Curiosities of Light and Sight

CHAPTER III.

SOME OPTICAL DEFECTS OF THE EYE.

More than one reference has been made to the fact that the sense of sight, even in its best normal condition, is characterised by certain defects and anomalies. Some of these arise directly from causes inherent in the design or structure of the eye itself, and may be broadly classified as physical; others are of psychological origin, and result from the erroneous interpretations placed by the mind upon the phenomena presented to it through the medium of the optic nerve and the brain.

Among the numerous physical defects of the eye none is more remarkable than the absence of means for properly correcting chromatic aberration. This defect is remarkable because it appears—at least to those who are without actual experience in the manufacture of eyes—to be one which might very easily have been avoided. So far as a mere theorist can judge, an achromatic arrangement of lenses would have been just as simple and just as cheap (if I may use the term) as the arrangement with which we find ourselves provided. It is true that we manage to go through life very well with our uncorrected lenses, and indeed it is hardly possible by ordinary observation to detect any evidence of the imperfection. Yet its existence in a glaring degree is undoubted, and can be readily demonstrated by a great variety of methods. The conclusion is inevitable that with achromatic eyes our vision would be improved, but whether there may not possibly exist reasons why such an improvement could only be achieved at a disproportionately high cost is a question which cannot at present be answered.

Without going into matters which are dealt with in every elementary text book of optics or general physics, it may be desirable to explain shortly what is meant by the terms chromatic aberration, and achromatism.

Fig. 11.—Refraction of monochromatic Light by a lens.

Let L L, Fig. 11, represent in section a circular convex lens, and P a luminous point, which is most conveniently supposed to be situated on the axis of the lens. Imagine P to be surrounded in the first instance by a glass shade which transmits only monochromatic red light. So much of the light from P as falls upon the lens will be refracted to a point at the conjugate focus F, and after passing this point will diverge again; the refracted light rays will, in fact, form a double cone, of which F is the apex. If a white screen be held at F, there will be focussed upon it a small clearly-defined image of the luminous point. If, however, the screen be moved nearer to or further from the lens, it will cut the cone of light, and the image will then no longer appear as a point, but as a circular red disk, which will be larger the greater the distance of the screen from F. Such a disk is known as a “diffusion circle.”

Suppose now that we substitute for the red glass, surrounding the source of light, a purple one capable of transmitting not only red rays but violet as well. The lens will cause both the red and the violet rays which pass through it to converge; but since the violet rays are more refrangible—more easily refracted or bent aside out of their straight course—than the red, there will now be two double cones, as shown in Fig. 12, where the contours of the red cones are represented by solid lines and those of the violet by dots.

Fig. 12.—Refraction of dichromatic Light.

The focus of the red rays will as before be at F, but that of the violet will be nearer to the lens, as at H, and this being so, it is evident that a well defined image of the purple source of light cannot possibly be formed upon a screen placed anywhere behind the lens. Held in the position indicated by the line C C, where it passes through the focus of the red rays, the screen cuts one of the cones of violet light, and the image at F will appear to be surrounded by a violet halo. Held at A A, the screen evidently receives an image with a red halo round it. Only at B B, in the plane where the surfaces of the red and violet cones cut one another, will it be possible to obtain an image without a coloured border; but here good definition is unattainable, for neither the red nor the violet rays are in focus, and the luminous point is represented by a purple disk or diffusion circle of sensible diameter.

If rays of every possible refrangibility are allowed to fall upon the lens, as is the case when the source of light is not shielded by any coloured glass, there will be formed an indefinite number of pairs of cones, the apices of which will lie along the straight line joining H and F. It is clear that all these cones cannot possibly intersect in a single plane, and consequently no position can be found where the edge of the projected image is perfectly free from colour, though at a certain distance from the lens, where the brightest constituents of the light—namely, the yellow and green—are approximately focussed, the coloured border is least conspicuous, and is of a purple tint, due to the mixture of the red and violet rays.

For these reasons a single glass lens cannot, except with homogeneous light, be made to give a perfectly distinct image of a luminous point, nor of an illuminated object, the surface of which may be regarded as an assemblage of points. Such a lens, therefore, is never employed when good definition is required. The confusion resulting from the unequal refrangibility of the differently coloured rays is said to be due to the chromatic aberration of the lens.

In connection with this matter, the history of physical optics contains an interesting little episode. It occurred to Sir Isaac Newton that although a single lens could never be free from chromatic aberration, yet it might be possible to arrange a so-called achromatic combination of lenses in such a manner as to overcome the defect and bring all the rays issuing from a point, whatever their refrangibility, to one focus. Experiments which he undertook for the purpose of testing the matter led him to form the conclusion that such a result could never be attained, the amount of colour dispersion in all substances being, as he stated, always exactly proportional to that of refraction. For this reason he confidently announced that it was useless to attempt the construction of a really good refracting telescope, and so great was the authority attaching to his name that for many years all efforts in that direction were abandoned.

Nevertheless from time to time certain philosophers ventured to surmise that Newton might perhaps have been mistaken, and the curious thing is that they all based their scepticism upon what they considered the self-evident fact of the achromatism of the eye. The system of lenses in the eye, they argued, being unquestionably achromatic, why should not an equally effective combination be constructed artificially?

At length, more than eighty years after Newton had made and published his fundamental experiments, it occurred to a working optician, John Dollond, that it might be worth while to repeat them, and upon doing so he at once found that Newton was wrong in his facts, the results as recorded by him being in direct opposition to the truth. With proper respect for the memory of a great man it is usual to speak of Newton’s observation as a “hasty” one, but if in these days a junior science student were to be guilty of a similar lapse, his conduct would not impossibly be stigmatised as grossly careless.

Having established Newton’s error, Dollond found little difficulty in constructing achromatic lenses of very satisfactory quality; telescopes of his manufacture long enjoyed the highest reputation, and the best optical instruments of the present day are the direct offspring of his invention.

Those who entertained the opinion that Newton’s conclusion was erroneous were therefore in the right, but it is remarkable that the reason upon which that opinion rested was altogether invalid, for, as I have said, the lenses of the eye are by no means achromatic. Of the many ways in which this can be demonstrated, the following is one of the most impressive.

Let a long and narrow spectrum of the electric light be projected upon a white screen, the prisms and lenses being carefully arranged in such a manner as to ensure that the upper and lower edges of the spectrum are clearly defined and strictly parallel. To an observer standing close to the screen, the spectrum will present the appearance of a bright parti-coloured rectangle. But viewed from a distance of a few feet the spectrum will not seem to be rectangular, its upper and lower edges no longer appearing to be parallel, but to diverge, fan-like, towards the blue and violet, as shown in Fig. 13. This is because the violet and some of the blue rays proceeding from an object at a little distance cannot by any effort be focussed upon the retina. They are too much refracted, and the mechanism by which the eye is adjusted is incompetent to diminish the convexity of the lenses sufficiently to enable them to project a clear image. Every point is expanded into a luminous circle, which is the larger the more refrangible the rays, and it is the extension of these diffusion circles beyond the proper boundaries of the image that gives the appearance of increased breadth.

It is a simple matter to counteract the effects of undue convexity by means of a concave lens. If a normal-eyed person, to whom the violet end of the spectrum when seen from a distance appears blurred and widened, will look at it through suitable glasses adapted for short sight, he will at once see it clearly defined and of its proper width.

Fig. 13.—Narrow Spectrum as seen from a distance.

Let a rectangular patch of white light having about the same dimensions as the rectangular spectrum be now thrown upon the screen. The light reflected from the patch will contain, as before, all the various spectral colours, but they will be mixed or superposed, instead of being spread out side by side. The patch will send forth, among others, can yellow and green rays, which the eye easily focus; it will also send out violet rays, which, as we have shown, cannot be focussed by the unassisted eye. Owing to the existence of diffusion circles there must necessarily be formed upon the retina a violet image larger than the approximately superposed images due to rays of brighter colours. Viewed from a distance therefore the white patch might be expected to exhibit a violet border. Yet it may be confidently asserted that the observer will not be conscious of seeing any such border, for though one actually exists, it is possessed of such comparatively feeble luminosity that it is lost in the glare produced by the brighter rays.

It is, however, possible to cut off these brighter rays by interposing between the projection lantern and the screen a combination of glasses which has been found by trial with a spectroscope to transmit only dark blue and violet light. The rectangle will then be of a blue-violet colour, and when looked at closely, will still be quite clear and sharply defined, but viewed from a little distance it will appear blurred and of an exaggerated size.

Another and perhaps even better way of demonstrating this last effect is to enclose the source of light (which should be a powerful one, such as an arc lamp or limelight) inside a box having a ground-glass window in one side. When the window is covered by the coloured glasses its outline cannot be clearly distinguished unless the observer is near, but if he uses suitable concave spectacles, he will be able to see it quite distinctly, even from a considerable distance.

It is well known that ideas of distance are associated with certain colours. A room gives one the impression of being larger when it is papered or painted a blue-violet colour than when its colouring is red. In the former case the walls seem to retire from the spectator, in the latter to approach him. So too a red spot upon a violet ground appears to be distinctly raised above the surface, while a violet spot upon a red ground appears to be depressed. These phenomena are fully explained by the imperfect achromatism of the eye. When we look at a red object, we have to adjust the crystalline lens by means of the ciliary muscle in exactly the same way as when we look at a near object; in both cases it is necessary to increase the convexity of the lens, and so diminish its focal length, in order to obtain a clear image upon the retina. And again, when we wish to see a blue or violet thing distinctly, the ciliary muscle must be relaxed and the convexity of the lens as far as possible diminished, just as if the gaze were directed to the horizon. We are accustomed to estimate the distances of things largely by the muscular effort required to focus their images, and thus it happens that the colour red comes to be associated in our minds with nearness, and violet with remoteness.

These psychological effects are perfectly well marked even with the impure colours met with in ordinary life, but they are naturally more evident when the colours observed are pure, like those of the spectrum.

A beautiful example is that presented by the pair of short bright spectra formed upon the screen when a double slit is used shaped like the letter V. The gorgeously coloured V seems to stand out in strong relief like a pair of inclined boards, the nearer edges being red, the farther ones violet. (See Fig. 14.)

Fig. 14.—Spectrum formed with V-shaped Slit.

In many other ways, and with little or no apparatus, any one may easily convince himself that the different constituents of white light are not equally refracted by the lenses of the eye. Look, for instance, at the incandescent filament of an electric lamp through a piece[7] of common dark blue cobalt glass, which has the property of obstructing the coloured rays corresponding to the middle of the spectrum, while transmitting the red and the blue. Seen from a distance of only a few inches, the filament appears to be pale blue with a bright red border, the blue rays being perfectly focussed, while the red form diffusion circles. Move some six or eight feet away and look again; the colours will now be reversed, the filament appearing red and the border blue-violet. From a still greater distance—about fifteen or twenty feet—the whole lamp-bulb will seem to be filled with a blue-violet glow, due to large diffusion circles, while the red image of the filament may be even more clearly defined than before. No doubt it is partly owing to the non-achromatism of the eye that distant arc lights always appear to have a yellowish hue, even when the air is quite clear; a considerable proportion of their blue and violet components must necessarily be lost by extensive diffusion.[8]

Again, look at a sunlit landscape or a printed wall poster through a combination of coloured glasses which will transmit only the violet end of the spectrum. You will find yourself for the time terribly short-sighted, everything appearing blurred and indistinct. But if you resort to the usual corrective for myopia, and put on a pair of concave spectacles, your normal vision will be restored; trees and houses will be seen as clearly as the feebleness of the light transmitted by the coloured glasses will permit, and the letters of the poster will become easily legible.Now, of course, the interposition of coloured glasses does not actually give rise to these blurred images; it merely enables one to detect their existence. Under ordinary conditions they always accompany the clearer images produced by the more luminous rays, and their presence cannot fail to exert a detrimental effect upon the general definition. Such blurs must at least tend to fog the darker portions of the focussed picture, and though we are not distinctly conscious of their existence, it is certain that if they were annulled the acuteness of our vision would be improved.

The diffusion circles produced by the red rays, when the eye is accommodated (as it commonly is) for the yellow and green, are less conspicuous than those due to the most refrangible rays. Yet I find it impossible to focus a red object, such as the filament of an electric lamp screened by a properly selected deep red glass, when placed at the ordinary distance of distinct vision—some nine or ten inches from the eye—without the aid of a convex lens. In this case one is not too short-sighted but too long-sighted to see the object distinctly; in other words, the lenses of the eye cannot refract the red rays sufficiently to produce well-defined images upon the retina, and the refraction has to be increased by artificial means.

Though, as I have said, it is difficult, or even impossible to detect any trace of a coloured border when looking at a bright object for which the eye is accommodated, it is quite easy to bring such borders into prominence if the object is at a distance a little too great or too small for distinct vision. A very remarkable device for the purpose is one due to von Bezold. This may be illustrated by using a non-achromatic glass lens, such as a common magnifying glass, to project a transparency or lantern-slide upon which is painted a target-like design, consisting of a series of circular black bands surrounding a circular black spot.[9] (See Fig. 15.)

Fig. 15.—Bezold’s Diagram.

Suppose the glass lens to represent the lenses of a gigantic eye (in a definite condition of accommodation) and the screen the retina. The imaginary eye is looking at the design on the lantern-slide, and when this is at the distance of most distinct vision a fairly well defined image of the target is formed upon the retinal screen.

Now gradually move the lantern slide towards the lens (or the lens towards the slide), thus bringing it too near for distinct vision. This has the effect of enlarging the diffusion circles formed by the less refrangible rays corresponding to the red end of the spectrum, and at the same time of diminishing those formed by the more refrangible rays corresponding to the violet end. The first result is that the circular dark bands become reddish brown, and the spaces between them bluish. As the distance between the lens and the slide is still further diminished, the tints become more varied and brilliant, until at last there appears a beautiful series of coloured rings around a bright red central spot.

These effects are not produced when the lens employed is an achromatic one; with such a lens the diffusion circles are all enlarged or diminished together, and a to-and-fro movement of the lantern slide (or of the lens) merely affects the definition of the image without causing any perceptible dispersion of colour.

Now it is noteworthy that the chromatic phenomena exhibited with the uncorrected glass lens are quite well shown by the lenses of the eye. It is only necessary to hold the lantern-slide before a bright background and gradually bring it so close to the eye that the design cannot be seen distinctly. The black bands will then appear to turn brown, the white ones blue, and the central spot bright red. The printed diagram (Fig. 15) will itself show the colours if it is held at a distance of four to five inches from one eye in a good light.

One more experiment may be referred to. Look with one eye at a well-lighted page of print, and with a strip of brown paper, held quite near the eye, cover about half the pupil. The black letters will now appear to be bordered with colour—blue towards the apparent edge of the brown paper, orange on the opposite side. If the letters are white on a black ground, as sometimes happens in the case of advertisements, the colours will be interchanged. The cause of the coloured borders will be readily understood from an inspection of the diagram Fig. 12; but it must be remembered that the images on the retina are inverted.

Thus it is proved beyond all question that the lenses of the eye do not form an achromatic combination.

Another peculiarity by which the eye is affected, and which does not occur in optical instruments, is that known as astigmatism. The surface of the cornea, which, with the aqueous humour, forms the outer lens, is not often perfectly spherical; generally it is shaped something like the bowl of a spoon, the curvature being greater vertically than horizontally. Rays issuing from a luminous point do not, after refraction by such a lens, cross at a single focus, but along two short straight lines, the one horizontal the other vertical, which are at different distances from the lens; thus a distinct image of a small point cannot anywhere be produced.

Fig. 16.—Effect of Astigmatism.

A very curious result follows from this deformity. If two straight lines are drawn at right angles to each other, as in Fig. 16, it is impossible to see both of them quite clearly at the same time. When the paper is held at a certain short distance from the eye—about eight or nine inches—the horizontal line appears black and well defined, while the other is rather grey and indistinct; at a greater distance the upright line seems to be the blacker. The effect is very well shown by the diagram, Fig. 17. To most persons the lines occupying the middle portion will appear either much blacker or much lighter than those at the two ends, though in fact they are exactly alike. When this form of astigmatism is excessive, it may be corrected by the use of spectacles fitted with cylindrical lenses.

Fig. 17.—Effect of Astigmatism.

But there is a different kind of astigmatism—irregular astigmatism it is called—to which every one is more or less a victim, and which cannot be relieved by any artificial appliances. Fortunately it does not often cause much practical inconvenience.

Irregular astigmatism is commonly demonstrated in the following manner. With the point of a fine needle, prick a very small hole in a sheet of tinfoil. Hold up the tinfoil to the light and look at the hole with one eye, the other being closed. Even at the distance of most distinct vision—ten inches or thereabouts,—there will probably be a ragged appearance about the hole, as if it were not perfectly round. But if you bring the tinfoil an inch or two nearer to the eye, the hole will not seem to be even approximately circular; it will assume the form of a little star with five or more distinct rays. The configuration of the star is not generally the same for the right eye as for the left; the rays may differ in number and in relative magnitude, and may be inclined at different angles to the vertical. Fig. 18 shows the stars as they appear to my two eyes, when the illumination is rather strong.

Fig. 18.—Star-like Images of luminous Point.

If several holes are pricked in the tinfoil, each will of course originate a separate star, and all the stars as seen by the same eye will appear to be figured upon the same model, though some may be larger or brighter than others.

Fig. 19.—Sutures of crystalline Lens.

There can be no doubt that the stellate form observed in these experiments, as well as that of the stars of heaven themselves (which with perfect vision would be seen simply as luminous points), is a consequence of the singular structure of the crystalline lens of the eye. This does not consist of one uniform homogeneous mass like a glass lens, but of a number of separate portions pieced together radially, as indicated diagrammatically in Fig. 19. In the eye of a newly-born child there are three such portions, and the radial junctions on one side of the lens are not opposite to those on the other, but are intermediate. In the figure the junctions at the front of the lens are represented by continuous lines and those at the back by dots. The number of sutures found in the adult lens is generally greater than six.

But while it is certain that these radial sutures are in some way closely connected with the luminous rays which appear to proceed from a bright point, it must be confessed that no adequate explanation has yet been given of the precise manner in which the phenomenon is brought about. Ophthalmologists seem to have been contented with vague statements about irregular refraction, but what kind of irregularity would sufficiently account for all the facts of observation has never, so far as I know, been exactly determined. The problem can hardly be very difficult of solution, and would, no doubt, readily yield to the joint efforts of a physicist and a physiologist.

The phenomena of irregular astigmatism as exhibited by a normal eye are exceedingly curious, and perhaps I may be allowed to refer briefly to one or two experiments which I have myself made on the subject.[10]

Fig. 20.—Multiple Images of a luminous Point.

Light from an enclosed electric lamp of twenty-five candle power was admitted through a circular aperture about ¹/12inch (2mm.) in diameter perforated in a brass plate; a sheet of ground glass and another of ruby-red glass were placed behind the aperture. When the little disk of monochromatic light thus formed was looked at through a concave lens of eleven inches focal length from a suitable distance—nearly two feet in my own case—it appeared as seven bright round spots upon a less luminous ground. The appearance is represented in a somewhat idealised form in Fig. 20; but the spots were not quite so distinct nor so regularly disposed as there shown, neither was their configuration exactly the same for the right eye as for the left.

On gradually increasing the distance each circumferential spot became at first elongated radially and afterwards split up into two circular ones; at the same time new spots were developed upon the luminous ground, the approximate symmetry of the figure being still retained. Fig. 21 represents a certain stage in this process of expansion. The appearance was happily likened by an observer who repeated the experiment to that of a large unripe blackberry.

As the distance was still further increased, the spots continued to multiply, ultimately becoming very numerous; their arrangement however soon became much less regular, and the definition of most of them less distinct. At about twenty feet there was seen a luminous patch, roughly circular in outline, and covered with irregular speckles; superposed upon this were strings of bright, partially overlapping spots, corresponding apparently to the sutures of the crystalline lens.

Fig. 21.—Increased number of Images.

When the hole was looked at from a moderate distance through a narrow slit (about ¹/30 inch wide) interposed between the eye and the lens, there was seen only a single row of circular spots, which were arranged sinuously, as shown in Fig. 22. A slight movement of the slit in the direction perpendicular to its length produced a wave-like motion of the circles, suggestive, as pointed out by the excellent observer before referred to of the wriggling of a caterpillar.

Fig. 22.—Multiple Images seen through a Slit.

By sufficiently increasing the distance between the source of light and the eye, as many as twenty-four or twenty-five bright spots might be made to appear in the row, but they could not be counted with any great certainty. At a still longer distance or with a lens of shorter focus (convex or concave) they became less distinct, and finally seemed to be resolved into a multitude of small blurred images—probably several hundreds—which were separated from one another by hazy dark lines.

Fig. 23.—Images of an electric lamp Filament.

I thought that the observations might be rendered easier if the source of light had a more distinctive and conspicuous form than that of a simple circle. Some experiments were therefore made with semi-circular and triangular holes, and these were in some respects preferable; but far better results were afterwards obtained by using as a source of light the horse-shoe shaped filament of an electric lamp, screened by a coloured glass. When such a lamp was looked at through a lens, concave or convex, of about six inches focus, from a distance of a few feet, the roughly oval patch of luminosity formed upon the retina, instead of being a mere ill-defined blur, such as would be produced if the transparent media of the eye were composed of homogeneous substances like glass or water, appeared to be made up of a crowd of separate images of the filament, some being brighter than others, as is shown in the diagram Fig. 23.

Fig. 24A.—Images with horizontal Slit.

Fig. 24B.—Images with vertical Slit.

If a spectroscope slit was interposed between the eye and the lens, and its width suitably adjusted, only a single row of filaments was observed, the appearances with the slit in horizontal, vertical, and intermediate positions being as represented in Fig. 24, A, B, C. As before, it was found possible by gradually retiring from the lamp to bring the number of images up to about twenty-five, but attentive examination showed that most of these really consisted of clusters, each composed of perhaps fifteen or twenty confused images of the filament. A stronger lens still further separated the constituents of the clusters, exhibiting a total number of indistinctly seen images which was estimated to amount to nearly five hundred. Assuming the diameter of the pupil of the eye to be one-fifth of an inch, these observations seem to indicate as a cause of the phenomenon some fairly regular anatomical structure, situated in or near the crystalline lens and composed of elements measuring about ¹/2000 inch in length or breadth. Whether the structure which gives rise to these multiple images is to be found in the fibres of the crystalline lens itself, or in the membranes which cover it, is a question upon which I will not venture an opinion.

Fig. 24C.—Images with oblique Slit.

It is indeed wonderful that an organ affected by peculiarities of which those that have been referred to are merely specimens, should give such well-defined pictures as it does when accommodated for the objects looked at.

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