On Polarization of Light by Reflexion. 289 
cos(i+-i)\ * 
soa(i=¥)) 
It is evident that ¢ never can become equal to 0°; that is, that the 
pencil cannot be so completely polarized by any number of reflex- 
ions at angles different from the polarizing angle, as it is by a single 
reftexion at the polarizing angle; but we shall see that the polariza- 
tion 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’, este = 28’ by another observation. 
Now.in these cases we have 
. for any number 1 of reflexions is therefore tan 1=( 
6 after Quantity of 
st Reflexion. 2nd ee hia tet light. 
Two reflexions at 61° 3/ . 6°45’ . 0° 47’ 
BO 28 2 DDO ht 5 ear 
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°: .< :-30: 202; Dae cee es Oe 
2. cae MMe tag eke oi Oe nest ie eee 
Bicep iS al eee ae Grae . 0.00460 
4 2s5 pogicp tig ie 1 0. . 0.00060 
Bit ig O22 0.00008 
The quantity jek sapthicinnt light is here also unappreciable after 
the fifth reflexion. 
In another experiment I found that light was wholly polarized by 
the separating surface of glass and water at the following angles : 
Values of 9. — Unpolarized Light 
By 2 — at a SP MIP BS er 0.0005 
B , BR OS 2 ARO BBS 24S" 0.0001 
In all these cases in successive reflexions were made at the same 
angle; but the formula is equally applicable to reflexions at differ- 
ent angles,— 
1. When both the igs are greater than the borg angle. 
Uapolerized Light. 
1 reflexion at 58° 2’, and 1 at 679 2’ . 0° 34’ .° 0.0002 
2. When one of the angles is above and the other below the po- 
larizing angle. 
