An Elementary Treatise on Optics/Chapter 14

by Henry Coddington

CHAP. XIV.

THE EYE.

134.The organ by which we are most usually, and most easily informed of the presence of external objects, and without which we should often be ignorant of their form, and always of their colour, is the eye, a most curious combination of parts so admirably contrived to answer all the purposes required, that nothing short of divine intelligence could have been capable of constructing it, and the mere imitation of it is far beyond the reach of human skill.

135.The eye is, in form, nearly spherical, as will be seen by referring to Fig. 147, which represents a horizontal section of the right eye.^[1]

Its several parts are as follows:

The cornea $A$ is a transparent membrane which covers the convexity in front of the eye. It is formed like a meniscus, being thickest in the middle.

The sclerotica $HIK$ is a thick tough coat, which covers the remainder of the eye, and is intimately united with the cornea round the edge of the convexity.

The choroid-coat $EFG$ lines the sclerotica; (but not the cornea): these two integuments are united rather loosely in general, except round the edge of the cornea, where they are firmly fastened together by a circular band, called the ciliary ligament.

The choroid is continued, so as to form, by a sort of doubling or fold, the ciliary processes, and is again continued in front of these.

This continuation is called the uvea, and is like a circular basin thinned away towards the center, where there is an aperture B.

This aperture is denominated the pupil. It is of various forms in different animals, and is capable of being contracted, or enlarged. In man it is always circular, but in animals of the feline kind, its vertical diameter is invariable, so that its figure varies from a circle to a straight line (Fig. 148.). In ruminating animals on the contrary, it is transversely oblong, and when contracted to the utmost becomes a horizontal straight line (Fig. 149.).

The change in the size or form of the pupil, is effected by certain muscles, which in general perform their office spontaneously, being of the kind called involuntary. The cat however is said to have a great command over this mechanism.

The iris is a coloured membrane coating the exterior surface of the uvea. It is of different hues in men, varying through many shades of blue, gray, brown, and green.

The interior surface of the choroid is covered with a dark mucus, in which is imbedded a fine net-work, called the retina. This proceeds from the optic nerve, which enters obliquely at the back of the eye through a tube (part of which is shown in the figure) which connects the eye with the brain, the coats of which, called the dura mater and pia mater, are by some writers said to be identical with the sclerotica and choroid. M. Cuvier says on this subject: "Le nerf optique parcourt la portion postérieure de la sclérotique par un canal d'un pouce et demi de longueur, dont les parois sont formées par la dure-mère; et il est très visible que les fibres blanches, qui font la base de la sclérotique, se détachent successivement de la face extèrne de la dure-mère, dont elles semblent être un épanouissement. Cela pourroit décider, en faveur des anciens, la question de savoir si la sclérotique est ou non une continuation de la dure-mère; question assez difficile à résoudre dans les autres animaux où ces deux membranes ne se touchent que dans une espace très mince." As to the other point, he seems to set it at rest, by saying of the optic nerve that "arrivé à la choroide, il la perce par un trou rond, fermé d'une petite membrane cribleé d'une multitude de petis pores, au travers desquels la substance medullaire qui a traversé les longs canaux dont ce nerf est composé, semble s'écouler pour se mêler intimement et former cette expansion nerveuse qui double toute la concavité de la choroide, et que l'on nomme rétine."

Within the eye, near the uvea, is suspended in a transparent membranous capsule, a jelly-like substance C in form of a double-convex lens of unequal radii, being less convex in front, than on the back; this is called the chrystalline lens. It is composed of a great number of laminæ, which are divisible into fibres, converging from the circumference towards the middle of the surface, and varying in hardness from the surface to the center, where the consistence is the greatest.

The space D behind the chrystalline, which is the largest in the eye, is occupied by the vitreous humour, a viscous fluid contained in a cellular sponge-like substance enclosed in a very fine transparent membrane.

The cavity between the chrystalline and cornea, which is partly divided by the uvea, is filled with a fluid called the aqueous humour, which consists merely of water, with small quantities of albumer and salt, and is quite limpid, and devoid of smell. It is said by some authors to be lighter than distilled water, in the ratio of 975 to 1000.

136. The proportions of the spaces occupied by the three humours of the eye vary in different animals, as may be seen from the following Table, taken from M. Cuvier's Anatomie Comparée, which shows the parts of the axis lying in the several humours:

Aqueous
Humour.

Chrystalline.

Vitreous
Humour.

—————— —————— —————— —————— Man 3/22 4/22 15/22 Dog 5/21 8/21 8/21 Ox 5/37 14/37 18/37 Sheep 4/17 11/17 12/17 Horse 9/43 16/43 18/43 Owl 8/27 11/27 8/27 Herring 1/7 5/7 1/7

The radii of the surfaces of the chrystalline are in

Man	as 12	to 16[2]
Dog	12	14[1]
Ox	6	21[1]
Rabbit	14	14[1]
Owl	16	14[1]

The specific gravities of the different parts are as follows, that of distilled water being 1:

In the Ox. In the Codfish. Aqueous humour 1 1 Vitreous humour 1.016 1.013 Christalline lens (mean) 1.114 1.165 Outer part of ditto 1.070 1.140 Inner 1.160 1.200

As to their refracting powers, they must be more considerable than their density indicates, on account of the inflammable particles which enter into their composition. It is possible also, that the proportional quantity of these inflammable particles may not be the same in the different humours, so that their refracting powers may not be exactly in the ratio of their densities. (Cuvier.)

Dr. Wollaston makes the refracting power of the vitreous humour equal to that of water, and that of the chrystalline lens of the ox greater in the ratio of from 1.38 to 1.447 to 1. Dr. Brewster gives the following Table deduced from experiments made on a recent human eye:

Refracting power of water 1.3358 the aqueous humour 1.3366 the— — — vitreous humour 1.3394 the— — — outer coat of chrystalline 1.3767 the— — — middle 1.3786 the— — — central part 1.3990 the— — — whole chrystalline 1.3839

Dr. Brewster gives also the following dimensions:

	Inch.
Diameter of the chrystalline	0.378
Diameter of the— — — cornea	0.400
Thickness of the chrystalline	0.172
Thickness of the— — — cornea	0.042

137. The construction of the eye being so far explained, we may now detail the circumstances attending vision, as far as we are acquainted with them.

The rays of light proceeding from any point, whether luminous of itself, or merely reflecting light, fall on the cornea of the eye, and are by that slightly refracted: they then enter the aqueous humour, which, being terminated in front by a convex surface, further diminishes their divergence: the uvea stops all the extreme rays, and suffers only those near the axis of each pencil to pass through the pupil:^[3] these enter the chrystalline, which, with the vitreous humour which succeeds it, completes the refraction, and collects all the different cones of light to points on the retina, which, it is supposed, is affected by them, and transmits the sensations excited in it by means of the optic nerve to the brain, where they become the means of conveying intelligence to the mind. It is admirably placed, so as to admit the greatest possible extent of view, as may be seen by comparing Figs. 150, 151, the latter of which shows what would be the effect of a diaphragm placed in front of the eye of such a magnitude, as to admit rays only to the central part of the chrystalline. It must necessarily be much smaller than the pupil, and would therefore afford very little light, or else allow no vision in any direction at all oblique to the axis of the eye.

Dr. Wollaston has ingeniously imitated this part of the construction of the eye in his periscopic lenses, composed of two plano-convex ones, joined at their plane sides, with an intervening diaphragm pierced at the centre (Fig. 152.). They concentrate rays of very great obliquity with wonderful accuracy.

The rays collected at the back of the eye form what is called in Optics, an image of an external object, which is of course inverted like that formed by a common convex lens. This image may be easily seen in the eye of a dead animal, when the outer coats are cut away from the back of it.(See Fig. 153.)^{[errata 1]}

138.It will naturally occur to the reader, that an eye of an invariable form can produce the image above described, only of an object at one particular distance from it, as rays proceeding from a point beyond that distance would converge within the eye, before they met the retina, and the image of a nearer object would be thrown outside of the eye. The great Author of nature has, however, not left his work so imperfect. By means of a certain muscular mechanism, which increases or diminishes at pleasure the convexity of the chrystalline, the form of the eye is modified, so as to throw on the retina distinct images of all objects, between very wide limits. Good eyes can see distinctly objects at a distance so great, that the rays proceeding from them, admitted through the pupil, must be to all sense parallel, and with equal facility, others placed at eight or nine inches from them.

139. Persons who have been accustomed for some time to look very much at near objects, as in reading, or engraving, are apt to become short-sighted.

Others again, such as savages, who are in the constant habit of looking out for game at a distance, cannot see a thing distinctly within arms-length; they are what is called long-sighted.

Both these imperfections proceed from the same cause. The chrystalline being constantly used in one state becomes fixed in it, and the muscles which serve to modify its form, lose their power from disease.

Old age generally brings on long-sightedness, which is commonly corrected by the use of spectacles with convex lenses, to assist the eye in giving the necessary convergence to rays proceeding from a near object.

In like manner, short-sighted persons use concave glasses, to enable them to discern distant objects, as the effect of such glasses is to give additional divergency to incident rays.

140. It is of consequence to a person of an imperfect sight to know the form or focal length of the lens best suited to assist his eye; this is easily found: suppose a short-sighted man can see distinctly only to the distance of 20 inches: he will be enabled to discern a very distant object by the help of a lens, which will produce an image of such an object at the distance of 20 inches, or which will make parallel rays diverge from a focus at 20 inches from him, (supposing the glass placed close to the eye;) that is, a concave lens of 20 inches focal length.

If the person we have been speaking of were to wear spectacles with concave glasses of 20 inches focus, he would be able to see distinctly any distant object. It does not, however, appear that they would not inconvenience him when he wished to look at a near object, one at the distance of 10 inches, for example.

By putting 10 for ∆, and 20 for F in the common formula,

1/∆″=1/F+1/∆;

we find

1/∆″=1/20+1/10=3/20=1/62/3.

If therefore this person can see distinctly without a glass, an object at about 6 inches from his eye, he will find no inconvenience from his spectacles, provided he does not use them to look at any thing nearer than 10 inches.

141. Let us see now how we can remedy the defect of vision in an aged person, who cannot discern an object within 24 inches from his eye.

A double-convex lens of 24 inches focus will make such an object appear infinitely distant; others within 24 inches will be removed to distances more or less considerable; the nearest object distinctly discernible will be that having its image at 24 inches from the eye. Putting 24 for ∆″, and −24 for F, we find

1/24=−1/24+1/∆; ∴ ∆=12.

From this we collect, that spectacles with convex glasses of 24 inches focus may be used for any object from 24 to 12 inches from the eye. Within the lesser of these distances the lenses are inefficient, and beyond the other, the image would be more than infinitely distant, that is, the rays entering the eye would be made convergent, and consequently unfit for vision.

142. There is a disease of the eye called the Cataract, in which the chrystalline lens losing its transparency, the patient becomes blind. The only cure known is to extract that part of the eye by the operation called couching, and allow its place to be filled by the aqueous humour.

In this case it is found that convex glasses are necessary to make the sight distinct, which shows that the refracting power of the chrystalline lens is stronger than that of the humour which is here substituted for it.

143. It may be observed, that all persons requiring either concave or convex lenses to assist their sight, should always chuse those of the least refracting power that will answer the purpose, as the use of them tends to increase the defect they are intended to remedy, namely, a defect in the power of accommodating the eye to the perception of objects at different distances from it.

144. The fact of images of external objects being produced by the eye, and serving as the medium of vision, has led to a great deal of discussion about the manner in which we take cognizance of external objects by the help of the senses. Sir I. Newton published in his Optics the following query, among others:

"Do not the rays of light in falling upon the bottom of the eye, excite vibrations in the tunica retina? which vibrations, being propagated along the solid fibres of the nerves into the brain, cause the sense of seeing."

And again,

"When a man in the dark presses either corner of his eye with his finger, and turns his eye away from his finger, he will see a circle of colours like those in a peacock’s tail. Do not these colours arise from such motions excited in the bottom of the eye by the pressure of the finger as at other times are excited there by light for causing vision? And when a man by a stroke upon his eye sees a flash of light, are not the like motions excited in the retina by the stroke?"

We may give the above as a specimen of some of the more sane speculations on this subject, with respect to which, as to many others connected with the reciprocal actions of mind and matter, the only knowledge at which the most profound philosophers have arrived, is, that like Socrates, they know nothing.

145. We pass over the question which has embarrassed many: "why external objects appear erect to the eye, whereas their images, by which it is supposed we judge of them, are inverted." People have debated this point very earnestly, and reasoned on it at great length, appearing to consider these images as something real that we could see or feel: the fact is merely this, that in vision the rays of light are collected to different points on the retina, and that by the various sensations there produced by them, we are informed of the existence of objects without us, probably in a manner analogous to that in which we are made sensible of those or other objects, by sensations excited in the organs of hearing.

We judge of the relative places of visible objects by the relative places of their images in the bottom of the eye, and it is probable that experience teaches us to connect corresponding phænomena in this as in many other cases, though it is not mentioned, we believe, in any account of persons having their sight suddenly restored, that they were at all at a loss as to the position of objects at first.

Some writers have endeavoured to explain why the two images, formed by our two eyes, do not excite in us the idea of two objects instead of one. We can only conjecture that the sensations excited in corresponding parts of the retinas are melted as it were into one, where the two optic nerves unite. Perhaps it is merely experience that leads us to form a correct judgment. Cheselden in his Anatomy gives an account of a person who had one of his eyes distorted by a blow, so that every object seemed double to him for some time, but by degrees he recovered his single vision, first of familiar objects, and afterwards of all others, though the distortion always remained. Now in this case, the images could not be formed on corresponding parts of the retinas, and moreover, the same sensation seems, at different times, to give rise to double and to single vision, the only difference being due to habit.

Persons who squint do not direct both eyes to the same object, yet their vision is single, and what is more remarkable, this defect is sometimes acquired and sometimes cured, without double vision being experienced.

146. While we are on the subject of sensations in the retina we may observe that there is one spot in the eye which is insensible, namely, that where the retina branches out from the optic nerve. This may easily be observed by placing three white patches of paper on a dark wall, at equal distances on the same horizontal line, and standing at about four or five times as far from the wall as the papers are from each other. If then one eye be closed, and the other be directed to one of the outside patches, the middle one will be quite invisible, though the other one, which is farther from the axis of the eye, is clearly perceptible.

Dr. Young makes this experiment rather differently. He says: "To find the place of the entrance of the optic nerve, I fix two candles at ten inches distance, retire sixteen feet, and direct my eye to a point four or five feet to the left of the middle of the space between them: they are then lost in a confused spot of light; but any inclination of the eye brings one or the other of them into the field of view."

147. It is undoubtedly experience alone that enables us to judge of the magnitudes and distances of objects by the sight, though the precise manner in which this takes place has never yet been satisfactorily determined.

All that the eye furnishes, in the first instance, is the angle, plane or solid, subtended by an external object: if this were the only criterion afforded, we should of course often imagine a small object to be larger than another greatly exceeding it, if the former were placed so much nearer the eye that it would mask the other, if they were in the same line from the eye. Now we know perfectly well, not only that children make constant mistakes of this nature, but that men are likewise very often deceived, when placed in situations in which they have not had previous experience to modify their observations. For instance, a native of this island placed for the first time of his life among the Alps, forms the most absurdly incorrect notions of the distances and magnitudes of the parts of those scenes, which are so much more extended than any to which he has been accustomed. An easier illustration of this may be had by ascending any eminence much greater than those which one is accustomed to look from. It is almost impossible to imagine that the human beings one sees below are of the same size as one's self, till a few minutes' consideration dispels the delusion.

148. The different means by which, according to Harris, we are enabled to correct our observations of distances, are

1. The change of conformation in the eye necessary for the distinct perception of objects at different distances.
2. The inclination of the axes of the two eyes, when directed to the same object.
3. The length of the ground plane, or the number of interveneing parts perceived in it.
4. The different appearances of known objects at different distances, or the known magnitudes of their least visible parts.
5. Different degrees of brightness and change of colour.

With regard to the two first of these, it is allowed on all hands that they can be available only for very short distances. Harris, in his concluding observation on them, says: "I think it is very manifest that with both our eyes we can distinguish, pretty accurately, the places of objects that are not above 5 or 6 feet distance from us. And indeed it seems necessary that we should have something within ourselves, or some means that never forsake us, whereby we might unerringly judge of distances so very near us: otherwise we might be frequently in danger of our lives, without perceiving it; as well as subject to perpetual mistakes, concerning objects so near as within the reach of our arm."

He had just observed as an illustration of this: "If I advance within 4 or 5 feet of an image projected before a concave speculum,^[4] I can define its place very precisely; and the image itself, though much smaller than the object, will appear very perfect and continue still at the same place, as I advance nigher: but on my retreating farther back than my first station, I begin to be less certain of its place, and the mistake lies on supposing it farther from me than it really is: my faculty of distinguishing distance in this case not being sufficient to overcome the prejudice arising from the greater faintness, and other imperfections of the image."

Speaking of the third means of judging of distance, he says: "An extent of ground lying before us, is itself properly an object, the visible length or magnitude of which, is the visible distance of an object placed at the farther end of it. The same observation is also just with respect to the side of a straight wall, or hedge, &c." This is particularly true when the extent of ground or wall, &c. is divided into portions, of the magnitudes of which we can form a tolerably correct estimate: but even this is of use only to a certain extent; for if there were placed before a spectator an unbounded straight line distinctly divided into feet, which would of course assist him extremely in judging of moderate distances, he would find that beyond a certain limit it would be impossible to count the divisions, and there could be collected but a very vague notion of their number. A rod of 10 feet in length placed on the ground, in a line with the body, at 100 yards distance, subtends but an angle of about 2 minutes of a degree, which is supposed to be the smallest appreciable, so that an object subtending such an angle, is called, by some writers on Optics, the minimum visibile.

To show how uncertain our estimates of distance by the eye often are, Harris proceeds: "It is manifest from observation, as well as from the nature of the thing, that a given extent appears longer, according as it contains a greater number of visible parts; and hence two remote and equal distances may appear very unequal, according to the different circumstances of the intervening parts, and the relative elevation of the spectator." "But without regarding the differences on this account, let the spectator have a given station or stand on even ground, and there will be many circumstances which may vary the apparent or visible distances. Thus a hedge having in it several grown trees, generally looks longer than a clipt hedge on the same extent of ground in the open field." "A river at first looks not so broad, as after we have had a side view of a bridge across it: and indeed a given extent of water does not appear so long as the same extent of land, it being more difficult to distinguish parts in the surface of the one than in that of the other." To this we may add, that in sailing on the ocean, when nothing is seen "nisi pontus et aër," the horizon appears very much less distant than when there are lands or vessels in view.

We proceed to the fourth means, namely, the different appearances of known objects, or the known magnitudes of their least visible parts.

There is, perhaps, not a more common or a more convenient way of estimating the height of buildings at a distance, than comparing it with that of men or cattle standing near them; and another has been used with nearly equal ease and probably greater accuracy, which is counting the courses of masonry in a wall, when they are of a known height, or which is still more certain, the number of rows of bricks, when that is the material used. This, however, amounts to nothing more than measuring an unknown magnitude by a known one, for the eye is not employed to determine the height of the man or horse standing by a building, or of the depth of a course of bricks: these are taken for granted, and all that is required of the eye is to tell how many times the one magnitude is contained in the other.

Different degrees of brightness, and different colours in known objects cause a difference of apparent distances.

It is well known that the farther an object is removed from the eye, cæteris paribus, the less distinctly it is visible, and the more its colour approaches to the natural blue of the air. We say cæteris paribus, because it is plain that in point of distinctness much must depend on the state of the weather in the case of known objects, and of those with whose external appearance we are not well acquainted, the apparent distance will depend very much on the brightness and distinct markings of the surface. In foggy weather all objects seem farther, and consequently larger than ordinary; a westerly landscape, in a clear morning with the sun upon it, seems nearer than it does later in the day.

"From the several preceding observations," continues Harris, "it appears, that after joining together all the helps we can have, our estimations of distances, beyond a certain limit, are gross and uncertain; and this limit also varies in different circumstances. And the more certain estimates we always make of near distances, seem, as has been before observed, to prove that in these cases, the ideas are principally formed from the motion of our eyes; otherwise the different colours and brightness of objects and also the magnitudes of such as we had not seen before would lead us into perpetual mistakes.

With respect to the relative brightnesses of the same object placed at different distances, it is to be observed that they would be exactly the same, if no light were stopped or dispersed in its passage through the air; for supposing the aperture of the pupil to remain the same, the quantity of light entering through it varies inversely as the distance of the object from the eye, but the area of the picture on the retina over which that light is spread varies in the same ratio,^[5] so that this picture is, in all cases, equally enlightened.

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1. This figure is copied from Dr. Young.
2. These are according to M. Cuvier, the actual magnitudes (in millimetres, I suppose.)
3. The magnitude of the pupil is regulated so as not to let in so much light as would hurt the eye, or confuse the refraction: for this reason it is more contracted, cæteris paribus, in looking at a near object than a distant one.
4. This is perhaps the best object that could be chosen for experiment, as it may be exhibited quite insulated, in a room where there is dust enough floating in the air to catch the condensed light.
5. The object and the image subtend the same angle at the center of the eye, and therefore the area of the image is to the visible area of the object, as the square of the distance from the center of the eye to the retina, to the square of the distance of the object from the eye, in which proportion the means are invariable.

Errata

1. Original: was amended to (See Fig. 153.): detail