r_> I RADIATION BIOLOGY 



i'lie ratio of area in object (source) space A , to that in image space Ao is 

 equal to the ratio of the solid angle of rays forming the image and leaving 

 the source, or expressed in terms of linear dimensions, 



L.NAi = L,NA,, 



which says that the product of a linear dimension of the source and the 

 numerical aperture of the rays leaving the source collected by the imaging 

 system is equal to the product of the same dimension of the image of the 

 source and the numerical aperture of the image-forming rays. 



Let us say that we wish to form an image of the source which is 0.005 

 mm in diameter with a condenser lens of NA = 0.5. Thus, 



0.005 X 0.5 = 0.0025. 



We assume a field lens for the source which has as high an aperture as the 

 condenser. Then. 0.0025 = LiO.5. 



Li = 0.005 mm. 



From this it is clear that only an area of the source of diameter 0.005 

 mm is contributing to the energy flowing into the cytoplasm. Should a 

 collecting lens of smaller numerical aperture be used, a larger area of the 

 source would contribute, but through a smaller solid angle and, assuming 

 the source to be uniform, the total energy would be the same. In order to 

 increase the amount of energy delivered into the cytoplasm in a given 

 time the product L2NA2 must be increased, the steradiancy of the source 

 must be increased, or both. 



This fundamental relation has been demonstrated in an example of sim- 

 ple image formation. It has been shown to hold as the limit no matter 

 how many image-forming steps are interposed between the source and the 

 final image used for irradiation. 



Consider, for example, a possible arrangement of optical components 

 (Fig. 4-1) for the determination of the action spectrum (see p. 384) of the 

 effects of ultraviolet radiation found in the preceding experiment. In this 

 system S is the source focused by a collecting lens on »S'Li, the entrance 

 slit of the monochromator .1/. .S'L,. is the exit slit of the monochromator 

 and / the image formed in the cytoplasm by the condenser. Then, 



LsNAs = Lsl.NAm = Lsl^NAm = L,NA,. 



In this case the slits of the monochromator serve as secondary sources. 

 The width of the slits {Lsl,, Lsl,) is determined by the dispersion of the 

 monochromator and the required width of the band of radiation to be iso- 

 lated (p. 148). This may establish a limiting value for the products 

 including these terms because of limitations inherent in available mono- 

 chromators. It is again emphasized that the establishment of a value for 

 any one of the products L^NA^ by experimental re(iuiremeuts or l)y 



