THE PARTIAL POLARIZATION OF LIGHT BY REFLEXION. 
73 
subject was first examined by Malus, but not with that success which attended 
most of his labours. Before I was acquainted with what had been done by 
M. Fresnel, or with the experiments of M. Arago on glass and water, I had 
made a number of very careful experiments on the same subject, and had re- 
presented them by formulae founded on the law of the tangents. These 
formulae, however, I found to be defective ; and I am persuaded, from a very 
extensive series of experiments, that the formulae of Fresnel are accurate ex- 
pressions of the phenomena under every variation of incidence and refractive 
power. If i is the angle of incidence, i' the angle of refraction, x the primitive 
inclination of the plane of the polarized ray to the plane of reflexion, and <p the 
inclination to which that plane is brought by reflexion, then, according to 
Fresnel, we have 
Tan <p — tan x 
cos (z + z 7 ) 
cos (z — z 7 ) 
When x is 45°, as in the preceding observations, then tan x = 1, and we have 
Tan <p = 
cos (z + z 7 ) 
cos ( i — i'Y 
In these formulae, which'are founded on the law of the tangents, i + i' is the 
supplement of the angle which the reflected ray forms with the refracted ray ; 
while i — i’ is the angle which the incident ray forms with the refracted ray, or 
the deviation produced by refraction. 
These formulae have been verified by M. Arago at ten angles of incidence 
upon Glass, and four upon Water ; but his experiments were made only in the 
case where x is 45°, and where tan x disappears from the formula. As my 
experiments embrace a wider range of substances, and also the general case 
where x varies from 0° to 90°, I consider them as a necessary basis for a law 
of such extensive application. 
The first series of experiments which I made was upon Plate Glass, in which 
the maximum polarizing angle was nearly 56° : hence I assume the index of 
refraction to be 1.4826. The following were the results: 
MDCCCXXX. 
L 
