34 On the Action of the Second Surfaces, &e. 
Let us now apply the results of the preceding analysis to M. 
ARaco’s experiment shown in Fig. 1. Suppose the angle of inci- 
dence to be 78° 7’, and let the light polarized-by reflexion at A (Fig. 
3-) be =m, and that polarized by one refraction also=m. Then 
sce the pencil 6s is common light, the polarized light in the whole 
reflected pencil AP, bs ism, whereas the light polarized by the 
two refractions is=2m}; so that M. Araco’s experiment makes two 
quantities appear sinicl: when’ the one is double that of the other. 
If the angle exceeds 78° 7’, the oppositely polarized light i in the pen- 
cil 6s will neutralize a portion of the polarized light in the pencil . 
AP, and the ratio of the oppositely polarized rays which seem to be 
compensated in the experiment, may be that of 3m or even 4m to 1. 
‘Having thus determined the changes which light undergoes by 
reflexion from plates, it is easy to obtain formule for computing the 
exact quantities of polarized light at any angle of incidence, either 
ee CBSor bs. 
- The primitive ray RA 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 cotw=cos(i—v). Hence we must 
adopt for the measure a the light reflected at C the formula of Fres- 
nel for polarized light whose plane of incidence forms an angle x with 
the plane of reflexion. The intensity of AC being known from the for- 
mula for’common light, we shall call it unity, then the intensity I of the 
two pencils polarized —« and as to the plane of reflexion will be 
sin?(t—w) = , n*(t—72') . 
i= ~ sin*(i-e)o°* e+ aGEr® 
(<< cos(t-++7i’ y= =) 
(cos(t— 2’) )? 
= 3 . cos(t-+-2 ) :) 
at (cos(¢— 7’) )2 :) 
In like manner if we ca l the ingensity of cB=1, we shall a 
sin? and 
and ae intensity I of the transmitted pencil bs 
cae Seem and — 
(1-2 een) 
Q=(1i- . ee 
“(eee 
