THE PARTIAL POLARIZATION OF LIGHT BY REFLEXION. 
83 
Such are the laws which regulate the polarization of light by reflexion from 
the first surfaces of bodies that are not metallic. The very same laws are 
applicable to their second surfaces, provided that the incident light has not suf- 
fered previous or subsequent refraction from the first surface. The sine of the 
angle at which <p or Q has a certain value by reflexion from the second surface, 
is to the sine of the angle at which they have the same value at the first surface, 
as unity is to the index of refraction. Hence <p and Q may be determined by 
the preceding formulae after any number of reflexions, even if some of the re- 
flexions are made from the first surface of one body and the second surface 
of another. 
When the second surface is that of a plate with parallel or inclined faces, 
its action upon light presents curious phenomena, the law of which I have de- 
termined. I refer of course to the action of the second surface at angles less 
than that which produces total reflexion. This action has hitherto remained 
uninvestigated. It has been hastily inferred, however, from imperfect data ; 
and the erroneous inference forms the basis of some optical laws, which are 
considered to be fully established. 
Among the various results of the preceding investigation, there is one which 
seems to possess some theoretical importance. If we consider polarized rays 
as those whose planes of polarization are parallel, then it follows that light 
cannot be brought into such a state by any number of reflexions, or at any 
angle of incidence, excepting at the angle of complete polarization. At all 
other angles the light which seems to be polarized, by disappearing from the 
extraordinary image of the analysing rhomb, is distinguished from really po- 
larized light, by the property of its planes of polarization forming an angle 
with each other and with the plane of reflexion. At the polarizing angle, for 
example, of 56° 45' in glass, the light reflected is 7 9-5 rays, and it is completely 
polarized, because the planes of polarization of all the rays are parallel ; but at 
an angle of incidence of 80°, where 392 rays are reflected, no fewer than 157 
appear to be polarized, though their planes of polarization are inclined 66° 26' 
to each other, or 33° 13' to the plane of reflexion. This appearance of polari- 
zation, when the rays have only suffered a displacement in their planes of 
polarization from an angle of 90°, which approximates them to the state of 
polarized light, arises from the law which regulates the repartition of polarized 
light between the ordinary and extraordinary images produced by double re- 
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