GENERATION, CONTROL,, .AND MEASUREMENT 209 



solid angle co subtended by the collimator is given approximately by 

 w = A IP radians, where A is the effective aperture area. Inserting 

 these quantities in Eq. (3-24) gives 



Pax = NaxT A\f{de/d\)Kf(A/f) = N^xT A\(dd/dX)KA 

 and 



(P/N)ax = KTA(dd/d\) AX. (3-25) 



Thus the relative power transmitted in a specified wave-length band per 

 unit source intensity is proportional only to the product of the trans- 

 mittance, the effective aperture area, and the angular dispersion of the 

 dispersing system and is independent of the aperture ratio. 



The irradiance or intensity at the exit sUt is the power per unit slit 

 area si; therefore 



The spectrographic speed or irradiance at the exit slit is proportional to 

 the angular aperture and inversely proportional to the square of the 

 aperture ratio, or // number, f/d. 



1. Aperture ratio. There has been considerable overemphasis on the 

 importance of large angular apertures or small values of the aperture ratio 

 in regard to irradiation and photometric monochromators. From the 

 preceding analysis of spectroscope transmission, it is evident that, for a 

 given source intensity and on the assumption that an adecjuate condensing 

 'system is available, the transmitted radiant power within a specified 

 wave-length band is independent of the focal length of the optics. As 

 the colhmator focal length is increased, the permissible width and length 

 of the entrance slit may be increased proportionately to maintain the 

 same wave-length band, but the subtended angle that has to be filled 

 by the condenser is decreased. The result is that the useful radiant power 

 that can be made to enter the slit is ultimately dependent only on source 

 intensity and the transmission of the condensing system. 



The same analysis can be applied to the focusing system. The total 

 power emerging from the exit slit is independent of the focal length of the 

 focusing lens or mirror. However, the power per unit area or irradiance 

 at the exit slit is proportional to the angular aperture but inversely pro- 

 portional to the scjuare of the aperture ratio. When the spectroscope is 

 used to irradiate the grains of a photographic emulsion, or a small bolome- 

 ter or thermocouple target, maximum irradiance is desired, and low aper- 

 ture ratios of //4 to //1. 5 are of real merit. On the other hand, when 

 biological objects are irradiated whose over-all dimensions are larger than 

 the exit slit, a short focal length is of little value. 



The principal disadvantage of lenses and mirrors of small aperture 

 ratio and therefore relatively short focal length is that the problems of 



