AND REFRACTION OF LIGHT. 3 



The principal results obtained in this paper, relate to the intensity 

 of the waves reflected at the common surface of two media, both for 

 light polarized in and perpendicular to the plane of incidence; and 

 likewise to the change of phase which takes place when the reflexion 

 becomes total. In the former case, our values agree precisely with 

 those given by Fresnel; supposing, as he has done, that the direction 

 of the actual motion of the particles of the luminiferous ether, is 

 perpendicular to the plane of polarization. But it results from our 

 formulae, when the light is polarized perpendicular to the plane of 

 incidence, that the expressions given by Fresnel are only very near 

 approximations; and that the intensity of the reflected wave will 

 never become absolutely null, but only attain a minimum value; which, 

 in the case of reflexion from water at the proper angle, is ^ P art 

 of that of the incident wave. This minimum value increases rapidly, 

 as the index of refraction increases, and thus the quantity of light re- 

 flected at the polarizing angle, becomes considerable for highly refract- 

 ing substances, a fact which has been long known to experimental 

 philosophers. 



It may be proper to observe, that M. Cauchy {Bulletin des Sciences^ 

 1830,) has given a method of determining the intensity of the waves 

 reflected at the common surface of two media. He has since stated, 

 {Nouveaux Exercices des Mathematiques,) that the hypothesis employed 

 on that occasion is inadmissible, and has promised in a future memoir, 

 to give a neiv mechanical principle applicable to this and other questions ; 

 but I have not been able to learn whether such a memoir has yet ap- 

 peared. The first method consisted in satisfying a part, and only a part, 

 of the conditions belonging to the surface of junction, and the con- 

 sideration of the waves propagated by normal vibrations was wholly over- 

 looked, though it is easy to perceive, that in general waves of this kind 

 must necessarily be produced when the incident wave is polarized perpen- 

 dicular to the plane of incidence, in consequence of the incident and 

 refracted waves being in different planes. Indeed, without introducing 

 the consideration of these last waves, it is impossible to satisfy the Whole 

 of the conditions due to the surface of junction of the two media. 

 But when this consideration is introduced, the whole of the conditions 



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