MATHEMATICS OF PHYSICAL PROPERTIES OF CRYSTALS 



61 



which is identical to the ju for field along .vi , but the final axes in this case 

 do not coincide with the final axes for E = Ei , but again, the greatest added 

 birefringence is utilized by viewing along X3. In the second case the Nicols 

 would be best set along Xi and X2, i.e., at 45° to .xi and .T2 whereas in the 

 first case they would be best set at 45° to .ti and X2. 



The strain Optics of Quartz 

 R-' = K'^" + me, 



where* 



If the strain is a simple tension along xi , 



K-' = 



K-" = 



Ki + mnti 



KT^° + Wi2€l 



Ki + W31C1 

 

 

 



applying 18.63 or 18.64 we find the birefringence along .ti to be: 



3 



Bn = Ms — Ml + y (Wi2 — W31) €1 



.0091 - .0148 €1 



Similarly the birefringence along .To is ^12 — .0091 — .225 £1 and ^13 = 

 — .207 ci. With a strain of 10~ , which is about a tenth of the breaking 

 strain, Bn would be 20.7 X 10~ , a quantity detectable in a thickness of one 

 millimeter. 



The values of ^21 • • • -S43 corresponding to birefringence along x^ for a 

 tension along .T2 etc., can be computed in just the same way. But ^51 • • • 

 Bes require rotations of 45° about .T3 to diagonalize, so the birefringences 

 can be computed by setting 6 — 45° in equations (19.6). 



* Lehrbuch der Kristalloptik — ^F. Pockels. 



