^ 4 REPORT ON PHYSICAL OPTICS. 



It is evident that the strata of ether in the two media, which 

 nre adjacent to the hounding surface, must undergo equal displace- 

 Lents parallel to that surface, inasmuch as one of them cannot 

 Ide on L other. Consequently the amplitude of the ^ration, 

 resolved in a direction parallel to the surface, must be the same in 

 the two media. Fresnel assumes that this equality at the bound- 

 ing surface is maintained at all distances ; and this furnishes him 

 with one relation among the amplitudes of vibration of the inci- 

 dent reflected, and refracted waves. A second relation among the 

 same' quantities is afforded by the law of the ** viva; but to apply 

 this it is necessary to know the relative densities of the ether in 

 the two media. Here Fresnel assumes that the elasticity of the 

 ether in these media is the same * but the density different ; and 

 this being taken for granted, it follows that "the two densities are 

 to one another inversely as the squares of the velocities of propa- 

 gation, and that therefore their ratio is given when the refractive 

 index is known. The amplitudes of the reflected and refracted 

 vibrations, and therefore also the intensities of the light in the two 

 pencils, are obtained by simple elimination between the equations 

 just mentioned. 



The expressions for the intensity of the light in the reflected ray 

 are different, according as the incident light is polarized in the plane 

 of reflexion or in the perpendicular plane.f The intensity of the 

 reflected light in the latter case vanishes when the sum of the 

 angles of incidence and refraction is a right angle ; and thus was 

 solved the difficulty, which in the opinion of Young, pronounced 

 but three years before" would probably long remain, to mortify 

 the vanity of an ambitious philosophy, completely unresolved by 

 any theory." "When common, or unpolarized light, therefore, is 



Sciences in the year 1823, entitled, " Memoire sur la Loi des Modifications que la Ee- 

 flexion imprime a la Lumiere polarisee." An incomplete extract of this memoir was 

 published in the Anvales de Chimie, 1825. The original paper was mislaid, and for a 

 time supposed to he lost ; it has lately, however, heen recovered among the papers of 

 M. Fourier, and has heen printed in the llth vol. of the Memoirs of the Institute. 



* Fresnel states that he had solved the problem of reflexion in the general suppo- 

 sition that the two media differ in elasticity as well as density, in the case of rays 

 polarized in the plane of reflexion ; and that the resulting formula was the same as 

 that at which he had already arrived on the more limited hypothesis. An, Chim., 

 torn, xxiii. 



t These two formula; were first published in the Atmales de Chimie, 1821 ; the 

 *econd without demonstration. 



