On Polarization of Light by Reflection. _ 289 
” . ; ayia 
for any number x of reflexions is therefore tan d= (SES ) 
cos(t — 7) 
It is evident that é 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 
reflexion at the polarizing angle; but we shall see that the polariza- 
tion is sensibly complete in consequence of the near approximation — 
of 4 to 0°. 
I found, for example, that light was polarized by two reflexions. 
from glass at an angle of 61° 3/, and 60° 28/ io another observation. 
Now in these cases we have 
@ after 6 after Quantity of 
Ist Reflexion. 2nd Reflexion. Unpolarized light. 
Miwo tehexions at.61°. 3’ . 69457... 0° 47’ ,~ 0.00037". , 
GDA 08. Me he Gey s ay. a OOO LS 
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 polarised by five 
reflexions at 70°. Hence by the formula we have 
| Values of 9. Unpolarized Light. 
Pcenexion ate 1098 sha) BOW OF Jeo 4) He (0.25892 
hh Bei hl inion wah SOc ot, 42% o OMB4S2 
eae i hee HP eh et Sen Pe AS. Bags 26,0/00460 
bie atures die Na); rat Neyg Ly yh tet) 3 oO ONOGD, 
MAS ee ch tote t Sid's ehen Oy Boi. de> .  OO0CRS 
The quantity of unpolarized 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 reflexions at 44° 514 . . 0°56’ . . 0.0005 
By 3 cies ere de 2h et se SORE QEEN Is.) OOO RE 
In all these cases the successive reflexions were made at the same 
angle; but the formula is equally applicable to reflexions at differ- 
ent angles,— 
1. When both the angles are greater than the polarizing angle. 
6  Unpolarized Light. 
1 reflexion at 58° 2’, and 1 at 6792’ . 0°34’ . 0.0002 
2. When one of the angles is above and the other below the po- 
larizing angle. 
