32 On the Action of the Second Surfaces of 
When the pencil R A is incidenton the first surface at the polari- 
zing angle or 56° 45’, the rotation produced by refraction at Ai 
about 2°, or the inclination 1=45°-+4+2°=47°; but the maximum ac- 
tion of the polarizing force at C is sufficient to make I=0° whether 
@ is 45° or 479°. Hence CB is completely polarized in the pl 
of reflexion, and the refractive action at 8 is incapable of chan 
the polarization when I=0°: the reason is therefore obvious w 
the two rotations at A and 8, of 2° each, — no effect at tl 
maximum polarizing angle. 
If we now call 
@ =Inclination to the plane of —— produced by the Ist re- 
fraction at 
yp’ =Inclination poduesd by the reflexion at C, 
oe’ =Inclination pasa oy, the 2nd = at 5, 
We shall have 
pea irite or tan —s Gav) oe 
- cos(t+7) cos (t-+7’) 
Pan. of stan @ (S (t—2’) ~~ (cos (t—7/) )? 
(cos (4-2) )? 2 
cos (st’)- ee 
These formule are suited to common light where r=45°, bai wh zs 
a varies they become - 
Cot »=cot x (cos (i—7’) ) 
se cos (i470) ) 
er 
Os (1 —2") )3 
Cot o”=(cotx nn): 
Resuming the formula for common light, viz. cot 9!” = isos 
Cot o/=cot £ (cos (t—2))= 
os (¢ — i }): 
cos (+7). 
it is obvious that when (cos (i- V))?=cos (i-+-4), Co g. ils & 
and 9” =45°; that is, the light is restored to common lig 2 
In glass where m=1.525 this effect takes place at 78° 7; 
below, 78° in diamond ; and a little above 80° in water. 
_ At an angle below this, 9 becomes less than 45°, and "the pen 
contains Tight polarized in the plane of reflexion ; while at all great- 
er angles gis above 45, and the pencil contains light polarized p 
pendicular to the plane of eelicxion. Hence we obtain the follow- 
ing curious law. — 
