254 Lord Rayleigh on the Reflexion of Light 



whence approximately, 



(64) 



ffa-ffi _ fB 



H~^2 2pD' 

 Introducing these relations into (60), (61), we find 



2/D ' " • * {bi)) 



ty (/* + »•»). B.M 



2/D * " * * W 



These equations indicate that the intensity of the reflected 

 light (M/ 2 + N /2 ) is proportional to that of the incident, with- 

 out regard to the polarization of the latter. Again, if the 

 incident light be unpolarized (M and N equal, and without 

 permanent phase relation), so also is the reflected light. But 

 what is more surprising is, that if the incident light be 

 polarized in or perpendicular to the plane of incidence, the 

 reflected light is polarized in the opposite manner. 



The intensity of reflexion may be expressed in terms of the 

 angle of incidence <£, for 



Pi \/ (P 2 J tr 2 )= cos </>, r/ s/ (p 2 + r 2 ) — sin $, 

 so that 



. M ' 2 + N/2= 4DwV M2 + N2) - * * • (67) 



When the angle of incidence is small, the intensity is propor- 

 tional to its square. And, as was to be expected, the reflexion 

 is proportional to B 2 . 



The laws here arrived at are liable to modification when, as 

 must usually happen in practice, the thickness of the plate 

 cannot be neglected. The incident light, on its way io the 

 twin surface, and the reflected light on its way back, is sub- 

 ject to a depolarizing influence, which in most cases compli- 

 cates the relation between the polarizations of the light before 

 entering and after leaving the crystal. One law, however, 

 remains unaffected. If the light impinging upon the crystal 

 be unpolarized, it retains this character upon arrival at the 

 twin face. We have shown that it does not lose it in the act 

 of reflexion, neither can it lose it in the return passage after 

 reflexion. Hence, if the light originally incident upon the 

 layer of crystal be unpolarized, so is the reflected light ulti- 

 mately emergent from it. 



