The stereoscope

by David Brewster

If the object is a white tea-cup, or bowl, however large, and if it is illuminated from behind the observer, the reflected image of the window will be in the concave bottom of the tea-cup, and it will not rise into a convexity if the illumination from surrounding objects is uniform; but if the observer moves a little to one side, so that the reflected image of the window passes from the centre of the cup, then the cup will rise into a convexity, when seen through the inverting telescope, in consequence of the position of the luminous image, which could occupy its place only upon a convex surface. If the concave body were cut out of a piece of chalk, or pure unpolished marble, it would appear neither convex nor concave, but flat.

Very singular illusions take place, both with one and two eyes, when the object, whether concave or convex, is a hollow or an elevation in or upon a limited or extended surface—that is, whether the surface occupies the whole visible field, or only a part of it. If we view, through the inverting telescope or eye-piece, a dimple or a hemispherical cavity in a broad piece of wood laid horizontally on the table, and illuminated by quaquaversus light, like that of the sky, it will instantly rise into an elevation, the end of the telescope or eye-piece resting on the surface of the wood. The change of form is, therefore, not produced by the inversion of the shadow, but by another cause. The surface in which the cavity is made is obviously inverted as well as the cavity, that is, it now looks downward in place of upward; but it does not appear so to the observer leaning upon the table, and resting the end of his eye-piece upon the wooden surface in which the cavity is made. The surface seems to him to remain where it was, and still to look upwards, in place of looking downwards. If the observer strikes the wooden surface with the end of the eye-piece, this conviction is strengthened, and he believes that it is the lower edge of the field of view, or object-glass, that strikes the apparent wooden surface or rests upon it, whereas the wooden surface has been inverted, and optically separated from the lower edge of the object-glass.

In order to make this plainer, place a pen upon a sheet of paper with the quill end nearest you, and view it through the inverting telescope: The quill end will appear farthest from you, and the paper will not appear inverted. In like manner, the letters on a printed page are inverted, the top of each letter being nearest the observer, while the paper seems to retain its usual place. Now in both these cases the paper is inverted as well as the quill and the letters, and in reality the image of the quill and of the pen, and of the lower end of the letters, is nearest the observer. Let us next place a tea-cup on its side upon the table, with its concavity towards the observer, and view it through the inverting telescope. It will rise into a convexity, the nearer margin of the cup appearing farther off than the bottom. If we place a short pen within the cup, measuring as it were its depth, and having its quill end nearest the observer, the pen will be inverted, in correspondence with the conversion of the cup into a convexity, the quill end appearing more remote, like the margin of the cup which it touches, and the feather end next the eye like the summit of the convex cup on which it rests.

In these experiments, the conversion of the concavity into a convexity depends on two separate illusions, one of which springs from the other. The first illusion is the erroneous conviction that the surface of the table is looking upwards as usual, whereas it is really inverted; and the second illusion, which arises from the first, is, that the nearest point of the object appears farthest from the eye, whereas it is nearest to it. All these observations are equally applicable to the vision of convexities, and hence it follows, that the conversion of relief, caused by the use of an inverting eye-piece, is not produced directly by the inversion, but by an illusion arising from the inversion, in virtue of which we believe that the remotest side of the convexity is nearer our eye than the side next us.

In order to demonstrate the correctness of this explanation, let the hemispherical cavity be made in a stripe of wood, narrower than the field of the inverting telescope with which it is viewed. It will then appear really inverted, and free from both the illusions which formerly took place. The thickness of the stripe of wood is now distinctly seen, and the inversion of the surface, which now looks downward, immediately recognised. The edge of the cavity now appears nearest the eye, as it really is, and the concavity, though inverted, still appears a concavity. The same effect is produced when a convexity is placed on a narrow stripe of wood.

Some curious phenomena take place when we view, at different degrees of obliquity, a hemispherical cavity raised into a convexity. At every degree of obliquity from 0° to 90°, that is, from a vertical to a horizontal view of it, the elliptical margin of the convexity will always be visible, which is impossible in a real convexity, and the elevated apex will gradually sink till the elliptical margin becomes a straight line, and the imaginary convexity completely levelled. The struggle between truth and error is here so singular, that while one part of the object has become concave, the other part retains its convexity!

In like manner, when a convexity is seen as a concavity, the concavity loses its true shape as it is viewed more and more obliquely, till its remote elliptical margin is encroached upon, or eclipsed, by the apex of the convexity; and towards an inclination of 90° the concavity disappears altogether, under circumstances analogous to those already described.

If in place of using an inverting telescope we invert the concavity, by looking at its inverted image in the focus of a convex lens, it will sometimes appear a convexity and sometimes not. In this form of the experiment the image of the concavity, and consequently its apparent depth, is greatly diminished, and therefore any trivial cause, such as a preconception of the mind, or an approximation to a shadow, or a touch of the concavity by the point of the finger, will either produce a conversion of form or dissipate the illusion when it is produced.

In the [preceding Chapter] we have supposed the convexity to be high and the concavity deep and circular, and we have supposed them also to be shadowless, or illuminated by a quaquaversus light, such as that of the sky in the open fields. This was done in order to get rid of all secondary causes which might interfere with and modify the normal cause, when the concavities are shallow, and the convexities low and have distinct shadows, or when the concavity, as in seals, has the shape of an animal or any body which we are accustomed to see in relief.

Let us now suppose that a strong shadow is thrown upon the concavity. In this case the normal experiment is much more perfect and satisfactory. The illusion is complete and invariable when the concavity is in or upon an extended surface, and it as invariably disappears, or rather is not produced, when it is in a narrow stripe.