RKPORT ON PHYSICAL OPTICS. 357 



covered the important fact, that when a ray of light is reflected 

 from the surface of glass or water at certain angles, the reflected 

 ray acquires all the characters which had been found to belong 

 to one of the pencils produced by double refraction. When re- 

 ceived upon a rhomb of Iceland spar, one of the two pencils into 

 which it is generally divided vanished in two positions of the 

 principal section with respect to the plane of reflexion ; while 

 in intermediate positions these pencils varied in intensity through 

 every possible gradation*. The same variations were observed 

 when it underwent a second reflexion at the same angle at 

 which the effect was produced by the first ; the twice reflected 

 light being a maximum when the plane of the second reflexion 

 coincided with that of the first, and vanishing altogether when 

 it was perpendicular to it,— the whole light in that case passing 

 into the refracted pencil. To represent the intensity of the re- 

 flected light, in any position of the plane of the second reflexion 

 with regard to the first. Mains assumed it to vary as the square 

 of the cosine of the angle -which these planes formed with one 

 another f. The accuracy of this law has since been verified by 

 the observations of M. Arago and others. 



From this law it follows that a beam of common light may be 

 represented as composed of two polarized beams of equal inten- 

 sity, whose planes of polarization are at right angles ; for when 

 such a compound beam is received upon a reflecting surface at 

 the polarizing angle, the intensity of the reflected light will be 

 constant, and independent of the position of the plane of re- 

 flexion. But though this compound beam so far exhibits the 

 character of common or unpolarized light, it must not be re- 

 garded (as it seems to be by many writers,) as its physical re- 

 presentative. It appears, in fact, from the theory of the com- 

 position of vibrations, that two rays of equal intensity polarized 

 at right angles compound a single ray polarized in a single 

 plane, when the difference of their phases is nothing or equal 

 to any integer number of semiundulations -, while in interme- 

 diate cases the polarization of the resulting light is either 

 circidar or elliptic. These indications of theory have been 

 confirmed in the fullest manner by a beautiful experiment of 

 Fresnel. 



On pursuing his inquiries Malus found that all other trans- 

 parent substances impressed upon the reflected light the same 

 modification ; and that the angle of incidence at which this effect 

 was produced, and which he called the angle of polarization, was 

 in general different for every different substance. He ascer- 

 tained, moreover, the relation between the angles of polarization 

 at the first and second surfaces of the same transparent medium, 

 * Memoires iVArcueil, torn. ii. p. 143. f Ibid., p. 254. 



