REPORT ON PHYSICAL OPTICS. 3G7 



amounting to neiirly 180°, while the coefficient of the vibration 

 itself is not much altered. The diamond therefore has no angle 

 of complete polarization ; and Professor Airy concludes that the 

 nature of the reflexion from this singular substance, in the 

 neighbourhood of the angle of maximum polarization, is differ- 

 ent from any that has been hitherto described. 



Fresnel's theory of reflexion has received experimental confir- 

 mation of a different kind, and to an extent which leaves little 

 ground to doubt of its truth. When a ray polarized in any plane 

 falls upon a reflecting surface at any angle, the reflected ray is 

 still polarized, but its plane of polarization is changed, — the 

 amount of the change depending on the incidence. The law of 

 this change is at once furnished by the theory of Fresnel; for 

 the tangent of the inclination of the plane of polarization of the 

 reflected ray to the plane of incidence, is equal to the ratio of 

 the displacements in the plane of incidence and in the perpen- 

 dicular plane. The formula thus deduced has been verified in 

 the most complete manner by the observations of Fresnel him- 

 self, and more fully since by those of M. Arago and Sir David 

 Brewster*. 



The views of the latter philosopher respecting the nature of 

 partially polarized light are founded upon the phenomenon of 

 the change of the plane of polarization by reflexion. If common 

 light be conceived to consist of two pencils oppositely polarized, 

 in planes inclined 45° on either side of the plane of reflexion, the 

 effect of reflexion, it is obvious, will be to bring each of these 

 planes nearer to the plane of incidence ; so that the planes of 

 polarization of the two pencils will approach each other, and form 

 an acute angle after reflexion. Partially polarized light, then, 

 according to Sir D. Brewster, consists of two polai'ized pencils, 

 whose planes of polarization form an acute angle ; and no por- 

 tion of it is in the condition of ordinary lightf . TJiis hypothesis 

 receives some support from the explanation which it affords 

 of the effects of successive reflexions. When light thus con- 

 stituted 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. 



* Annales de C/iimie, torn. xvii. ; Phil. Trans. 1830. 



t Sir David Brewster has computed, on these principles, the quantity of 

 light apparently polarized in the plane of incidence, by a single reflexion at any 

 angle ; adopting Fresnel's expression for the intensity of the reflected ray. The 

 agreement of the formula with the observations of M. Arago is found to be 

 as near as can be expected in such comparisons. " On the Law of Partial 

 polarization of Light by Reflexion," Phil. Trans. 1830. 



