212 The Microscope. 



tre thick, crown-glasa lens 1 millimetre thick, radius of curvature 

 1 ; second doublet f and | thick, and radius 4 ; third doublet f 

 and f thick, and radius 10, The front vertex of the second and 

 third doublets coincides in each case with the second principal 

 plane of the underlying doublet. Our figure is drawn to scale^ 

 multiplied by 10 lineally, and the surrounding medium is as- 

 sumed to be the air, having its refractive index n^ = 1. 



First doublet. — The front surface of its flint-glass lens being 

 flat has the principal foci at infinity, being to each other how- 

 ever 1 to n. Its 2d surface has by the formulae (where n = 1.6,. 

 and r = — 1) 



nr 1.6 8 r 1 5 



n-1 .6 o 71-1 .6 3 



For the lens as a whole, the first principal focal length 



/: 



Here the first and last terms of the denominator disappear 

 relatively to the infinity of the central term. 



loo f 5 



Thus / = = — = — 



n oo 1.6 3 



5 



Also the second focal length g =z - f z= . 



3 



/i i A t t h 5 



Anteplane, a^ 



f'l 9i + i !/i ^i ^'-6 16 



92 i Hi ^ 



Postplane, a.^ = =: — = O 



J\ (J^ -f t CX) 



Thus the 1st principal plane ( fi in the figure) is ^ above the 

 vertex V,,, and the 2d principal plane (/2) coincides with the 

 back vertex (Vi) of the flint-glass lens. 



Its crown-glass lens gives for its principal focal lengths {j\ g} 

 (having w := 1 .5, and r = 1 for its front curve, and = -1 for its back 



r 1 nr 



curve), first surface, fi — = — = =: — 2; g^^ = 



n-1 1.5-1 71-1 



