130 



nutting: brightness of optical images 



in which M = 



f.i 



VI 



r. 



~ = xM\m log 

 ^o L 



1 



T 



1 + ^ 



I + T 1 + T 

 a2 



1 -m2 



(1 + ?«)- 



and T = m'^s 



T/D 



Fig. 1 



X.e 



SV 



/fa 



In tlie special case of a very distant object, this expression 

 simplifies to ■k log (1 H-a^) or for narrow apertures to the ordinary 

 formula / ^I^Tra-. When image and object are at equal distances 



(m = l), 



/ 1 „ 8 + a2 



— = -TV a- — 



/o 2 (4 + a'Y 



The relative brightness of image and object, computed by the 

 above formulae for any lens aperture F /D and any magnifica- 

 tion m =vju is given in the following table: 



