The stereoscope

by David Brewster

Before proceeding, however, to this subject, we must explain the manner in which half and quarter lenses unite the two dissimilar pictures.

Fig. 17.

In [Fig. 17] is shewn a semi-lens mn, with its section m′n′. If we look at any object successively through the portions aa′a″ in the semi-lens mn, corresponding to aa′a″ in the section m′n′, which is the same as in a quarter-lens, the object will be magnified equally in all of them, but it will be more displaced, or more refracted, towards n, by looking through a′ or a′ than through a or a, and most of all by looking through a″ or a″, the refraction being greatest at a″ or a″, less at a′ or a′, and still less at a or a. By means of a semi-lens, or a quarter of a lens of the size of mn, we can, with an aperture of the size of a, obtain three different degrees of displacement or refraction, without any change of the magnifying power.

If we use a thicker lens, as shewn at m′n′nm, keeping the curvature of the surface the same, we increase the refracting angle at its margin n′n, we can produce any degree of displacement we require, either for the purposes of experiment, or for the duplication of large binocular pictures.

When two half or quarter lenses are used as a stereoscope, the displacement of the two pictures is produced in the manner shewn in [Fig. 18], where ll is the lens for the left eye e, and l′l′ that for the right eye e′, placed so that the middle points, no, n′o′, of each are 2½ inches distant, like the two eyes. The two binocular pictures which are to be united are shewn at ab, ab, and placed at nearly the same distance. The pictures being fixed in the focus of the lenses, the pencils ano, a′n′o′, bno, b′n′o′, will be refracted at the points n, o, n′, o′, and at their points of incidence on the second surface, so as to enter the eyes, e, e′, in parallel directions, though not shewn in the Figure. The points a, a, of one of the pictures, will therefore be seen distinctly in the direction of the refracted ray—that is, the pencils an, ao, issuing from a′, will be seen as if they came from a′, and the pencils bn, bo, as if they came from b′, so that ab will be transferred by refraction to a′b′. In like manner, the picture ab will be transferred by refraction to a′b′, and thus united with a′b′.

Fig. 18.

The pictures ab, ab thus united are merely circles, and will therefore be seen as a single circle at a′b′. But if we suppose ab to be the base of the frustum of a cone, and cd its summit, as seen by the left eye, and the circles ab, cd to represent the base and summit of the same solid as seen by the right eye, then it is obvious that when the pictures of cd and cd are similarly displaced or refracted by the lenses ll l′l′, so that cc′ is equal to aa′ and dd′ to bb′, the circles will not be united, but will overlap one another as at c′d′, c′d′, in consequence of being carried beyond their place of union. The eyes, however, will instantly unite them into one by converging their axes to a remoter point, and the united circles will rise from the paper, or from the base a′b′, and place the single circle at the point of convergence, as the summit of the frustum of a hollow cone whose base is a′b′. If cd, cd had been farther from one another than ab, ab, as in Figs. [20] and [21], they would still have overlapped though not carried up to their place of union. The eyes, however, will instantly unite them by converging their axes to a nearer point, and the united circles will rise from the paper, or from the base ab, and form the summit of the frustum of a raised cone whose base is a′b′.

In the preceding illustration we have supposed the solid to consist only of a base and a summit, or of parts at two different distances from the eye; but what is true of two distances is true of any number, and the instant that the two pictures are combined by the lenses they will exhibit in relief the body which they represent. If the pictures are refracted too little, or if they are refracted too much, so as not to be united, their tendency to unite is so great, that they are soon brought together by the increased or diminished convergency of the optic axes, and the stereoscopic effect is produced. Whenever two pictures are seen, no relief is visible; when only one picture is distinctly seen, the relief must be complete.