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XIII. On the Reflection and Refraction of Light. 
By G. A. Schott, B.A. (Canib.), B.Sc. {Bond.), formerly Scholar oj Trinity 
College, Cambridge. 
Communicated by K. T. Glazebkook, M.A., F.R.S. 
Received Novembei’ 29, 1893,—Read Janaary 18, 1894. 
Introduction. 
The object of the following paper is to examine how far the hypothesis of a thin 
layer of transition between two transparent media will explain in detail the phenomena 
connected with the elliptic polarization produced by reflection at the boundary of two 
such media. 
This problem has been approached by the following writers :—L. Lorenz, 
‘ PoGGENDOEFF Annalen,’ 114, p. 460; Van Ryn van Alkemaade, ‘Wiedemann 
Annalen,’ 20, p. 23 ; and P. Drude, ‘ Wiedemann Annalen,’ 34 and 36. 
Lorenz starts on the basis of the elastic solid theory, assuming that Fresnel’s 
formulae hold for a very small change of refractive index, and deduces expressions 
holding for a finite change of refrangibility, which are slight modifications of Fresnel’s 
formulae, and clearly unsound, since a rigid elastic solid theory must lead to Green’s 
formulae, and not to Fresnel’s, as a first approximation. Fresnel’s formulae ought 
not without examination to be assumed to hold even for a very small change of 
refractive index, for the rate of change of refrangibility in crossing the boundary 
must be very rapid in order to produce a finite change, in a distance of the order of a 
wave-length. 
Van Lvn van Alkemaade treats only of the electromagnetic theory of light— 
by successive approximation. His expressions fur the change of phase are the same 
as in the following paper, namely (with notation changed from his), 
tan (p_L) = 2 S/Tq cos i^ — -—— ^ and tan (pi I) = 2 S/iq cos i^ -- ; 
but for the amplitudes he gets 
{Rif = 
tan® (zq — ij) 
tan® (L + h) 
[1 + tan^ (pll)], 
(El 1)2 
sin® (L - h) 
sin® (z'o + h) 
[1 + tan2(p||)], 
28.12.94 
