134 The Luminiferous Medium, 



Eliminating li between these two equations, and using the 

 formulae 



sin 2 T Co 2 pi 



sin 2 i C* p 2 ' 

 we obtain the equation 



Z. _ sm (^ ~ r ) 

 g sin (i + r) 



Thus when the light is polarized in the plane of reflexion, the 

 amplitude of the reflected wave is 



Q-l -T\ (ft ^ -0*\ 



- \-. r x the amplitude of the incident vibration. 



sin pj + r) 



Fresnel shows in a similar way that when the light is 

 polarized at right angles to the plane of reflexion, the ratio of 

 the amplitudes of the reflected and incident waves is 



tan (i - r) 

 tan (i + r) 



These formulae are generally known as Fresnel' s sine-law and 

 FresneTs tangent-law respectively. They had, however, been 

 discovered experimentally by Brewster some years previously. 

 When the incidence is perpendicular, so that i and r are very 

 small, the ratio of the amplitudes becomes 



Limit , 



^ + r 



or 



where ju 2 and //i denote the refractive indices of the media. 

 This formula had been given previously by Young* and Poisson,f 

 on the supposition that the elasticity of the aether is of the 

 same kind as that of air in sound. 



When i + r = 90, tan (i + r) becomes infinite : and thus 

 a theoretical explanation is obtained for Brewster 's law, that if 

 the incidence is such as to make the reflected and refracted rays- 



* Article Chromatics, Encycl. Britt. Suppl. t Mem. Inst. ii. (1817). 



