Page:Encyclopædia Britannica, Ninth Edition, v. 14.djvu/612

592 LIGHT

Fig. 14.

Spectrum.

If A be a narrow bright line of light, parallel to the edge of the prism, it will appear to be drawn out into a rectangle consisting of images of the line ranged parallel to one another, and due to the various homogeneous constituents of white light in order of their refrangibility. If the light do not contain rays of every degree of refrangibility, some of these images will be wanting, and there will be corresponding dark lines or bands crossing this spectrum (as it is called). The amount by which any part of this spectrum is shifted from the true position of the bright slit depends (cæteris paribus) upon the amount of the refraction. It also depends on the angle of the prism. And, for a given angle, the length of the spectrum depends upon the difference between the refractive indices for the red and the violet rays. This is called the dispersion.

Dispersion.

If a second prism, of the same glass, and of the same angle, as the first, be placed in a reversed position behind it (as indicated by the dotted lines in the figure), the effect of the two would be simply that of a plate of glass with parallel faces; the emergent rays would each be parallel to its original direction, and there would be no separation of colours. The reversed prism would therefore undo the work of the direct prism. Then we should have no dispersion, but we should also have no refraction. We have, however, as has already been shown, an increase of divergence, i.e., the image is nearer to the eye than the object. Blair, Brewster, and Amici devised combinations of two pairs of prisms of the same glass, those of each pair having their edges parallel, such that the combination acted as a sort of achromatic telescope of low power.

Newton, from some rough experiments, hastily concluded that the amount of dispersion is in all substances proportional to that of the refraction. If such were the case it is easy to see that prisms of two differently refracting materials and of correspondingly different angles, combined (is above described) so as to annul the dispersion, would likewise annul the refraction. Thus Newton was led to suppose that refraction without dispersion is impossible.

Achromatism.

It was found by Hall in 1733, and afterwards (independently) by Dollond, that this idea is incorrect – that, in fact, we have in certain media large refraction with comparatively small dispersion, and vice versa, and thus that the dispersion may be got rid of while a part of the refraction remains. James Gregory had previously conjectured that this might be done by using, as is done in the eye, more media than one. Thus we have for certain specimens of flint and crown glass, whose optical constants were carefully measured by Fraunhofer, the following values of the refractive index for three definite kinds of homogeneous light: –

C D F Flint glass 1-6297 1-6350 1-6483 Crown glass 1-5268 1-5296 1-5360

The rays C and F are in the red and greenish blue respectively, and are given off by incandescent hydrogen. D is the orange-yellow ray of sodium.

When the angle of the prism is very small (the only case we treat here), we may consider Arv as approximately a straight line, whose length is (cæteris paribus) proportional to the angle of the prism. Also the distances Ar, Av, are to one another in the proportion of the refractive indices of red and violet rays, each diminished by unity. Hence, for a prism of flint glass such as was employed by Fraunhofer, the distances from A to its images formed by these three kinds of homogeneous light respectively are very nearly as

630, 635, 648.

When a prism of crown glass is used they are nearly as

527, 530, 536.

The. differences between the numbers for C and F are

For flint glass 18 , , crown glass 9

or as 2:1. Hence if we make the small angle of the crown- glass prism twice that of the flint, and observe A through the two prisms, with their edges turned in opposite direc tions, the C and F images will coincide. Both, however, will be displaced fro:n the real direction of A as if a prism had been employed, with its edge turned as that of the crown glass was, and to the same extent as that prism would have displaced them had its refractive index been about 1 21 and the same for the two kinds of light C and F. In fact, the displacements by the flint prism are as

630, 648,

and those by the crown prism (to the opposite side) are as

1054, 1072.

The differences, in favour of the crown prism, are as

424, 424.

Irrationality of dispersion.

This combination of prisms is called achromatic, or colourless, but is not perfectly so. For if we inquire into the displacement of the D image, we find that it is as

635

for the flint prism; but as

1060

in the opposite direction, for the crown prism. Hence its whole displacement is as

425,

a little greater than that common to C and F. The reason for this is obvious from Fraunhofer's numbers given above. The interval from C to D is to that from C to F in a greater ratio in crown than in flint glass, – so that the spectra given by these media are not similar. The rays of higher refrangibility are more separated in proportion to those of lower refrangibility in flint than in crown glass. This is the irrationality of dispersion – which, so far as we yet know, renders absolute achromatism unattainable. Three lenses in combination give a better attempt at achromatism than can be made with two; and some re-