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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 albino’s; that is to say, the choroid contains no black pigment, but a transparent matter, and when placed before a brilliant object, the image can be seen inverted on the retina. The experiment succeeds also with the eye of a sheep or a cow, if the sclerotic has been lessened. The optic centre of the eye is the point where the secondary axes cross; the optic axis passes through the geometrical axis of the organ, and directs itself spontaneously towards the point that attracts the eye.

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 contour of the second pin, we at last succeed, and the first once more appears ill-defined. It is only since the experiments of M. Cramer and M. Helmholtz that the explanation of this phenomenon could have been given. M. Cramer has succeeded in determining on the living eye the curved ray of the cornea, and of the two surfaces of the crystalline lens. In so doing he followed Samson’s method, and observed the images thrown by a luminous object, whose rays strike the different refracting surfaces of the eye. A candle, L (fig. 98), is placed before the eye, O, and throws as in a convex mirror a straight image of the flame, A (fig. 99). The other portion of the light, which has penetrated the pupil, falls on the crystalline lens, and produces likewise a second straight image, B. Then the light refracted by the lens reaches the posterior surface; a portion is reflected on a concave mirror, and gives the inverted image, C, very small and brilliant. M. Cramer observed it through a microscope, and studied the variations in the size of images when the eye passed from the observation of adjacent to distant objects. He stated:—

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. We make a narrow opening in a screen, and fix behind this opening a violet glass, penetrable only by red and violet rays. We then place a light, the red rays of which reach the eye of the observer after having passed through the glass and the opening in the screen. If the eye is adapted to the red rays, the violet rays will form a circle of diffusion, and a red point encircled with a violet aureola is seen. The eye may also be brought to a state of refraction, so that the point of convergence of the violet rays is in front, and that of the red rays behind the retina, the diameters of the red and violet circles of diffusion being equal. It is then only that the luminous point appears monochromatic. When the eye is in this state of refraction, the simple rays, whose refrangibility is maintained between the red and the violet rays, unite on the retina.

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, which M. Helmholtz represents thus (fig. 101): at c as it is presented to the right eye, and at d as seen by the left.

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 circles of diffusion increase relatively the dimensions of small objects much more than of large ones, with regard to which, the dimensions of the small circles of diffusion which the eye furnishes, when properly accommodated, become insensible.

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 throughout the whole duration of the period. To verify the truth of this law, we will make use of some discs, such as that represented in fig. 105. The innermost circle is half white and half black; the middle circle has two quarters, or half its periphery, white, and the outer circle has four eighths’ white, the rest being black. If such a disc is turned round, its entire surface will appear grey; only it is necessary to turn it with sufficient force to produce a continuous effect. The white may also be distributed in other ways, and provided only that on all the circles of the disc the proportion of the angles covered with white is the same, they will always exhibit the same grey colour. Instead of black and white we may make use of different colours, and obtain the same resultant colour from all the circles, when the proportion of the angles occupied by each of the colours in the different circles is the same.

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 varied modifications. If, for instance, we place on a disc covered with blue and red sectors of equal size, a black disc, of which the sectors are alternately filled in or empty, the disc, as it turns round, will appear blue if the black sectors of the upper disc exactly cover the [red] sectors of the lower disc; and it appears red, if, on the contrary, the blue sectors are covered with the black; while in the intermediate positions we obtain different mixtures of red and white, and during the rotation of the disc may vary the colour insensibly by a gentle touch. By dividing the different sectors with broken or curved lines, instead of straight ones, we can produce an arrangement of coloured rings of great variety and beauty. To give the top greater speed, we set it in motion by drawing a string twined round its stem. The simplest method, as shown in fig. 108, consists in the employment of a handle similar to that of the German top. It is a hollow cylinder of wood set into a handle with two circular holes; and at right angles with these is a groove for the passage of the string. The stem of the top is passed through the holes of the cylinder, one end of the string is fixed in the small hole in the stem, and is rolled round by turning the top in the hand. The part of the stem on which the string is twisted becomes sufficiently thick for the top to remain suspended to the handle; then holding it a little above the table, and giving the string a powerful pull, we set the top in motion, and as the string unrolls it falls on the table, where it will continue its rotation for some time. The top represented in fig. 109 is constructed so that the discs may be firmly pressed by the stem, which is necessary in experiments for demonstrating Newton’s theory of the mingling of colours. We make use for this purpose of a variety of discs, made of strong paper of different sizes, having an opening in the centre and a slit, as in fig. 110; each of the discs is covered uniformly with a single colour; and if two or more are superposed, with their slits placed one over the other, we obtain sectors, the size of which we may vary at will, so that we can modify in a continuous manner the proportions of the colours. The most perfect construction is that of Busold’s chromatic top (fig. 111), which should only be employed for very rapid rotations. The disc, which weighs 5 lbs., is made of an alloy of zinc and lead, about an inch and a quarter in diameter. The brass axis terminates at its lower end with a blunt point of untempered steel; the cylindrical part of the axis is roughened to encourage the adherence of the string; the axis is placed between the clamps of a vice, and a plate is put underneath; we then pull the string firmly with the right hand, and when the top is in motion it is separated from the clamps. By pulling the string very powerfully it is possible to obtain a speed of sixty turns in a second, and the movement will be kept up for three quarters of an hour.

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 in circles at an equal distance from each other, presenting the successive phases of a periodical movement. This disc is placed on another opaque circle of rather larger diameter, which has on its margin as many openings as the first disc has figures. The two discs are placed one on the other, and are fixed in the centre by means of a screw at the anterior extremity of a small iron axis, the other end being fitted into a handle. To make use of this contrivance we place ourselves in front of the glass, towards which we turn the disc with the figures, placing the eye so as to see the figures through one of the holes of the large disc. Directly the apparatus begins to turn round, the figures seen in the glass appear to execute the particular movements which they represent in different positions. Let us designate by means of the figures 1, 2, 3, the different openings through which the eye successively looks, and point out by the same numbers the figures in the radiuses thus numbered. If the experimenter looks in the glass through opening 1, he will see first figure 1, which appears in the glass to pass before his eyes; then the rotation of the disc displaces opening 1, and the cardboard intervenes, until opening 2 appears; then figure 2 takes the place of figure 1, until it in turn disappears, and opening 3 presents figure 3 to view. If these figures were all similar, the spectator would have but a series of visual impressions, separate but alike, which by a sufficiently rapid rotation mingle together in one durable impression like a perfectly immovable object. If, on the contrary, the figures differ slightly from each other, the luminous sensations will also mingle in a single object, which will however appear to be modified in a continuous manner, conformably with the differences of successive images. With a difference of speed, we obtain a new series of phenomena. A most simple contrivance of this kind is a top of C. B. Dancer, of Manchester (fig. 113). It will be seen that the axis carries another disc, pierced with openings of different shapes, to the edge of which a thread is attached. This second disc is carried along by the friction of the axis, but its rotation is less rapid because of the great resistance offered by the air to the piece of thread which participates in the movement. If the lower disc has several differently-coloured sectors, they produce a very motley appearance, which seems to move sometimes by leaps, and sometimes by continuous motion. We must distinguish between the phenomena of successive contrast and simultaneous contrast.

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, and then suddenly direct them towards a uniform white surface, we experience the sensation of the object as it is, but it appears coloured with a complementary tint; that is to say, it has the colour which, superposed on the genuine tint, we obtain from pure white. Thus a red object produces a consecutive green object. The experiment can be tried by gazing at the sun when it is setting, and then directing one’s eyes towards a white wall in the same direction.

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 line of separation of the two colours; the piece of grey then stretching into the green will present as deep a red as the red foundation on the other side. If the line of grey colour exactly covers the line of separation between the two colours, the contrasting colour is more feeble; the edges of the grey paper then present complementary strips of colour. Similar effects may be obtained by superposing, in gradually diminishing layers, strips of thin paper, so as to form successive bands of different thicknesses. If it is then lit up from behind, the objective intensity is evidently constant through the extent of each layer; nevertheless every strip appears darker at the edge touching a more transparent layer, and lighter at the edge in contact with a thicker layer. The dull tints of China ink, superposed in layers, will produce a similar effect. The phenomena are produced by means of rotative discs of most beautiful and delicate gradations of colour. Let us give the sectors of the disc the form represented by fig. 114, and make them black and white; and when in rotation we shall see a series of concentric rings of a shade that becomes darker and darker towards the centre. The angular surface of the dark portions is constant in each of these rings. The intensity, therefore, of each ring is uniform during rapid rotation; it is only between one ring and another that the intensity varies. Each ring also appears lighter on its inner side when it borders on a darker ring, and darker on its outer side when in contact with a lighter ring. If the differences of intensity in the rings are very slight, one can scarcely judge sometimes if the inner rings are darker than the outer; the eye is only struck by the periodical alternations of light and shade presented by the edges of the rings. If, instead of white and black, we take two different colours, each ring will present two colours on its two edges, although the colour of the rest of the ring will be uniform. Each of the constituent colours presents itself with more intensity on that edge of the ring which borders on another ring containing a smaller quantity of the colour. Thus, if we mix blue and yellow, and the blue predominates in the exterior and the yellow in the interior, every ring will appear yellow at its outer, and blue at its inner edge; and if the colours present together very slight differences, we may fall into the illusion which causes the differences really existing between the colours of the different rings to disappear, leaving instead, on a uniformly coloured background, the contrasting blue and yellow of the edges of the rings. It is very characteristic that in these cases we do not see the mixed colours, but seem to see the constituent colours separately, one beside the other, and one through the other.

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.