ON THE REFLEXION AND REFRACTION OF LIGHT. 247 



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 yiy part 

 of that of the incident wave. This minimum value increases 

 rapidly, as the index of refraction increases, and thus the 

 quantity of light reflected at the polarizing angle, becomes con- 

 siderable for highly refracting substances, a fact which has been 

 long known to experimental philosophers. 



It may be proper to observe, that M. Cauchy (Bulletin ctes 

 Sciences, 1830) has given a method of determining the inten- 

 sity of the waves reflected at the common surface of two media. 

 He has since stated, (Nouveaux Exercises des Mathematiques^] 

 that the hypothesis employed on that occasion is inadmissible, 

 and has promised in a future memoir, to give a new mechani- 

 cal 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 junc- 

 tion, and the consideration of the waves propagated by normal 

 vibrations was wholly overlooked, though it is easy to perceive, 

 that in general waves of this kind must necessarily be produced 

 when the incident wave is polarized perpendicular 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 may be satisfied, and the principles 



