MATHEMATICS OF PHYSICAL PROPERTIES OF CRYSTALS 59 



In a few special cases (18.7) may be simplified. If (<^, 6) falls along an 

 optic axis gi = 1' — V° and go — V + V° whence 



3 



Ba = ^ [(Ai - A2) cos' V° - (A2 - A3) sin' F°] . . . . (19.61) 



if ^ = 



iid= 90' 



B = (nz — Mi)(l — cos" (j) sin V°) 



5 = M2 - Ml + -4^ (^1 - ^^) 

 Ml + M2 



2 T/ON 



(19.62) 



+ ^ (Ai - A3 - (Ai - A2) cos' 0) . . (19.63) 



if = 



J5 = (m3 - Ml) (sin' V° - sin' ^) + y (Ai - A2 - (Ai - A3) sin 6) . . (19.64) 



if = 90° 



^ = (^,3 - ;xi)(l - cos' d cos' V°) 



3 

 + ^ (Ai - A3 - (A2 - A3) cos 6) . . (19.65) 



The Electro Optics of Quartz 

 For quartz, in the equation K~ = K~ -\- zE 



Z = 



If E is in practical volts* 

 Zll = 0.47 X 10""' 

 Z41 = 0.20 X 10"'" 



Obviously the £3 component produces no effect so we shall examine the 



effects due to the components £1 and Eo separately. If £ = I I £1 



\0/ 



K-' = 



which can be diagonalized 



Computed from F. Pockels data, see his Lehrbuch der Kristall-Optik, (B. G. Tuebner). 



