The Microscope. 213 



1.5 nr r 



^=. = 3 ; second surface, /2 = = — 3 ; f/a = — = 2. 



1.5-1 w-1 n-1 



hh -2+-3 6 



/2 - f/l + « 5 



Thus its first principal plane (ci of the figure) is | above its 

 front vertex, Vi ; and its second principal plane, C2, is § below its 

 back vertex V2, the minus sign indicating that it is to be meas- 

 ured downwards. For the doublet as a whole (using sub-script 

 letters f and c to mark the parts of the flint and crown-glass 

 lenses already found); we have for the first transit (which rep- 

 resents the thickness of the imaginary equivalent lens) the dis- 

 tance/2 -Ci, between the back principal plane of the front lens 

 doublet, and the front principal plane the back lens ; this dis- 

 tance/2 - Ci = f . 



Hence for the first principal focal length of the doublet, 



/./. f X (-1) _ 30 



~/-9/+~ -f-(-f) + f 13 



30 

 Second principal focal length, g, = -/ = 



Ante-plane of doublet = 



13 

 t}t f X f 10 



fc-9f-\-t -«-(-!) + § 13 

 gd § X § 36 



Post-plane of doublet = 



fc-9 + t -f + t + f 65 



This signifies that the 1st principal plane of the doublet is fj 

 above the first principal plane of its front lens (above /^ in tV 

 figure), and that its 2d principal plane is If above the 2d princi 



