86 Wheeler — Experimental Investigation on the Reflection 



ished.* It would thus seem to be established that the theory 

 stands in need of correction in the case of reflection from 

 liquids, while remaining entirely competent in the case of 

 solids. 



Now the boundary conditions from which the equations of 

 Fresnel are deduced assume an abrupt, discontinuous change in 

 physical properties as one passes through the surface separating 

 the two media. As such physical discontinuity is, a priori, highly 

 improbable, it is natural to seek the source of the observed dis- 

 crepancies in a thin transition layer where the two media inter- 

 penetrate, and the physical properties change continuously 

 though rapidly between the constant values tliey possess beyond 

 the limits of the layer on either side. On this hypothesis it is 

 natural to expect a thinner transition layer and hence a closer 

 approximation to the conditions of a discontinuous change in 

 the case of solids than of liquids. Thus admitting that such 

 layers must exist in all cases, we must conclude from the 

 experiments mentioned that it is only in the case of liquids 

 that they attain a sufficient thickness to be appreciable. 



But while the existence. of the transition layer seems a fairly 

 certain inference from the phenomena of reflection, it is equally 

 certain that the greater part of the divergences of experiment 

 from the predictions of theory are to be ascribed to films of 

 surface contamination due to dirt or polisher. Such films may 

 be exceedingly thin — of the same order of magnitude in fact 

 as the transition layer. In any given case both the layer and 

 the film may be present and the observed ellipticity be due to 

 their combined action. The principal difference in the effect 

 produced by these two causes would be due to the fact that in 

 the case of the transition layer its index of refraction must 

 vary between those of the two media ; while in the case of the 

 film of surface contamination its index should be approxi- 

 mately 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,f who has shown that on the assumption that the thick- 

 ness of the film is small compared with the wave length 



*Wied. Ann., xxxvi, p. 532, 1889. 



f Wied. Ann., xxxvi, p. 865, 1889. 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. 287. Also in the Physical Optics, by Wood, 

 1905, p. 296 ; and in Winklemann, Handbuch der Physik, 2d Auf. 7, 1906, 

 vol. vi, p. 1256. 



