merwin: measurement of refractive index 



531 



the angles a and ai, within the crystal, and the angle /3 in the air 

 where they are parallel. The emergent waves are supposed to 

 totally interfere in one of the observed dark rings. In r and s, 

 between normals from the sur- 

 face, there are the same number 

 of waves, then the difference in 

 phase between the two waves en- 

 tering the microscope is expressed 

 0) m -, mi€i 



by the equation 



- / 



X X 



in which I is the number of wave- 

 lengths that the extraordinary 

 wave is in advance of the ordi- 

 nary wave as determined by the 

 serial number of the dark ring, 

 counted outward from the optic 



axis; X is the wave-length in air; co the ordinary refractive index; 

 and ei the refractive index of the extraordinary wave whose 

 normal makes the angle ai with optic axis, e is the thickness of 

 the section. 



sinjS 



sin a = 



, and 7?i = 



u 



cos a 



Then 7n = 



1- 



sm^^ 



0)^ 



Now rtii = m cos (ai — a) = m (cos a • cos ai + sin a • sin aO 



(1) 



Then - — - I = dm (cos a ■ cos ai + sin a ■ sin ai) for a negative 

 X 



crystal. For a positive crystal / is positive, therefore in the 



general case, after substituting 



. _ ei e (cos a ■ cos ai -|- sin a • sin ai) _ 



coe 



XCOSa 



tie , . 



^— cos «! -f- sin «! 



X cos a 



sin- a 



COS a 



(2) 



