10 VISION WITH THE COMPOUND MICROSCOPE 



dvf 



= O F, suppose. 



If in = 0, or the ray be parallel to the axis before refraction. \\c 

 have from (8) 



/ _ g 5 _. j m /r , and the equation to the refracted ray becomes 

 y - SL m" = m" (x - NO, or y = m" (./ - N' + fy ; 



.-. when y = 0, x = N' - ? = ON'- 



= O F', suppose. 

 F and F' are called the ' focal points.' 



du 



OF = ON+ -7-7-^ \ , , 



H (u f u) duu 



OF' = ON' . , ^~/"/ 



/u (u r u) duu' 



The focal distance -/=OF-OE = OE'-OF' 

 = Af 1 



k 



Similarly, it may be shown that if there be two lenses, and sub- 

 script numbers refer to the first and second lens respectively, 

 E, E r , F, F' refer to the entire system, and if 

 3 = OE 2 -OE/, 



i = ^ = P\ (\ H \) d \ u\ u \', 

 J\ 



V 2= *? = /"2 (2 ; ^2) ^2 2 W 2^ 

 /2 



Un C> Vi 



We are now prepared to wo?*^ o^ a?i example of the Gauss system 

 by tracing a ray through two or more lenses on an axis, showing h<>\\ 

 any conjugate may be found through two or more lenses on that axis. 1 



1 Remembering our object, and the assumed conditions of some for whom we 

 write, we do not hesitate to preface this with the following notes to remind the 

 reader of the sense attached to certain mathematical expressions. 



c means infinity. A plane surface of a lens is considered a spherical surface of 

 an infinite radius. Any number divided byco = any number divided byO = oo; 



