82 
DR. liREAVSTER ON THE LAW OF 
2. When one of the angles is above and the other below the polarizing- angle. 
6 Unpolarizcd 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 journal that 
the light of a candle is polarized at 53° and 78°. 
cos (* + if) 
In reflexions at different angles, the formula becomes tan & = 
cos (I + I') 
cos (i — i ) 
X cos + ~ r ~ ) ’ ^ anc ^ 1 being the angles of incidence. In like manner if a , b, c, 
(1, e, &c. are the values of or 6 for each reflexion, or rather for each angle of 
incidence, we shall have the final angle or tan 6 — tan a X tan b X tan c X 
tan d, &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 polarization takes place in dimi- 
nishing 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 <p, or rather at what value of Q, the light entirely 
disappears from the extraordinary image, we shall be able by inverting the 
formula 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 i and i', that is, on the index of 
refraction, and as this index varies for the different colours of the spectrum, it 
Is obvious that Q will have different values for these different colours. The 
consequence of this must be, that in bodies of high dispersive powers, the unpo- 
larized light which remains in the extraordinary image, and also the light 
which forms the ordinary image, must be coloured at all incidences ; the 
colours being most distinct near the maximum polarizing angle. This neces- 
sary result of the formula, I found to be experimentally true in oil of cassia, and 
various highly dispersive bodies. In realgar for example <p is = 0 at an angle 
of C9° 0' for blue light, at 68° 37' for green light, and at 6G° 49' for red light. 
Hence there can be no angle of complete polarization 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 colour, which may be easily 
determined by the formula. 
