When there are several prisms, the algebraical sum is to be taken as in the case of dispersion. A prism of ordinary flint glass of about i cm. base is thus found to have a resolving power for sodium yellow light of about i,000, while a prism of io cm. base would have a resolving power of io,000.
Purity of Spectrum.—In practice, it is necessary to give the slit a finite breadth, and the actual separating power must ac cordingly always be less than the theoretical resolving power.
Types of Gratings.—The diffraction grating is of great im portance to the spectroscopist as providing him with the means of producing spectra of great dispersion and purity. The first gratings were made by Fraunhofer about 1820, by winding thin wire over two fine screws of equal pitch kept an inch or two apart by bars of metal ; the wires were soldered to the screws, and the whole framework was sawn in two along the axes of the screws, so as to make two gratings. With these wire gratings Fraunhofer was able to measure the wave-length of sodium light with considerable accuracy.
Modern gratings are made by ruling equidistant parallel lines with a diamond point on a plate of glass or speculum metal. Those in most general use have about i 5,000 lines per inch, but good gratings with 30,000 lines per inch have been ruled and may some times be used with advantage. Among the most successful in the production of gratings was H. A. Rowland, of Baltimore, many of whose gratings are still in use and are highly prized. Excellent gratings have also been ruled by R. W. Wood with Rowland's engine, by Prof. A. Michelson, of Chicago, and at the British National Physical Laboratory. The well known "Thorp gratings" are celluloid replicas of Rowland gratings and find extensive uses in physical laboratories.
Gratings ruled on glass are called "transmission gratings." In these, the rulings act in the same way as the wires in Fraunhofer's gratings. Most gratings, however, are ruled on speculum metal and are called "reflection gratings"; speculum metal is chosen because it has the valuable property of reflecting light of all wave-lengths, so that the ordinary grating can be used for ultra-violet and infra red as well as for visible spectra. Transmission gratings may also be used, but less effectively, as reflection gratings.
Elementary Theory.—The production of spectra by a grating may be best explained by the consideration of a transmission grating, consisting of alternate opaque and perfectly transparent spaces, as coarsely illustrated in fig. 14. A parallel beam of light of a single wave-length from a slit and collimator, with the slit parallel to the rulings, is supposed to fall at normal incidence on the grating. Some of the light will pass directly through the grating in the direction of incidence and may be brought to a focus as an image of the slit—called the central image—by a suitable lens. Each clear space, however, may be considered to be divided up into an indefinitely large number of small "elements," each of which may be supposed to act as a source of light, giving rise to cylindrical wavelets. Some of the light is, therefore, found in other directions besides that of the incident light. To investi gate what happens in the direction AP, inclined at an angle 0 to the incident light, let CB be drawn from the edge of an aperture C in the direction at right angles to AP, which is from the edge of the adjacent aperture A. If now 0 be such that AB be just the length of one wave, the light coming from A in the direc tion AP will differ in phase by one whole wave from that proceed ing from C, and the two will reinforce each other. The first, second, and succeeding elements of the first aperture will thus be respectively reinforced by the corresponding elements of the sec ond aperture, so that the waves from the whole of the two apertures will reinforce each other in the direction AP. Similarly for other pairs of consecutive apertures across the whole grating, so that the light proceeding in the direction AP may be focussed as a second image of the slit in light corresponding in colour to that of the incident light. A similar image will obviously be formed at the same distance on the other side of the normal. Other images of the slit will also be formed in directions at larger angles to the normal, such that AB is equal to other integral mul tiples of the wave-length. The appearances with monochromatic light will accordingly be as roughly indicated in fig. 14c.