430 Dr. G. J. Stoney on Microscopic Vision. 



place where the objective forms its image of the microscopic 

 object. 



This is what happens to one of the beams. Let ns still 

 farther confine our attention to the course pursued by its 

 axial ray, i. e. the ray which coincides with the fine drawn from 

 the middle of the objective field perpendicular to those plane 

 waves w T hich form the beam before entering the objective. 

 This axial ray starts from the point on the optic axis of the 

 microscope where this optic axis pierces image C. When the 

 course of the ray is traced through and past the objective it 

 is found a second time to intersect the optic axis, at the point 

 where this axis pierces image D, the focal image. Let a and 

 /3 be its inclinations to the optic axis before and after it passes 

 through the objective. Then by Lagrange's Theorem 



n sina = M sin/3, ....... (1) 



where M is the magnifying power of the objective, i. e. the 

 number of times that the image D is larger than the image C ; 

 and where n is the refractive index of the medium between 

 C and the objective, the refractive index of the air which 

 intervenes between the objective and D being taken as unity 

 [otherwise n would have to be the ratio of the two refractive 

 indices]. 



Now if we take two beams, whose axial rays are in the 

 same meridian plane *, and which are inclined to the optic 

 axis at angles a and a', then the ruling in image C, to which 

 they will give rise, has a spacing 



e 1 = X 1 /(sin a — sin a'), . . . . . . (2) 



\ ± being the wave-length in the medium which is in front of 

 the objective. Similarly the spacing of the ruling which 

 these same beams produce when they reach image D is 



6 2 = X 2 /(sin/3-sin/30, (3) 



where \ 2 is the wave-length in air. Hence we find that the 

 ratio of e 2 to e x is 



e 2 __ X 2 ( sm «— sin a!) 



^""^(sin/S-sin/SO ' W 



and this, when we replace X 2 /\ by n, and put in the values 

 of n sin a and n sin a! given by equation (1), becomes 



7 2=M > (5) 



* A meridian plane means a plane passirg through the optic axis of 

 the microscope. 



