VISION AND OPTICAL ILLUSIONS—THE EYE DESCRIBED—ACCOMMODATION OF THE EYE—CHROMATIC ABERRATION—SPINNING TOPS. The eye is an optical instrument that may be compared with those constructed by physicists themselves; the media of which it is composed have surfaces like those which enter into the construction of optical instruments. It was Kepler who at the end of the eighteenth century discovered the passage of light into the eye. Soon after the discovery of the inner chamber he found that the eye realized the conditions that Porta had combined to obtain the reflection of external objects. Fig. 95.—Structure of the eye. We will now briefly state that the coats of this organ are constituted of a fibrous membrane, T (fig. 95), termed sclerotic, which is opaque, except in the anterior portion of the eye, where it forms the transparent cornea. The crystalline, C, enshrined behind the cornea, is the convergent lens of the inner chamber; it is covered with a transparent membrane, or capsule, and is bathed in two fluids, the aqueous humour, between the crystalline humour and the cornea, and the vitreous body, a gelatinous humour lodged between the crystalline and the back of the eye. The image of exterior objects which is produced by the passage of light through these refracting surfaces, is received by a nervous membrane, the retina, B, formed by an expansion of the optic nerve, N. We must also mention the choroid, a membrane lined with a dark pigment, which absorbs the light, and prevents interior reflections, and in front of the crystalline lens, a curtain with an opening, H, called the iris, which gives to the eyes their colour of blue, grey, or black. The opening in the centre of the iris is called the pupil. The penetration of light through the surfaces of the eye is easily demonstrated. An object throws divergent rays on the cornea, a part penetrates into the eye and falls upon the retina, leaving a perfectly retained image of the object. Magendie has proved in the following manner the truth of this mathematical deduction. The eye of a rabbit is very similar to an Fig. 96.—Diagram of mode of vision. We will now point out in what distinct vision consists. A screen placed behind a lens will only receive the image of a lighted object, A B, if placed in a position, R R (fig. 96). If placed nearer at R R, or further off at R´ R´, the light from the object is thrown on the screen, and the image is confused. To prove the imperfection of sight which is shown by the application of these theoretic rules, MM. Boutan and d’AlmÉÏda10 cite the following experiment:—If the head of a pin is placed from one to two inches from the eye, nothing will be perceived but a confused haziness of vague outline. The distance of distinct vision is that at which an object of small dimensions may be placed to be plainly perceived. This distance, which averages fifteen inches, varies with different individuals. It can be determined for different sights by means of an apparatus constructed by Lepot. A white thread, a, is stretched horizontally on a dark board (fig. 97). We look at it by placing our eye at one end behind a little screen pierced with an aperture, O; it then appears much reduced in length, but either nearer or farther off it seems to enlarge and swell, having the appearance of a white surface, becoming larger and larger in proportion as we move away from the point at which it is seen most distinctly. In this manner we can easily obtain a measure of the distance of distinct vision. One of the most remarkable properties of the eye consists in the faculty which this organ possesses of seeing different distances. If we consider it as a dark chamber, there is but one distance at which an object will be perfectly visible; nevertheless a metal wire, for example, can be seen as well at a distance of seven, as ten, fifteen, or twenty inches by good sights. Fig. 97.—Experiment for sight. This faculty of accommodation in the eye is thus demonstrated: we place two pins, one in front of the other, one eye only being open; we first look at the nearest pin, which appears confused if it is near the eye, but by an effort of will the image becomes clear. If, while preserving the clearness of the image, we then carry our attention to the second pin, we find that it, too, presents a confused appearance. If we make an effort to distinguish the Fig. 98.—M. Cramer’s experiment. Fig. 99.—Images in the eye. 1. That the image, A, formed on the surface of the cornea, remains the same size in both cases; the form of the cornea therefore remains unaltered. 2. That the image, B, formed on the upper surface of the lens, diminishes in proportion as the eye is nearer the object; the surface therefore becoming more and more convex, as the focal distance diminishes—a result indicated by the theory that it is possible in the vision of near objects to receive the image on the retina. 3. That the third image, C, produced on the posterior surface of the lens, remains nearly invariable. We may confirm Cramer’s statements by an easy experiment. We place ourselves in front of the eye of someone who looks in turn at two objects placed on the same black line at unequal distances from him, and are able to distinguish by the dimension of the images of the candle, which object it is that he is regarding. M. Helmholtz has carried M. Cramer’s methods to perfection, and has been able to formulate a complete theory of all the phenomena of accommodation. The laws of optics show that the rays emitted by a luminous point may unite at another point by the action of the refracting surfaces of the eye. Nevertheless, a white light being composed of rays of diverse refrangibility, particular effects, known under the name of chromatic aberration, are produced through the decomposition of light, which we will proceed to study, under M. Helmholtz’s auspices11. There is another kind of aberration of luminous rays of one colour emitted through a hole, which generally only approach approximately to a mathematical focus, in consequence of the properties of refracting surfaces; it is called aberration of sphericity. The phenomena are as follows:— Fig. 100. 1. We take for our object a very small luminous point (the hole made by a pin in some black paper, through which the light passes), and having also placed before the eye a convex glass, if we are not near-sighted, we fix it a little beyond the point of accommodation, so that it produces on the retina a little circle of diffusion. We then see, instead of the luminous point, a figure representing from four to eight irregular rays, which generally differ with both eyes, and also with different people. We have given the result of M. Helmholtz’s observations in fig. 100; a corresponds to the right eye, and b to the left. The outer edges of the luminous parts of an image, produced in this way by a white light, are bordered with blue; the edges towards the centre are of a reddish yellow. The writer adds that the figure appears to him to have greater length than breadth. If the light is feeble, only the most brilliant parts of the figure can be seen, and several images of the luminous point are visible, of which one is generally more brilliant than the others. If, on the other hand, the light is very intense,—if, for example, the direct light of the sun passes through a small opening,—the rays mingle with each other, and are surrounded by aureola of rays, composed of numberless extremely fine lines, of all colours, possessing a much larger diameter, and which we distinguish by the name of the aureola of capillary rays. Fig. 101. The radiating form of stars, and the distant light of street-lamps belong to the preceding phenomena. If the eye is accommodated to a greater distance than that of the luminous point,—and for this purpose, if the luminous point itself is distant, we place before the eye a slightly convex lens,—we see another radiating image appear, If the pupil is covered on one side, the side opposite to the image of diffusion disappears; that is to say, that part of the retinal image situated on the same side as the covered half of the pupil. This figure, then, is formed by rays which have not yet crossed the axis of the eye. If we place the luminous point at a distance to which the eye can accommodate itself, we see, through a moderate light, a small, round, luminous spot, without any irregularities. If the light, on the contrary, is intense, the image is radiated in every position of accommodation, and we merely find that on approaching nearer, the figure which was elongated, answering to a distant accommodation, gradually diminishes, grows rounder, and gives place to the vertically elongated figure, which belongs to the accommodation of a nearer point. When we examine a slender, luminous line, we behold images developed, which are easily foreseen, if for every point of the line we suppose radiating images of diffusion, which encroach on each other. The clearest portions of these images of diffusion mingle together and form distinct lines, which show multiplied images of the luminous line. Most persons will see two of these images; some, with the eyes in certain positions, will see five or six. Fig. 102. To show clearly by experiment the connection existing between double images and radiated images from points, it is sufficient to make in a dark sheet of paper a small rectilinear slit, and at a little distance from one end, on a line with the slit, a small round hole, as shown at a in fig. 102. Looking at it from a distance we shall see that the double images of the line have exactly the same distance between them that the most brilliant parts of the starred figure of diffusion have from the point, and that the latter are in a line with the first, as will be seen at b (fig. 102), where in the image of diffusion of the luminous point, we only see the clearest parts of star a of the figure. On lighted surfaces, to which the eye is not exactly accommodated, multiplied images are often remarked through the passage from light to darkness being made by two or three successive steps. A series of facts which have been collected under the title of irradiation, and which show that brightly-lighted surfaces appear larger than they are in reality, and that the dark surfaces which surround them appear diminished to a corresponding degree, explains this by the circumstance that the luminous sensation is not proportional to the intensity of the objective light. These phenomena affect very various appearances, according to the form of respective figures; they are generally seen with the greatest ease and intensity when the eye is not exactly accommodated to the object examined, either by the eye being too near or too far off, or by using a concave or convex lens, which prevents the object being seen clearly. Irradiation is not completely wanting, even when the accommodation is exact, and we notice it clearly in very luminous objects, above all when they are small; small Fig. 103.—Experiment 1. 1. Luminous surfaces appear larger. We can never judge exactly of the dimensions of a slit or small hole through which a bright light escapes; it always appears to us larger than it really is, even with the most exact accommodation. Similarly, the fixed stars appear in the form of small luminous surfaces, even when we make use of a glass which allows of perfect accommodation. If a gridiron with narrow bars—the spaces intervening being exactly equal to the thickness of the bars—is held over a light surface, the spaces will always appear wider than the bars. With an inexact accommodation, these phenomena are still more remarkable. Fig. 103 exhibits a white square on a black foundation, and a black square on a white foundation. Although the two squares have exactly the same dimensions, the white appears larger than the black, unless with an intense light and an inexact accommodation. Fig. 104.—Experiment 2. 2. Two adjacent luminous surfaces mingle together. If we hold a fine metallic wire between the eye and the sun, or the light of a powerful lamp, we shall cease to see it; the lighted surfaces on all sides of the wire in the visual range pass one into the other, and become mingled. In objects composed of black and white squares, like those of a draught-board (fig. 104), the angles of the white squares join by irradiation, and separate the black squares. 3. Straight lines appear interrupted. If a ruler is held between the eye and the light of a bright lamp or the sun, we perceive a very distinct hollow on the edge of the ruler in the part corresponding to the light. When one point of the retina is affected by a light which undergoes periodical and regular variations, the duration of the period being sufficiently short, there results a continuous impression, like that which would be produced if the light given during each period were distributed in an equal manner through Fig. 105.—Disc which appears uniformly grey by reason of its rotation. If we paint on a disc a coloured star, which is detached from a foundation of another colour (fig. 106), during the rapid rotation of the disc the centre affects the colour of the star; the outer circle assumes that of the background, and the intermediate parts of the disc present the continuous series of the resultant colours. These results are in accordance with the theory of the mixture of colours. Fig. 106.—Disc with a star painted on the background of another colour. Rotative discs, which are so much used in experiments in optical physiology, were employed for the first time by MÜsschenbroeck; the most simple is the top. M. Helmholtz ordinarily uses a brass spinning-top, which fig. 107 represents at a third the natural size. It is set in motion by the hand, and its quickness may be increased or moderated at will; but it cannot be made to spin quicker than six rounds in a second; this motion will be kept up for three or four minutes. Thus, with a feeble movement of rotation, a uniform luminous impression can only be obtained by dividing the disc into four or six sections, on each of which we repeat the same arrangement of colours, light, and shade. If the number of repetitions of the design is less, we obtain, with a bright light, a more or less shot-coloured disc. Fig. 107.—M. Helmholtz’s top for studying the impression of light on the retina. It is easy to place designs on the disc, even when in motion, or to make any desired modification, by superposing on the first disc another disc with sectors, of which we can vary the position by slightly touching it, or even blowing on it, thus producing during the rotation of the disc very Fig. 108.—Spinning a top with coloured discs. Fig. 109.—Top for experiments demonstrating Newton’s theory of the mingling of colours. Fig. 110.—Disc. Besides tops, we may make use of different kinds of discs, with an axis rotating between two clamps; they are moved either by a kind of clock-work, or by the unrolling of a string, like the tops. Generally, however, these contrivances have this inconvenience, that the discs cannot be changed without stopping the instrument, and partly taking it to pieces. On the other hand, we have the advantage of being able to turn them on a vertical plane, so that we can conveniently carry on our experiments before a numerous auditory, which is a more difficult matter with tops. Montigny contrived to obtain the mingling of colours by means of a turning prism, which he caused to throw its shadow on a white screen. The Thaumatrope is a small rectangle of cardboard, which is made to rotate on an axis passing through the centres of the longest sides. We shall describe it at greater length when we come to consider a new apparatus known under the name of the Praxinoscope. Fig. 111.—Busold’s chromatic top. More complicated contrivances have also been constructed on the same principle, by which one may perceive the rotating disc through slits which turn at the same time. We will now describe the construction of some discs invented by Plateau under the name of the Phenakistoscope. These discs are made of strong cardboard, from six to ten inches in diameter (fig. 112), on which a certain number of figures (eight to twelve) are placed Fig. 112.—Rotating disc. Fig. 113.—Mr. Dancer’s top. Phenomena of successive contrast develop what are called accidental images. If we fix our eyes for a considerable time on a coloured object, Phenomena of simultaneous contrast arise from the influence exercised over each other by different shades and colours which we see simultaneously. That we may be certain that we have really obtained phenomena of this kind, the experiments must be arranged in such a manner that accidental images are not produced, and that the part of the retina affected by the sensation of colour does not receive, even momentarily, a passing image. Fig. 114.—Disc, which exhibits, when in rotation, a series of concentric rings. The phenomena of simultaneous contrast appear with the greatest clearness with slight differences of colour, and are therefore exactly the contrary of phenomena of successive contrast, which are favoured by strong oppositions of colour and light. We can, in general, characterise phenomena of simultaneous contrast as governed by this law, common to all perceptions of the senses: the differences clearly perceived appear greater than the differences equal to them, but perceived with greater difficulty, either because they only affect the observation in an uncertain manner, or that the memory fails to judge of them. A man of middle height appears small beside a tall man, because at the moment it is forcibly impressed on us that there are taller men than he, and we lose sight of the fact that there are smaller. The same man of medium height appears tall beside a man of small stature. We can easily make experiments on simultaneous contrast with a sheet of transparent paper. We fasten together a sheet of green and a sheet of rose-coloured paper, so as to obtain a sheet half red and half green. On the line of separation between the two colours we place a strip of grey paper, and cover the whole with a sheet of thin letter-paper of the same size. The grey strip will then appear red at the edge touching the green, and green at the edge touching the red; the centre presenting an intermediate shade. It presents a still more decided appearance if the grey strip is perpendicular with the All the experiments we have described afford great interest to the student; they can easily be performed by those of our readers who are particularly interested in these little-known subjects. Any one may construct the greater part of the appliances we have enumerated, and others can be obtained at an optician’s. The discs in particular are extensively manufactured, and with great success. A mirage |