EEFLEXION AND REFEACTION OF POLARIZED LIGHT. 87 



ray acquires all the characters which had been found to belong to 

 one of the pencils produced by double refraction. "When received 

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

 is generally divided vanished in two positions of the principal sec- 

 tion 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 pro- 

 duced 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 reflected light, in any position of 

 the plane of the second reflexion with regard to the first, Malus 

 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 intensity, 

 whose planes of polarization are at right angles ; for when such a 

 compound beam is received upon a reflecting surface at the po- 

 larizing angle, the intensity of the reflected light will be constant, 

 and independent of the position of the plane of reflexion. But 

 though this compound beam so far exhibits the character of com- 

 mon or unpolarized light, it must not be regarded as it seems to 

 be by many writers as its physical representative. It appears, in 

 fact, from the theory of the composition 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 semi-undulations ; 

 while in intermediate cases the polarization of the resulting light 

 is either circular 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 transpa- 

 rent substances impressed upon the reflected light the same modifi- 

 cation ; and that the angle of incidence at which this effect was 



Memoirea fArcueil, torn. ii. p. 143. 

 t Ibid., p. 264. 



