﻿438 On Departures from Fresnel's Laws of Reflexion. 



refraction. Further, (B) vanishes at the Brewsterian angle, 

 even though there be refraction. A slight departure from 

 these laws would easily be accounted for by a difference 

 between fjb x and fi, such as in fact occurs in some degree 

 (diamagnetism). But the effect of such a departure is not 

 to interfere with the complete evanescence of (B), but 

 merely to displace the angle at which it occurs from the 

 Brewsterian value. If /x 1 //A=l + /i, where li is small, calcu- 

 lation shows that the angle of complete polarization is changed 

 by the amount 



8g= -( ^+i)(»«-i )> • • • • (I)) 



n being the refractive index. The failure of the diamond 

 and dense glass to polarize completely at some angle of 

 incidence is not to be explained in this way. 



As I formerly suggested, the anomalies may perhaps be 

 connected with the fact that one at least of the media is 

 dispersive. A good deal depends upon the cause of the 

 dispersion. In the case of a stretched strings vibrating 

 transversely and endowed with a moderate amount of 

 stiffness, the boundary conditions would certainly be such 

 as would entail a reflexion in spite of equal velocity of 

 wave-propagation. All optical dispersion is now supposed 

 to be of the same nature as what used to be called anomalous 

 dispersion, i. e. to be due to resonances lying beyond the 

 visible range. In the simplest form of this theory, as given 

 by Maxwell * and Sellmeier, the resonating bodies take their 

 motion from those parts of the eether with which they are 

 directly connected, but they do not influence one another. In 

 such a case the boundary conditions involve merely the con- 

 tinuity of the displacement and its first derivative, and no 

 complication ensues. When there is no refraction, there is 

 also no reflexion. By introducing a mutual reaction between 

 'the resonators, and probably in other ways, it would be 

 possible to modify the situation in such a manner that the 

 boundary conditions would involve higher derivatives, as in 

 the case of the stiff string, and thus to allow reflexion in 

 spite of equality of wave-velocities for a given ray. 



P.S. Jan. 15. — Some later observations upon a surface 

 of fused quartz are of interest. The plate, prepared by 

 Messrs. Hilger, was -J inch square, and the surfaces were 

 inclined at a few degrees so as to separate the reflexions. 



* Cambridge Calendar for 1869. See Phil. Mag. vol. xlviii. p. 151 

 (1899) : Scientific Papers, vol. it. p. 413. 



