418 LIMITS OF OPTICAL CAPACITY OF THE MICROSCOPE. 



l^ow according to the known laws of refraction at a spherical 

 surface, whose radius he = r, the value of their principal 

 focus is 



From which follow 



F" ri' ^ ^ 



F" —F'=r (4^) 



Further 



F' F" . F" F' 



_1_ + -4^ = 1 and + -— - = 1 



ah ^ Ih cic be 



Or 



Ij, II— F" ^^^ Ic _ Ic—F' 



ah ~ F' ac F" 



Division of the last two equations gives 



Ih.ac __ F" {hh—F") 

 ah. he " F' ihc—F') 



But by equation (4^) 



lh=hc -^ r ==lc ■\- F" — F' 



And 



Ih — F" = hc- F' 



Hence 



Ih . ac ^ _Z1_ = JL!_ according to equation (4^ 



ah .he F' n 



Therefore equation (3) 



a! . fi ' n_ 



a" . /3" — n' 



