OF TRANSPARENT PLATES UPON LIGHT. 
151 
from plates, it is easy to obtain formulae for computing the exact quantities of 
polarized light at any angle of incidence, either in the pencil CBS or bs. 
The primitive ray R A being common light, AC will not be in that state, but 
will have its planes of polarization turned round a quantity x by the refraction 
at A ; so that cot x = cos ( i — i'). Hence we must adopt for the measure of 
the light reflected at C the formula of Fresnel for polarized light whose plane 
of incidence forms an angle x with the plane of reflexion. The intensity of AC 
being known from the formula for common light, we shall call it unity, then 
the intensity I of the two pencils polarized — x and -j- x to the plane of reflexion 
will be 
, sin I 2 ( i — i') 
sin 2 (z + 2) 
COS 2 X + 
tan 2 (i — 2) 
tan 2 ( i + 2) 
sin 2 x 
and 
Q = I 
- 2 
cos ( i + 2) \ 2 
(cos (i — 2) y) 
/ cos (i + 2) \ 2 
\(cos ( i — 2) y) 
) 
In like manner if we call the intensity of CB = 1, we shall have 
Tan x — 
cos (i + 2) 
(cos (i — 2)f 
and the intensity I of the transmitted pencil bs 
I == 1 
sin 2 (z — 2) 
sin 2 (t + 2) 
cos 2 X + 
tan 2 [i — 2) 
tan 2 (z + 2) 
sin 2 x 
and 
Q 
-( 
I l 
(cos ( i — z 7 )) s \ 3 
cos (z + 2) J 
1 + ( (cos (i - 2))* y 
V cos (i + 2) / 
< 
) 
I shall now conclude this paper with the following Table computed from the 
formulae in pages 148, 149, and showing the state of the planes of polarization 
of the three rays AC, CS, and bs. 
