80 F. E. Wright — Oblique Illumination in 



In minerals with large optic axial angle (2 V nearly 90° as in 

 olivine) the rise and fall of the interference colors away from 

 the center of the field is so slight that practically the same 

 interference color covers the entire field and one is at a loss to 

 determine, by this method, which quadrant contains the acute 

 bisectrix. 



The mathematical proof of the above statement is not diffi- 

 cult. In fig. 18a let 1ST be the direction of the optic normal 

 in stereographic projection ; A 19 A 2 be the two optic axes, 

 and B the direction of propagation of a wave transmitted 

 obliquely through the plate perpendicular to the optic normal 

 N. If d be the thickness of the plate, then the length d' 

 (fig. 18&) of the path of the wave OB is 



d' = -*— (1) 



cos r 



where r = NOB. The birefringence y / — d for the direction 

 B is readily found from the standard approximate birefringence 

 formula 



y — a = (y — a) sin 1 . sin 2 (2) 



wherein 6 X and # 2 are the angles BA X and BA 2 included by the 

 direction B with the two optic axes A 1? A 2 respectively. In 

 this particular case 6 X = < BOA, = < BOA 2 == V . In the 

 spherical triangle BEA, we have 



cos BA 2 = cos BE . cos EA X or ,„v 



cos 6 X — cos (90 - r) cos V ^ ' 



where EA, — Y, which is half the optic axial angle A,A 2 . 



The path difference A B or interference color of the wave 

 propagated along OB varies directly with the length of path 

 OB {d f ) and the birefringence, y' — a' . 



A B = d' . (y' - a') (4) 



On substituting in this equation the value from (1), (2), (3), 

 we find 



A B = — — (y - a) (1 - sin 2 r . cos 2 V) ( 5 ) 



cos r 



The path difference An x °r the optic normal OX is 



A N ^ d.(y -a) (<6) 



From (5) and (6) we obtain by division 

 A B _ 1 — sin 2 r cos 2 V 



A N cos r 



(?) 



