158 POLARIZATION OF LIGHT. 



as a polarizer ; for the reflected beam is necessarily far more 

 intense than that produced by a single surface. 



(171) It has been shown, that when a beam of light 

 polarized by reflexion, is suffered to fail upon a second re- 

 flecting surface at the polarizing angle, the intensity of the 

 twice-reflected beam will vary with the inclination of the 

 planes of reflexion, being greatest when these planes are 

 coincident, and vanishing when they are perpendicular. In 

 all cases, the intensity varies as the square of the cosine of the 

 angle formed by the two planes of reflexion. This law was at first 

 conjecturally assumed by Malus ; its truth has since been 

 verified by the experiments of Arago. 



It follows, as a consequence of this law, that a ray of com- 

 mon light may be conceived to be composed of two polarized 

 rays of equal intensity, whose planes of polarization are per- 

 pendicular.* For if light, thus composed, is incident on a 

 reflecting surface, and if a, and 90 - a, denote the angles 

 which the plane of reflexion makes with the planes of polari- 

 zation of the two pencils, the intensity of the reflected light in 

 one of these rays will be I cos 2 a, and that in the other I sin 2 a, 

 denoting the intensity of each of the incident pencils ; and 

 the sum of these, or the total intensity of the reflected light, 

 is 



I (cos 2 a + sin 2 a) = I. * 



* This is not be undertood as describing the actual physical character 

 of ordinary, or unpolarized light. This may be more correctly represented 

 as polarized light, whose plane of polarization is incessantly changing ; so that, 

 in a given time, there are as many polarized rays in any one plane as in any 

 other at right angles to it, This agreement has been verified experimentally 

 by Professor Dove, by impressing mechanically a rapid motion of rotation upon 

 the plane of polarization of the light ; the phenomena presented by the resulting 

 light agreeing in all respects with ordinary or unpolarized light. 



