88 REPORT ON PHYSICAL OPTICS. 



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

 general different for every different substance. He ascertained, 

 moreover, the relation between the angles of polarization at the 

 first and second surfaces of the same transparent medium, and 

 found that their sines were in the ratio of the sines of incidence 

 and refraction ; so that when the medium is bounded by parallel 

 surfaces, and the light incident on the first at its polarizing angle, 

 the transmitted portion will meet the second surface also at Us 

 polarizing angle, and the light reflected from both will be wholly 

 polarized.* Malus was unable, however, to discover any con- 

 nexion between the polarizing angle and the other properties of 

 the substances; and he concluded that the power of polarizing 

 light by reflexion, which different bodies possessed at different 

 angles, was wholly independent of their other modes of action 

 upon light. 



Sir David Brewster commenced, not long after, an extensive 

 series of experiments, with the view of determining the angles of 

 polarization of different media, and of connecting them by a law. 

 These researches terminated in the discovery of the law perhaps 

 the most beautiful in the whole range of this interesting science 

 that " the tangent of the angle of polarization is equal to the 

 refractive index." This law, when translated into geometrical 

 language, declares that, when the ray is wholly polarized by re- 

 flexion, the angles of incidence and refraction are complementary, 

 so that the reflected and refracted rays form a right angle. The 

 law applies to the case of reflexion from the surface of the rarer, as 

 well as that of the denser medium; and it follows from it that 

 the two angles of polarization at the bounding surface of the same 

 two media are complementary, f 



Malus observed that when the angle of incidence was either 

 greater or less than the polarizing angle, the properties already 

 described were only in part developed in the reflected pencil. 



Me'moire* fArcueil, torn. ii. p. 1 52. M. Arago has extended the same law to the 

 case of partial polarization, and has found that the sines of the angles at which the 

 first and second surfaces of a transparent medium polarized light hy reflexion in an 

 equal degree are to one another in the ratio of the sines of incidence and refraction ; so 

 that the pencils reflected from the two surfaces of a parallel plate, at any incidence, 

 contain the same proportion of polarized light. 



t " On the Laws which regulate the Polarization of Light hy Reflexion from 

 transparent Bodies." Phil. Tram. 1815. 



