The Echelon Grating.—Since the resolving power of a grat ing is proportional to the product (mN) of the order of the spectrum and the total number of rulings, it may be increased in either of two ways. The first is to increase the number of rulings, but a limit is set to this by the practical difficulty of maintaining the rulings at a constant distance apart. The alterna tive method, which cannot be carried far with gratings of ordinary construction, is to use higher orders of spectrum. This, however, is very effectively done by a form of grating called the echelon, which was devised by Michelson in order to throw most of the light into one or two spectra of very high order. A number of glass plates of equal thickness (usually about a centimeter) and equal breadth, but each shorter than its predecessor by an equal amount (which may be about a millimeter) are superposed on each other to form a series of steps, like a staircase. Parallel light from a collimator, with the slit parallel to the edges of the steps, is then passed through the larger end. At each step the light is retarded by an equal amount, and diffraction spectra are produced when the light is focussed by a lens in the usual way.
Echelon gratings have been very successfully produced by Adam Hilger, Ltd., London, and an example given by this firm will illustrate the possibilities of such gratings. If the number of plates be 21, thickness, io mm., and height of step, i mm., while the refractive index for X5,890 is 1-5746, the instrument should be capable of separating lines about this wave-length which differ by only 0.027 angstrom units; in other words, the resolving power would be 218,00o, and the order of spectrum observed would be the ro,38oth. The successive orders are very close together, and on this account the light from the source is first passed through a spectroscope so that an image of the spectrum is focussed on the slit of the echelon instrument; only a very small range of wave-lengths then passes through. The lines are usually observed in the direction of the incident light, and under these conditions practically all the light is concentrated in a single order.
The echelon is clearly not intended for ordinary spectroscopic observations, but it is very valuable for analysing the fine struc ture of individual lines, small displacements of lines produced by pressure or other change of experimental conditions, and for revealing the close components into which a line may be split under the influence of a strong magnetic field. (See ZEEMAN
EFFECT.) Other High-Resolution Instruments.—Other instruments in which the effect of a large path-difference is used to produce high resolution are the Fabry-Perot interferometer and the Lum mer-Gehrcke parallel-sided glass or quartz plate. (See LIGHT.) In each of these instruments, light from the original source is divided into a number of component beams of comparable intens ity, which re-unite after having traversed paths differing succes sively by equal distances of perhaps a few centimetres. Rein forcement, giving a bright line or fringe, will take place when the effective path difference of neighbouring beams is an integral multiple of the wave-length, and it is readily seen that large path differences correspond to high resolution. For consider two neigh bouring wave-lengths, X and Xd-dX. The path difference, e, corresponding to m waves of the one will be equal to mX, and that corresponding to m waves of the other will be m(X-I-dX). The difference between these two quantities—i.e., the interval between the positions of reinforcement for the two waves—will thus be mdX= e.dX/X=e/R, where R is the resolving power. If, therefore, this interval be regarded as constant, at the value which just allows the wave-lengths to be distinguished, it is clear that R increases proportionately to e.