Resolving Power of a Prism.— If one had a prism spectroscope which was practically per fect so far as all the optical parts are con cerned, he would yet find that the ability of the prism to separate light-waves of different lengths was subject to still another limitation — a limitation which arises ultimately from the fact that light-waves have an appreciable length. This ability to separate radiations is known as "resolving power" and is measured by the ratio where ' is the difference of the wave d( length and L the mean wave-length of t%% o spec tral lines which can just be resolved by the dispersion piece in question.
Rayleigh has proved that a prism can just resolve two lines when the difference of their refractive indices op is given by the following equation dp = A where t: and t, are the 12= ti thickness of glass traversed by the extreme rays on either side of a parallel beam passing through the prism.
If now be expressed in terms of dl by means of a dispersion formula such as the fol lowing, due to Cauchy, we have B 2BAl11-= A -I-- , and (5,1=- where A and B are constants depending upon the kind of glass employed in the prism.
From these it follows that the resolving power, R, for prism is A R (St Al • This equation is fundamental in describing the spectroscopic value of a prism. It means that the resolving power varies directly as the width of the prism and inversely as the cube of the wave-length of the light examined. It tells us also just how thick a prism of any given glass must be, at its base, in order to separate two lines having a given difference of wave-length. The prism spectroscope was first effectively used by Fraunhofer (1817-28); but it was not until 1859 that Kirchhoff and Bunsen demonstrated the power of the instrument in chemical an alysis, and in a study of the sun's physical condition.
The Grating Spectroscope.—So far as its auxiliary parts are concerned this piece of ap paratus is very like the prism spectroscope: but as regards its essential feature, the dispersing piece, the two instruments are radically differ ent. For the dispersion which is produced by a prism rests ultimately upon the fact that waves of longer length travel through glass at a higher speed than those of shorter length: while the dispersing effect of a grating is due to the fact that when waves of different lengths are forced to pass through a narrow opening, they are all spread out like a fan—diffracted the longer waves being more spread out, how ever, than the shorter ones. If a gas flame,
turned low, or an incandescent electric lamp be examined through a single narrow slit in a vis iting card, a number of spectra will be seen on each side of a central bright image. These have been called, by Fraunhofer, "spectra of the first class." They are not used in spectroscopy. If, however, the same source of light be viewed through two or more fine parallel equidistant slits, placed close together, say less than one sixty-fourth inch apart, another series of spectra will be observed. These are the combined effect of light passing through several openings; they are known as "spectra of the second class" and are practically the only ones in the grating spectroscope. These narrow equidistant parallel slits were first prepared by Fraunhofer (1821) who formed them by wrapping fine wire over the thread of two parallel screws, then solder ing the wires to the screws and cutting away one entire side of the little cage thus formed. Such a device he called a grating. The modern grating is made by ruling straight lines with a diamond point on a flat plate of highly polished speculum metal. Good gratings have usually from 5,000 to 20,000 lines per inch. Here the light is reflected from the unruled surface be tween two successive furrows made by the diamond ; and diffraction occurs exactly as if the light had passed through a narrow aperture of the same width. Such a device is called a reflection grating, and when placed where the prism stands in an ordinary prism spectroscope we have what is called a grating spectroscope.
When a beam of parallel rays emerges from the collimator and falls upon a grating placed with its rulings parallel to the slit of the col limator, part of the light is reflected according to the laws of ordinary reflection and forms, in the focal plane of the view-telescope, what is known as the central image. The remainder of the light, however, is spread out on either side of this central image, the blue light being de viated least and the red light (longest waves) being deviated most. Unlike the prism the grating yields several spectra distributed on each side of the central image.