208 RADIATION BIOLOGY 



spacing the components, and first-surface mirrors are much more easily 

 damaged by careless handling and corrosive atmospheres than lenses. 

 However, the fragile surfaces of aJuminized mirrors can be partially pro- 

 tected by evaporating a protective film on the aluminum. 



The effective aperture area of a spectroscope is the area of the beam 

 as it traverses the dispersing system. This beam is usually square or 

 rectangular in cross section and often smaller in area than the circular 

 aperture of the collimator or focusing optics. Various methods may be 

 used for expressing the aperture diameter, or linear aperture, but for most 

 practical purposes it is expressed as the diameter de of a circle of an area 

 equivalent to that of the used portion of the prism or grating. The // 

 number, or aperture ratio, then becomes f/de. This quantity is usually 

 greater than that of the collimator or focusing optics. 



Condensing Systems. The application of the lens formula, Eq. (3-6), 

 shows that, if the condenser lens or mirror is of the same size as the 

 collimator, its focal length must be less. If the image magnification of 

 the source is 1, the condenser focal length must be half that of the colli- 

 mator in order to subtend the same angle as the collimator. It can be 

 shown (Sawyer, 1944) that for a perfect optical system the image of the 

 source is never brighter than that of the source itself. Both lenses and 

 mirrors can be used as condensers, but mirrors often necessitate a crowded 

 arrangement of source and entrance slit. Advantage can often be taken 

 of the chromatic aberration of a lens to compensate partially for non- 

 uniformity of the spectral energy distribution of the source and the power 

 transmission of the monochromator. 



Relative Power Transmission. The most useful criterion for the evalu- 

 ation of an irradiation monochromator is the relative power P transmitted 

 per unit source intensity A^ within a wave-length interval AX. For sim- 

 plicity, consider a symmetrical monochromator with collimator and focus- 

 ing systems of equal aperture area A and focal length / and entrance and 

 exit slits each of width s and length I. Let all transmission losses due to 

 vignetting or diaphragming or to absorption in lenses and prisms, and 

 all reflection losses due to gratings and mirrors be included in the one 

 coefficient T, which may be treated as an over-all transmittance. Assume 

 that the source has a radiance of A^ w steradian~^ cm~" and is sufficiently 

 large so that a condensing lens or mirror can be chosen which will produce 

 an image covering the slit. The angular aperture co of the condensing 

 system is assumed to be equal to that of the collimator. The radiant 

 power, in watts, entering the slit is then 



Pax = N^^Tslw. . (3-24) 



The allowable width of slit s for a given AX is a function of focal length / 

 and dispersion dd/d\; then s = AX f(dd/d\). The slit length I is a design 

 factor that is likewise proportional to the focal length: I = Kf. The 



