (Fig. 7, a) and bi-concave lenses (b), there are plano-convex (c),

Fig.

plano-concave (d), converging concavo-convex or converging meniscus (e), and diverging concavo-convex or diverging meniscus (f). Rays of light passing obliquely through any of these forms of lenses are refracted or bent towards the thickest part of the lens.

Fig. 9.

The principal axis is a line drawn through the optical centre at right angles to the lens (Fig. 8, A o), and rays passing through this are not refracted; all other lines passing through the optical centre not at right angles to the lens are called " secondary axes " (Fig. 9, a '«).

Rays passing along the secondary axes are refracted.

but as the emergent and the incident rays are in the same direction, and the refraction in low-power lenses is very slight, the refraction can be ignored, and the rays assumed to pass along in a straight line.

Convex Lenses. — Parallel rays passing through a convex lens unite on the opposite side of the lens at a point called the " principal focus " (Fig. 8, p f).

At the principal focus an inverted real image of the object is formed. Let a b (Fig. 9) be an object at some considerable distance from the lens. Any ray passing from the point a through the optical centre of the lens c will be unrefracted {vide supra), and the image of a will be somewhere on this line on the other side of the lens

— let it be at ^; all other rays passing from A will be refracted on passing through the lens, and will focus at a. In the same manner an image of B is formed at b, and all other points between A and B will form an image between a and b, so that we get an inverted image a b oi a b formed at the principal focus of the lens.

The distance between the principal focus and the optical centre is called the " principal focal distance " ; it is positive, and convex lenses are known by the plus sign : + .

Rays passing from the principal focus (p f) through the lens emerge as parallel rays on the opposite side (Fig. 8).

Divergent rays from a point l (Fig. 10) beyond the principal focus f meet at a point / beyond the principal

LENSES II

focus f' on the other side of the lens. If the point L is twice the focal distance of the lens, then / will be at the same distance on the other side. These two points are called " conjugate foci," and are interchangeable; that is, the object may be at l or /, and the image is respectively at / or L.

If a luminous point be between the convex lens and the principal focus, the rays will still be divergent when they leave the lens on the opposite side, and consequently no real image is formed; but a magnified virtual image is formed beyond the principal focus on the same side, at a point called the " virtual focus," and this virtual image

Fig. II.

is seen by an observer on the opposite side of the lens, the light from the points a and h appearing to thr^ observer to come from a' and h' (Fig. ii).

Concave Lenses. — Parallel rays passing through a concave lens diverge, and consequently never come to a focus ; but these divergent rays, if prolonged backwards, will meet at a point f (Fig. 12).

This point is the (virtual) principal focus of a concave lens.

If an object be placed beyond the principal focus of a concave lens, an observer on the opposite side of the lens will see a virtual, erect, smaller image on the same side as the object; thus, rays from a and h will appear to come from a' and h' , and the object « 6 is seen as a' h' (Fig. 13). As concave lenses have a negative focal distance, they are denoted by the minus sign:]-.

Cylindrical Lenses.— In addition to spherical lenses cyhndrical lenses are required — these are lenses cut out of a cylinder; convex cylinders are cut from a solid cylinder (Fig. 14, a), concave cylinders from a hollow cylinder (Fig. 14, h), which may be regarded as the mould of convex cylinders. Cylinders have the property of not

I refracting any rays that pass along their axis, but rays passing at right angles to the axis undergo the maximum refraction corresponding to the strength of the lens. According to the angle at which the rays impinge upon the lens, they undergo more or less refraction, as this

LENSES angle is further away from, or nearer to, the axis of the cyUnder. A cylinder has no one focal point, but a line of foci parallel to its axis.

Cylindrical lenses are employed to correct regular astigmatism.

The axis of a cylindrical test lens is marked by a small line on the glass, or by making the sides of the lens, parallel to the axis, opaque.

Numeration of Lenses. — The lens whose focal distance is I metre is taken as a unit, and its refractive power is called one Dioptry or Dioptre (" d "). A lens of twice the power of this — viz., 2 d — has a focal distance of ^-; i.e., 50 cms.; a lens of half the power — viz., •5 D — has a focal length of 2 metres, and so on. The

focal distance of a lens no = '

n

Under the old system, a lens whose focal distance was I inch was taken as the unit, and a lens whose focal length was 10 inches was called jV* 3^ inches ^, and so on. The great disadvantage of this method of numeration was the inability to make it international, because the inch is not an international measure.

To convert the old numeration into the new, divide the denominator into 40; thus, lens \ is V-==S d, and vice versa, Jo convert dioptres into inches, divide the dioptre into 40, and the result is the focal length in inches; thus, 4 D = -*3^= 10 inches focal length, expressed as to-

The following table shows at a glance the approximate equivalent of the old and new numeration :

)ioptres.

Inches.

Dioptres.

Inches.

•12

0-25

4-50

0.37

0-50

5-50

0-62

6|

0-75

^1,

0-87

5"

I

1-25

ID

1-50

II 1-75

2'25

i7i

2.50

2-§-

2-75

3-50

II

Testing Lenses. — It is important to be able to test a lens and find out its optical value. Instead of going through the process of finding its principal focus, and measuring the distance of this from the lens centre, we place in front of it lenses of the opposite value; thus, if we wish to find the strength of a convex glass, we neutralize it with concave glasses.

A finer test is to employ the parallactic movement. If we look at a distant object through a convex glass and move the glass, the object appears to move in the opposite direction; if we use a concave glass, the object appears to move in the same direction. So long as there is any movement we must place up concave or convex glasses, according as the displacement of the object is " against " or " with."

In testing cylinders we have to ascertain not only the value, but also the direction of the axis.

LENSES 15

When cylinders are moved in front of the eye in the direction of the axis, objects looked at through them are not displaced; but the smallest rotation of the cylinder causes displacement, which reaches its maximum when the movement of the cylinder is in the direction at right angles to its axis. In this position neutralize with cylindrical lenses of the opposite value, bearing in mind that displacement takes place " against " the movement so long as a convex lens predominates, and " with " the movement so long as a concave one predominates. The axes of the two lenses must coincide.

When testing a sphero-cylindrical glass, the spherical lens should be first neutralized.

A great saving of time is effected by testing glasses with the Geneva lens measure and the Maddox cylinder-axis finder.

The Combination of Lenses — Convex Spherical Lenses. — The ordinary way for such lenses to be ground is to work half the power needed on each surface ; thus, when + 4* is required, each surface of the lens is made equal to +2, as if two plano-convex glasses of -1-2 had their plane surfaces cemented together.

Another method of working a convex lens is to grind the surface away from the eye as a convex lens of higher power than is required, and the other surface concave of such a strength as to reduce the convex surface to the desired amount. Thus, when -1-4 is ordered, one surface can be made +7 and the other surface -3, or one surface can be -1-6 and the other -2. Such lenses are called " periscopic *'; they enlarge the field of distant vision, as the eye in all its movements is at the same distance from the surface of the glass, but their chief advantage is in enabling the glasses to be placed nearer the eye without being touched by the lashes.

* In the following pages, the numeration of lenses will always be in dioptres, and " d " after the numeral will be generally omitted.

Concave Spherical Lenses. — These are usually made with half the strength required, on each surface. A certain amount of periscopic effect may be obtained by grinding the surface nearer the eye more concave, and reducing the other: thus, —8 may be, and usually is, made — 4 on each surface, or the surface nearer the eye may be made —6 and the other — 2 ; or the lens may be ground as a diverging meniscus (Fig. 7, f) ; thus, if - 3 is required, the surface next the eye is ground as -5, and the other surface as +2.

Cylindrical Lenses. — When a cylinder only is prescribed, it is ground on one surface, the other surface remaining plane. When combined with a spherical lens, it is usual to grind the sphere on one surface, and the cylinder on the other. When a convex sphere and cylinder are required, the periscopic effect can be produced by grinding a concave cylinder on the surface nearer the eye, and increasing the spherical strength by the amount of the cylinder. Thus, supposing +2 cyl. axis vert, c:; +3 sph. is needed, it may be ordered thus:

— 2 cyl. axis horizontal c^ +5 sph.

In ordering glasses for mixed astigmatism (see page 137), the periscopic effect is produced by combining a convex cyhnder with a concave sphere, and mounting the latter next the eye.

As it is very important to divide the strength of the lens between the two surfaces when dealing with high powers, a cylinder, if also required in such a case, must be worked on one of the spherical surfaces. These lenses are called Toric lenses, and any combination of spherical lens (•25 to 18), with cyHndrical lens (from •25 to 3) can be supplied. Thus, if — 14 sph. oj - 2 cyl. axis horizontal is required, one surface is made - 7, and the other - 7 sph. c::> - 2 cyl. These toric lenses are very useful in high myopia, and also in aphakia.

Bi'Focal Lenses (see Presbyopia, page 151). — Where

BI-FOCALS 17

different lenses are required for distance and reading, bi-focal lenses are generally prescribed.

The earliest forms of these glasses were straight split bi-focals, also called " Franklin " glasses, the lenses being two separate lenses divided horizontally and in the middle. Against the many disadvantages of this form of bi-focal was the one advantage that the lower lens could be slanted and made more or less parallel with the book or paper that was being read.

An improvement on these " split " bi-focals consisted having the reading addition cemented on by Canada dlsam, either as in Fig. 15 or as a small round wafer.

The disadvantage of both these forms was chiefly manifested by the dividing line between the lenses being visible and constantly causing annoyance to the wearer. Another disadvantage of the cemented bi-focals is the tendency of the balsam to dry or crystallize.

The next improvement did away with the visible line, and these bi-focals are called " invisible bi-focals." They are of two kinds, one the so-called " Kryptok," where a concavity is ground in the lower part of the distance glass, and the reading glass, of a higher refractive index, is fused into it; the other, the final perfected form of invisible bi-focals is the " Luxe," which consists of one glass only. The glass is made from a solid piece of crown glass with the two lenses ground invisibly on its surface. The chief advantage of these " Luxe "

bi-focals is that the centring of both portions is more under control, and there is no chromatic aberratioii, which is so often present in the fused form.

Spherical Aberration. — In most lenses the rays passing through the peripheral part of the lens do not focus at the same spot as those which pass through the central portion. In convex lenses, when the peripheral rays focus in front of the central rays, the aberration is spoken of as positive ; and when the peripheral rays focus behind the central, as negative. The crystalline lens suffers from spherical aberration, but it is more or less hidden by the contraction of the pupil. During mydriasis this aberration may interfere considerably with vision, but may be corrected by placing in the trial frame an opaque disc with a central circular opening. If the refraction is being estimated, this opening should not be smaller than 4 mm. in diameter.

Chapter II Optical Properties Of The Normal Eye

The eye is constructed in the form of a photographic camera. As in the camera, there is a closed darkened box open in front, where there is an arrangement of lenses to focus an object on the back, at which spot there is the apparatus for receiving the perfectly-formed image : the plate in the camera, the retina in the eye.

As in the camera, there are two conditions which must exist in the eye : firstly, the media must be transparent ; and, secondly, the focusing must be so arranged that a perfect image of the external object is formed on the retina — i.e., the principal focus of the eye must coincide with the retina.

All deviations from this latter condition are called errors of refraction and accommodation.

The Refraction of the Normal Eye at Rest— i.e., in the Absence of any Effort of the Accommodation — Dioptric Apparatus of the Eye. — The simplest form of a dioptric apparatus is when two media of different refractive power are separated by a spherical surface.

Such a system is represented by Fig. i6, where X y z is di spherical surface separating a less refractive medium on the left from a more refractive medium on the right. The line o A passing perpendicularly to the surface of the sphere and through its centre at N is called the " optic axis."

All rays passing .^normally to the surface, such as R N and s N, like the optic axis, pass through n, and undergo 19 no refraction; N, the centre of the sphere, is called the " nodal point."

The point y where the optic axis cuts the sphere is called the " principal point."

Rays c, d, parallel to the optic axis in the less dense medium, unite somewhere on the optic axis at the point F, called the " posterior principal focus."

On the optic axis, in the less dense medium, there is another point (f'), called the " anterior principal focus," whence divergent rays passing into the denser medium are refracted, and become parallel to the optic axis as at zf.

Fig. i6.

These four points — the principal point, nodal point, and anterior and posterior principal focus — are called " cardinal points " of the system.

In the eye the system is much more complicated. A ray of light passing into the eye meets the following surfaces and media in the order named: Anterior surface of the cornea, substance of the cornea, posterior surface of the cornea, aqueous, anterior surface of the lens, substance of the lens, posterior surface of the lens, and vitreous. Thus there are four surfaces and, if we include the air, four media. As the anterior and posterior surfaces of the cornea are parallel, we may neglect the substance of the cornea, and consider the two surfaces as one. Again, as the indices of refraction of the aqueous

THE CARDINAL POINTS 21

and vitreous are identical (see page 4), we may assume them to be one medium. In this manner the eye is reduced to three surfaces and three media.

These three surfaces — the cornea, and the anterior and posterior surfaces of the lens — are symmetrically centred round the optic axis of the whole system, which may now be reduced to a compound system, consisting of the cornea and a bi-convex lens ; we find the principal points p' p" (Fig. 17) and the nodal points n' n" of the cornea and lens ; and, finally, take the mean of these two points, and get p the principal focus and N the nodal point. Such an eye is known as the " reduced eye," and was suggested by Listing.

The positions of the cardinal points of the reduced eye are —

Principal point, in the aqueous, 2 '3448 mm. behind the anterior surface of the cornea.

Nodal point, in the lens, '4764 mm. from its posterior surface, and about 15 mm. from the retina.

Posterior principal focus, 22 •81 9 mm. behind the anterior surface of the cornea — i.e., on the retina of the normal eye. (This is the length of the standard eye.)