150 
DR. BREWSTER ON THE ACTION OF THE SECOND SURFACES 
of 82° 44'. At all angles beneath this the pencil contains light polarized in 
the plane of reflexion ; but at all angles above it, the pencil contains light pola- 
rized perpendicular to the plane of reflexion, the quantity increasing from 
82° 44' to its maximum, and returning to its minimum at 90°. 
By comparing these deductions with the formula and table for reflected light 
given in my paper On the Laws of the Polarization of Light by Refraction, the 
following approximate law will be observed. When 
Cos (i — i') = cos (i + i') All the incident light is reflected. 
(Cos (i — i ') ) 2 = cos ( i + *’) Half the incident light is reflected. 
(Cos (i — i') ) 3 = cos (i + i') A third of the incident light is reflected. 
(Cos ( i — i ') )n = cos (i + i ') An nth part of the incident light nearly is 
reflected. 
This law deviates from the truth by a regular progression as n increases, 
and always gives the value of the reflected light in defect. Thus 
Angles of Incidence. Values of n. Differences. 
82° 44' 2 0 
78 34 3 12 
75 38 4 21 
08 56 8 38 
66 4 11 43 
61 22 20 50 
Let us now apply the results of the preceding analysis to M. Arago’s experi- 
ment shown in Fig. 1. Suppose the angle of incidence to be 78° 7', and let the 
light polarized by reflexion at A (Fig. 3.) b e=m, and that polarized by one refrac- 
tion also = 7)i. Then since the pencil bs is common light, the polarized light 
in the whole reflected pencil AP, bs is —m, whereas the light polarized by the 
two refractions is = 2m ; so that M. Arago’s experiment makes two quantities 
appear equal when the one is double that of the other. If the angle exceeds 
78° 7', the oppositely polarized light in the pencil b s 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 3 m or 
even 4 m to 1 . 
Having thus determined the changes which light undergoes by reflexion 
