290 On Polarization of Light by Resflewidi. 
6 Unpolarized Light. 
1 reflexion at 53°, and 1 at 58° 2’. . 0° 12’ . 0.000024 
This experiment requires a very intense light, for I find in my jour- 
nal that the light of a candle is polarized at 53° and 78°. 
In reflexions at different angles, the formula becomes tan 6= 
cos (t-++2/) cos (I+1’) 
cos (t—2’) “cos (I—I’)’ 
like manner if a, 6, c, d, e, &c. are the values of » or 4 for each re- 
flexion, or rather for each angle of incidence, we shall have the final 
angle or tan é=tan a Xtan 6 Xtane x tand, &c. 
It is scarcely necessary to inform the reader that when a pencil of 
light reflected at 58° 2’ is said to be polarized by another reflexion at 
67° 2’, it only means, that this is the angle at which complete polar- 
ization takes place in diminishing the angle gradually from 90° to 67° 
2’, and that even this angle of 67° 2/ will vary with the intensity of the 
original pencil, with the opening of the pupil, and with the sensibility 
of the retina. But when it shall be determined experimentally at what 
value of ; or rather at what value of Q the light entirely disappears 
from the extraordinary image, we shall be able by inverting the for- 
mula to ascertain the exact number of reflexions by which a given 
pencil of light shall be wholly polarized. 
As the value of Q depends on the relation of 2 and 2’, that is on the 
index of refraction, and as this index varies for the different colors 
of the spectrum, it is obvious that Q will have different values for these 
different colors. ‘The consequence of this must be, that in bodies 
of high dispersive powers, the unpolarized light which remains in the 
extraordinary image, and also the light which forms the ordinary im- 
age, must be colored at all incidences; the colors being most dis- 
tinct near the maximum polarizing angle. ‘This necessary result of 
the formula, I found to be experimentally true in oil of cassia, and va- 
rious highly dispersive bodies. In realgar for example 9 is = O at an 
angle of 69° 0’ for blue light, at 68° 37’ for green light, and at 66° 
49’ for red light. Hence there can be no angle of complete polariza- 
tion for white light, which I also found to be the case by experiment; 
and as Q must at different angles of incidence have different values 
- for the different rays, the unpolarized light must be composed of a 
certain portion of each different color which we be easily determi- 
ned by the formula. 
Such are the laws which regulate the polarization of light by re- 
flexion from the first surfaces of bodies that are not metallic. ‘The 
I and ¢ being the angles of incidence. i 
