152 HADIATION BIOLOGY 



ovtM-all width of tlio grating to the wave length, or more specifically on 

 the number of wave lengths of phase dilTerence between the waves, pro- 

 ceeding in a given direction from the extreme slits of the grating. As 

 this phase dilTerence increases, as with increasing order number, the 

 width of the angular intensity distribution decreases, and hence the 

 spectroscopic resolving power increases. 



The angular dispersion of a grating — the variation of wave length of 

 maximum intensity with angle — likewise increases with increasing order 

 number, and also w-ith decreasing spacing between the slits. Analytically, 



where jS = angle of diifracted beam with grating normal 

 n — order number 

 d = spacing between slits. 



While both spectral resolution and angular dispersion are favored by 

 the use of higher ditTraction orders, the problem of overlapping orders 

 becomes acute for high-order numbers. The third diffraction order of 

 Xi will overlie the second order of 1.5Xi and the first order of 3Xi, etc. 

 Fre(iuently filters or elementary prism devices may be added to sur- 

 mount this difficulty and permit the use of second- or third-order spectra. 



The grating, transmission or reflection, may be on a plane surface, in 

 which case it is illuminated with parallel light from a collimating lens or 

 mirror, and the emergent beams are focused to a spectrum with a tele- 

 scope lens or mirror. Or the grating, if reflecting, may be ruled on a 

 concave surface, in which case it will serve as its own focusing element, 

 permitting the elimination of the collimating and telescope elements 

 (Beutler, 1945). Such concave gratings are then effective throughout 

 any wave-length region for which a reflecting surface may be made, since 

 the need for any transparent dielectric is eliminated. The images formed 

 by such gratings are, however, generally astigmatic, unless the grating is 

 illuminated with a parallel beam, as in the Wadsworth mounting (Sawyer, 

 1951, Chap. 6; Harrison et al., 1948, Chap. 4). 



Gratings may be produced with higher resolving power than any prism 

 instrument. By the use of replica technicjues, many copies can be made 

 from one master at moderate cost. However, grating instruments neces- 

 sarily waste light in unused orders, although this drawback can be mini- 

 mized by proper ruling of the reflecting strips which can serve to direct 

 most of the energy into one order (Wood, 1944; Babcock, 1944; Stamm 

 and Whalen, 1946). 



The use of grating dispersing elements in monochromators is a rela- 

 tively recent development (French et al., 1947), although commercial 

 designs employing plane reflection gratings are now available (Bausch 

 and Lomb, 19.")1) (see Fig. 4-14). The u.se of such monochromators may 



