20 METHODS OF PETROGRAPHIC-MICROSCOPIC RESEARCH. 
A 'F' are the principal focal lengths of the system. To express these relations 
in mathematical form we observe that the distance F'\Fi or D is conjugate 
f f 
to F'jF' with respect to the lens Lj. Accordingly F'jF' = ~- Similarly 
the distance FF^-^. 
h' 
To find the equivalent focal lengths we have by definition /= - and 
tan u 
h h 
f = , ; also by definition the rear focal length of L\ t f\= 7- where 
tan u tan u\ 
h = H\A, the distance of the ray H\E from the axis. For the conjugate 
points F'i and F' the relations (6), (7), and (8) are valid, from which the 
equation - T = TT 1S readily derived, provided both F\ and F' are in 
tan MI ft 
air, as is the case in the microscope. This equation combined with the 
above expression for u', becomes 
tan u' D 
Similarly 
h' M 
tanw D 
The four quantities FF\, F' 2 F', f, and / define the optical behavior of the 
system in the formation of images and will be used frequently in the fol- 
lowing pages. 
