THE PARTIAL POLARIZATION OF LIGHT BY REFLEXION. 
81 
<p being the inclination for one reflexion. Hence when 6 is given by observation, 
we have tan <p = The formula for any number n of reflexions is there- 
/cos ( i -f- i!\\ n 
fore tan & = ( 7 ^— — ) . It is evident that 6 never can become equal to 0°; 
\COS (l + l ) ) 'l ’ 
that is, that the pencil cannot be so completely polarized by any number of 
reflexions at angles different from the polarizing angle, as it is by a single 
reflexion at the polarizing angle ; but we shall see that the polarization is 
sensibly complete in consequence of the near approximation of 6 to 0°. 
I found, for example, that light was polarized by two reflexions from glass 
at an angle of 61° 3', and 60° 28' by another observation. Now in these cases 
we have 
Two reflexions at 61° 3' 
60 28 
6 after 
1st Reflexion. 
6° 45' . 
5 38 . 
6 after 
2nd Reflexion. 
0° 47' . 
0 33 . 
Quantity of 
Unpolarized Light. 
. 0.00037 
. 0.00018 
The quantity of unpolarized light is here so small as to be quite inappreciable 
with ordinary lights. 
In like manner I found that light was completely polarized by five reflexions 
at 70°. Hence by the formula we have 
Values of 6. Unpolarized Light. 
1 reflexion at 70° 20° 0' . . . . 0.23392 
2 7 32 ... . 0.03432 
3 2 45 ... . 0.00460 
4 1 0 . . . . 0.00060 
5 0 22 ... . 0.00008 
The quantity of unpolarized light is here also unappreciable after the 5th 
reflexion. 
In another experiment I found that light was wholly polarized by the sepa- 
rating surface of glass and water at the following angles : 
Values of 6. Unpolarized Light. 
By 2 reflexions at 44° 51' . . . 0° 56' . . . 0.0005 
By 3 42 27 . . . 0 26 . . . 0.0001 
In all these cases the successive reflexions were made at the same angle ; 
but the formula is equally applicable to reflexions at different angles, — 
1. When both the angles are greater than the polarizing angle. 
( Unpolarized Light. 
1 reflexion at 58° 2', and 1 at 67° 2' . . 0° 34' . . 0.0002 
MDCCCXXX. 
M 
