122
Light Waves and Their Uses
The efficiency of the grating depends on the order m of the spectrum and the number n of lines in the grating, /. e., on the product of the two. Hitherto the efforts of makers of gratings have been directed toward increasing n as much as possible by making the total number of lines in the grating as great as possible. It has been found that as many as 100,000 lines can be ruled side by side on a metallic surface; but in ruling 100,000 lines it is extremely difficult
FIG. 88
to get them in their proper position. Very little attention has as yet been directed toward producing a spectrum of a very high order. The chief reason for this is that the intensity of the light in the spectra of higher orders diminishes very rapidly as the order increases. The first spectrum is by far the brightest; the second has an intensity of something like one-third of the first, and the succeeding spectra are still fainter. There have been, occasionally, gratings in which the diamond point happened to rule in such a way as to throw an abnormal proportion of light in one spectrum. Such are exceedingly rare and exceedingly valuable. It seems to be a matter of chance whether the diamond rules such gratings or not. It was with the double purpose of multiplying the order of the spectrum, and at the same time of throwing all the light in one spectrum, that the instrument shown in Fig. 88 was devised.
Action of Magnetism on Light Waves 123
The method of reasoning which led to the invention of this instrument may be of interest. We will suppose that, in order to throw the light in one spectrum, the diamond j>oint could be made to rule a grating with a section like that shown in Fig. 89, the distance between the steps being exactly equal and the surfaces of the grooves perfectly polished.
Suppose that the light came in the direction indicated nearly normal to the surface of the groove. The light would be reflected back in the opposite direction, and that
which came from each _
FIG. 89
successive groove
would differ in phase from that from the adjacent grooves by a number of waves corresponding to double the difference in path. The retardation, instead of being one wave, would be twice the number of waves in this distance. If the distance between the grooves were very large, the number of waves in this distance would also be very large, so that the order of the resulting spectrum would be correspondingly high. Further, almost all the light returns in one direction, so that the spectrum we are using will be as bright as possible.
We have thus shown, at least theoretically, the possibility of producing a very high order of spectrum, and at the same time of getting almost all the light in one spectrum. However, the necessary condition is that the distances between the grooves be equal within a very small fraction of a light wave. This is a difficult, but not a hopeless, problem. In fact, we may obtain the desired retardation