Light at certain Metal-Liquid Surfaces. 231 



media ; while in the case of the film of surface contamination 

 its index should be approximately constant, and its value 

 might be greater or less than or intermediate between those 

 of the two media. 



Mathematically the effects to be expected from either the 

 transition layer or the film can be thrown into identical form, 

 the only difference in the two cases being that imposed on the 

 interpretation of the results by the possible values of the 

 index of refraction, as indicated above. The mathematical 

 theory of such layers or films has been worked out in great 

 detail by Drude *, who has shown that on the assumption 

 that the thickness of the film is small compared with the 

 wave-length of the light employed, its effect can be expressed 

 as a correction term to the ordinary Fresnel equations. The 

 form of this correction term shows that when the reflexion 

 takes place from the surface of a substance of greater index 

 than that in which the light is incident, we should expect a 

 positive ellipticity at the polarizing angle for any film which 

 has an index lying between those of the two media, and 

 a negative ellipticity for a film with a grealer index than 

 that of either medium. Thus a real transition layer can 

 theoretically produce only a positive ellipticity, while a 

 negative ellipticity must always be attributed to films of 

 surface contamination with indices greater than that of the 

 reflecting substance. Of course all of an observed positive 

 ellipticity may not be due to a transition layer, for the matter 

 contaminating the surface may have an index intermediate 

 between those of the two media ; but a negative ellipticity 

 is theoretically a certain criterion of a film of contamination. 

 Lord Rayleigh's experiments mentioned above are thus in 

 striking accord with the theory. 



The same general considerations hold in the case of the 

 reflexion from metals. Here, however, since metals naturally 

 produce an elliptic (or a circular) polarization at all angles 

 ot incidence, the effect of the transition layer or film of 

 contamination will be to change the ellipticity and the phase 

 difference of the two components of the vibration from the 

 values they would have if the film were not present. The 

 theory, based on the same assumption as in the case of the 

 reflexion from transparent substances f, shows that, providing 

 the index of refraction of the film or layer is greater than 



* Wied. Ann. xxxvi. 1889, p. 865. A brief development of the theory 

 of the transition layer is given in the ' Theory of Optics/ by Drude, 

 translated by Mann and Millikan, 1902, p. 217. Also in YVinkelmann, 

 Handbuch der PTiysik, 2 ,e Aufl. 1906, vol. vi. p. 1256, and in the ' Physical 

 Optics/ bv Wood, p. 296. 



t Wied. Ann. xxxvi. 1889, p. 8G5. 



