﻿FresneVs Laws of Reflexion. 437 



diminished, but it remained bright enough to allow the 

 absence of colour to be ascertained, especially when the lamp 

 was temporarily brought nearer. An ordinary candle-flame 

 at the same (2 feet) distance was easily visible. 



In order to allow the use of the stopper, the strip was 

 removed from the bottle-prism when the observations were 

 concluded, and it stood for four days exposed to the atmo- 

 sphere. On re-examination it seemed that the reflexion at 

 ^=45° had sensibly increased, a conclusion confirmed by 

 a fresh treatment with hydrofluoric acid. 



It remains to consider the theoretical bearing of the 

 two anomalies which manifest themselves (i.) at the 

 polarizing angle, and (ii.) at other angles when both media 

 have the same index, at any rate for a particular ray. 

 Evidently the cause may lie in a skin due either to con- 

 tamination or to the inevitable differences which must occur 

 in the neighbourhood of the surface of a solid or fluid 

 body. Such a skin would explain both anomalies and is 

 certainly a part of the true explanation, but it remains 

 doubtful whether it accounts for everything.. Under these 

 circumstances it seems worth while to inquire what would 

 be the effect of less simple boundary conditions than those 

 which lead to FresnePs formula?. 



On the electromagnetic theory, if 7 &i are respectively 

 the angles of incidence and refraction, the ratio of the 

 reflected to the incident vibration is, for the two principal 

 polarizations^ 



tan^/tanfl — fi/^ ^ ^ ^ 



tanflj/tanfl-l-zz//*! 



tan ^/tan — K/Kq , -o x 



tan^/tanfl + K/K^ [ j 



in which K, //. are the electric and magnetic constants for 

 the first medium y K l5 fi l for the second * The relation 

 between and Q x is 



Kj/*! : K/a = sin 2 : sin 2 0\ (0) 



It is evident that mere absence of refraction will not secure 

 the evanescence of reflexion for both polarizations, unless we 

 assume both fi l = fju and K^K. In the usual theory /i, is 

 supposed equal to /uu in all cases. (A) then identifies itself 

 with FresnePs sine-formula, and (B) with the tangent- 

 formula, and both vanish when K X = K corresponding to no 



* "On the Electromagnetic Theory of Light," Phil. Mag. vol. \ii. 

 p. 81 (1881); Scientific Tapers, vol', i.-p. 521. 



