422 
MR. R. T. GLAZEBROOK 014 DOUBLE REFRACTION 
slit formed by reflexion at the face of incidence. From this and the known direction 
of the incident light we can calculate the angle of incidence. 
Let this be <f>. Let the deviation be D and the angle of the prism i. Let V be 
velocity of the light in air, v in the crystal. Let 0 be the angle of emergence, 0' 0' 
the angles which the wave normal in the crystal makes with the faces of the prism. 
Then we have 
sin 0_sin <// 'l 
~ 0T~ 
i 
sin -\|r_sin 0' 
v 
f+0'=*' 1 
0+0=D+i'J 
sin 0 sin 0' 
sin 0 sin 0' 
. sin 0 + sin 0 sin 0' + sin 0' 
’sin 0 — sin 0 sin 0'—sin 0' 
tan 
= tan 
0 ' + 0 ' 
tan 
0 —\Jr 0 + "0 
cot 
( 1 ) 
( 2 ) 
(3) 
whence we can find 0' — 0', and since 0' + 0' is known, we can get at once <f> and f/, 
and then v is given by either of the formulae 
Y sin 0 sin 0 
v sin 0' sin -0' 
(4) 
But since we know the position of the faces of the prism with reference to the optic 
axis, we can find the angle between the wave normal and the optic axis, and if 
p x , fx. 2 be the reciprocals of the principal velocities, p that of a velocity in a direction 
making an angle 6 with the optic axis, we have by Huyghen’s construction, 
1_cos 2 6 sin 2 6 
o o I o 
P~ Pi" PY 
( 5 ) 
and from this p l3 p>, 6 being known, we can find p. 
