On Polarization of Light by Reflexion. 285 
( cos(t-++ 7 ) 4 
9 
tan2—_ 
cos(t—2) 
That is, Q=1—2 os aa) 
1+-|tan een ae ¥) 
As the quantity of reflected light is here supposed to be 1, we 
may obtain an expression of Q in terms of the incident light by 
adopting the formula of Fresnet for the intensity of a reflected 
Thus 
cos(t —7/) 
+(e 
s(@ 
ray. 
: sin? (t—2’) tan*(i—#) 
=a (Fee) Ha cE) (:- - = 
v) 
As tan v=1 in common light, it is omitted in the preceding for- 
mula, 
This formula may be adapted to partially polarized rays, that is, 
to light reflected at any angle different from the angle of maximum 
polarization, provided we can obtain an expression for the quantity of 
reflected light 
M. Placwes s general formula has been adapted to this species of 
rays, by considering them as consisting of a quantity a of light com- 
pletely polarized in a plane making the angle « with that of incidence, 
and of another quantity 1—a in the state of natural light. Upon this 
principle it becomes 
; sint(i—v’) 1-+-acos*x  tan?(t ad 5 Bae cos? x 
~~ sin?(t-+7/) 2 tan?(i+7) ° 2 
But as we have proved that partially polarized rays are rays whose 
planes of polarization form an angle of 2x with one another, as al- 
ready explained, x being greater or less than 45°, we obtain a sim- 
pler expression for the intensity of the reflected pencil, viz, the very 
same as that for polarized ari ‘ 
sin? (i—7 
I= sin? sin? (¢-+7 ) 
Hence we have 
2(¢—2 tan?(4—? 
Q= (SF eos a-- ees 7}sin*2) 
cos ey 
x (: ~ ( cooley 
i tan cos(i—7’) 
Vou. XXII.—No. 2. 37 
2 Sg 
ee 
an? (¢— 
tan? (7-+7’) 
——-COS aed 
