260 Mr. S. S. Richardson on 



II. The Ordinary Foucault Prism. 



Referring to fig. 3, OP represents the face of the crystal, 

 OY the optic axis, OR' the transmitted ray, and PQ the 

 transmitted wave-front. The coordinates of P are a? 1? y x . _,, 



Fig. 3. 



(a) Extraordinary rays. Taking the equation of PQ in 

 the form 



y = mx ± y/(a?m 2 + b 2 ) , 

 we obtain 



tancf) 



_ #i,yi+ V b 2 x\* + o?y\ + a 2 b 2 



The coordinates of P are a , 1 = OPcosB ; y 1 = OPsinB. 



A 1 S0 P=^ = ^4. 



sin A sin A 



Hence by substitution, 



+. a. — tl pef^o sin B cos B + sin A \/ \x 2 cos 2 B -f //, 2 sin 2 B — sin 2 A 

 an9_ /V~ (/x e 2 cos 2 B-sin 2 A) 



. . . (4) 

 the positive value of the root being taken since the larger 

 value of <f> is obviously required. 



