358 FOURTH REl'ORT 1834. 



and found that their sines Mere in the ratio of the sines of inci- 

 dence and refraction ; — so that when the medium is hounded hy 

 parallel surfaces, and the light incident on the first at its po- 

 larizing angle, the transmitted portion will meet the second 

 surface also at its polarizing angle, and the light reflected from 

 both be wholly polarized *. Malus was unable, however, to 

 discover any connexion between the polarizing angle and the 

 other properties of the substances ; and he concluded that the 

 power of polarizing light by reflexion, which diff"erent bodies 

 possessed at diff'erent 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 diff'erent media, and of connecting them by a law. 

 These researches terminated in the discovery of the law, — per- 

 haps 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 geo- 

 metrical language, declares, that when the ray is wholly polar- 

 ized by reflexion, 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 bound- 

 ing 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. 

 Neither of the two pencils into which it was divided by a rhomb 

 of Iceland spar ever wholly vanished ; but they varied in inten- 

 sity between certain limits, these limits being closer the more 

 remote the incidence from the angle of complete polarization. 

 From this he naturally concluded that in these circumstances a 

 ]}ortion only of the reflected pencil had i-eceived the modifica- 

 tion to which he had given the name of polarization, — that por- 

 tion increasing as the incidence approached the polarizing an- 

 gle ; — and that the remaining portion was unmodified, or in the 

 state of common light. In this supposition Malus has been fol- 

 lowed by most subsequent philosophers. A different view of 



* Memoires d'Arcueil, torn. ii. p. 152. M. Arago has extended the same 

 law to the case of partisil polarization, and has found that the sines of the angles 

 at which the first and second surfaces of a transparent medium polarize light by- 

 reflexion in an equal degree, are to one another in the ratio of the sines of in- 

 cidence 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. 



f " On the Laws which regulate the Polarization of Light by Reflexion from 

 transparent Bodies," Phil. Trans. 1815. 



