REFLEXION AND REFRACTION OF POLARIZED LIGHT. 99 



the explanation which it affords of the effects of successive reflexions. 

 When light thus constituted is received upon a second reflecting 

 surface, in the same plane of incidence, the planes of polarization 

 of the two pencils will be brought nearer, and so continually; 

 until by a sufficient number of reflexions, these planes will, as to 

 sense, coincide with the plane of incidence, and the resulting light 

 will appear to be wholly polarized in that plane. 



This ingenious theory seems open to an objection already 

 noticed, namely, that the light resulting from the union of two 

 oppositely polarized pencils cannot, in all respects, be taken as the 

 physical representative of common or unpolarized light. It also 

 involves this further difficulty, that the positions of the planes of 

 polarization of the two oppositely-polarized portions are entirely 

 arbitrary ; and that if they be differently assumed, the results will 

 be physically different. Thus, for example, if the two planes be 

 taken, one coincident with the plane of reflexion itself, and the 

 other with the perpendicular plane, neither of these planes will be 

 changed by reflexion, although the intensities of the corresponding 

 pencils will. 



Sir David Brewster has also investigated experimentally the 

 effect of refraction upon the plane of polarization of the refracted 

 ray ; and he has found that the law of the change may be ex- 

 pressed by a very simple and elegant formula.* This formula is a 

 necessary consequence of Fresnel's theory, although Fresnel him- 

 self does not seem to have observed it. Its discovery by Sir David 

 Brewster adds one to the many instances of rare sagacity by which 

 this philosopher is guided in his experimental inquiries. The par- 

 tial polarization of light by refraction has been considered by Sir 

 David Brewster in the same memoir. In the investigation of the 

 quantity of polarized light in the refracted pencil, he employs a 

 principle similar to that which he had already applied to the re- 

 flected ray; and he arrives at the result that the quantities of 



formula with the observations of M. Arago is found to be as near as can be expected in 

 such comparisons. " On the Law of PartialPolarization of Light by Reflexion." Phil. 

 Trans. 1830. 



* a and ' being the azimuths of the planes of polarization of the incident and re- 

 fracted rays, estimated from the plane of reflexion, and i and i' the angles of incidence 

 and refraction, 



cot a' = cot a cos (* ') 



" On the Laws of the Polarization of Light by Refraction." Ph il. Tram. 1830. 

 H2 



