CLASSICAL THEORY OF LIGHT 741 



whence, approximately, 



so that the narrowness of the peak, as one might say, is proportional 

 to the order thereof as well as to the total number of lines in the grat- 

 ing.^ If the grating were infinitely wide, an unlimited sequence of 

 perfectly-evenly-spaced identical units, the peaks would be infinitely 

 narrow; light of a definite wave-length would be diffracted only in 

 certain perfectly definite discrete directions. 



Alikeness, closeness, and multitude of rulings are therefore the 

 desiderata of a grating; alikeness, because without it the first condition 

 for the formation of sharp diffraction maxima would be lacking — 

 closeness, so that the maxima of lower orders, the only ones sufficiently 

 intense to be perceived, may be spread out widely enough for conven- 

 ience of observation — multitude, so that the diffracted beams shall be 

 narrow and sharp, easy to set upon and easy to discriminate from one 

 another. The degree of closeness which is required depends upon the 

 spectral range which is to be explored. Ordinary "optical" gratings 

 ruled with a diamond on metal or on glass are acceptable throughout 

 the visible spectrum and the range to which the title "ultra-violet" 

 is commonly restricted, extending from the visible down to wave- 

 lengths of the order of one hundred Angstroms. They are however 

 too fine for the remoter infra-red, for the study of which coarse lattices 

 of wire have been used ; a fortiori they are much too fine for Hertzian 

 or radio waves, for which it is no exaggeration to say that a colonnade 

 might operate as a grating; and they are commonly considered much 

 too coarse for X-rays, though during the last two or three years 

 several men of science have achieved the great technical feat of forcing 

 optical gratings to measure wave-lengths which formerly were thought 

 accessible to crystals only. Crystals are too fine for the visible spec- 

 trum, and too coarse for certain of the gamma-rays which proceed from 

 the collapsing nuclei of atoms undergoing transmutation. Crystals 

 with spacings of unusual width from atom-plane to atom-plane are 



* These facts are usually expressed as statements about the "resolving power" 

 of a grating; for if the incident light contains two not very different wave-lengths, 

 they will form two peaks of each order not very far apart, and the possibility of 

 distinguishing these two — of "resolving" them, to use the technical term — will 

 depend upon the narrowness of each. If arbitrarily one says that two such peaks 

 are just distinguishable when the summit of one falls upon the minimum adjacent to 

 the other — in which circumstance the difference 8\ between their wave-lengths 

 may readily be proved equal to the quotient of the mean of their wave-lengths, X, 

 by 2Mn — then by this criterion a grating is able in its nth order to discriminate two 

 adjacent lines of the spectrum, if their wave-lengths differ by more than that amount; 

 and by definition the resolving power of the grating in its nth order is X/5\ = 2Mn, 

 the product of the number of rulings by the order. 



