1893.] 



Experiments on the Reflection of Light. 



71 



It is, moreover, worthy of note that i* is a very small angle, whose 

 maximum value is less than 2°. 



3. In a paper published in the Phil. Trans, for 1891 I 

 deduced formulae giving the amplitudes of light reflected at the 

 surface of a transparent magnetized medium, by means of the 

 hypothesis that Hall's effect can exist in dielectrics. When 

 the lines of magnetic force are perpendicular to the reflecting 

 surface the equations giving the amplitudes A', B' of the reflected 

 wave in terms of the amplitudes A, B oi the incident wave are 

 (30) and (31) of that paper, and are as follows : 



A (Ucosi — Vco&r) 



A' = 



B' = - 



Ucos i + Fcosr 



+ 



2iqBV co^i 



U{U cos r+ V cos i) ( ZJcos i + V cos r) 

 B (U cos r — V cosi) 

 IT cos r + V cos i 



+ 



2iqA V cos i 



....(4), 



....(5), 



U (Ucos r + Vcosi) (Ucos i + V cosr) 



where U, V are the velocities of light in air, and in the transparent 

 medium when unmagnetized, i and r the angles of incidence and 

 refraction, and q a quantity which is directly proportional to the 

 magnetic force. The magnetic permeability k is supposed to 

 be unity *, and the directions of the various quantities are shewn 

 in the figure. 



Fig. 1. 



I shall now transform these formulae in the same manner 

 as Eisenlohr has transformed Fresnel's sine and tangent formulae, 



* In the case of an iron reflector we have no right strictly speaking to put h 

 equal to unity; but as the formulae which will ultimately be deduced are of a 

 tentative character and do not profess to be founded upon a rigorous dynamical 

 theory, little would be gained by retaining h. 



[Prof. J. J. Thomson suggests on p. 422 of his Electricity and Magnetism that 

 iron may not retain its magnetic properties when subjected to such rapidly alternat- 

 ing waves as waves of light. Sep. 1893.] 



