TRANSACTIONS OF SECTION A. 811 



\). On tlie Electromagnetic Theory of Reflection on the Surface of Crystals. 



By Dr. CiiAs. E. Curry. 



When ordinarj^ light strikes the surface of an isotropic insulator, as glass, at 

 tfuch an angle that the retiected and the refracted rays form a right angle with 

 each other, the retiected ray is found to be linearly polarised (Brewster's law). 

 To my knowledge, however, little is known about the light reflected from the 

 surface of crystals. 



In the treatment of the brbaviour of light on the surface of crystals it is 

 customary to make use of the so-called ' uniradial azimuths ' introduced by 

 MacCullagh ; their determination depends on the properties of the given crystal 

 (the reflecting surface used, &c.), and the angle of incidence of the given wave, but 

 not on the azimuth, in which the given oscillation is taking place. These uniradial 

 azimuths are, as we know, rotated through certain angles upon reflection. Are 

 there now angles of incidence c^, for which the uniradial azimuths coincide with 

 each other after reflection ? The general condition for such a coincidence is ^ 



sin <9„ sin (<^ -(^J 



tan 6^ sin 'cp^ 



sin V sin (th ~<h\ 



(1) 



cos 6g sin (^ - ^^) cos (0 + (^^) - tan e^ sin -cp^ 



sin v^ sin (^ - <^ J 



cos 6^ sin (^ - <^J cos ((^ + ^^) - tan e^ sin -^^, 



where o refers to the ordinary and e to the extraordinary wave ; ^^ and denote 

 here the angles of refraction of tlie ordinary and extraordinary wave respectively, 

 <9„ and 6^. their respective azimuths, and e^ and e^ the small angles between the 

 directions of propagation of these waves and those of their so-called rays. 



This cnnditiou (1) may be regarded as an equation for the determination of the 

 angle <^ ; we observe that it does not contain the azimuth 6 of the incident wave. 

 It thus follows : when ordinary light strikes the surface of the given crystal at 

 such an angle ^, determined by this equation, it will be reflected as linearly 

 polarised, as in the case of an isotropic insulator, or certain phenomena as those 

 of interference will make their appearance; which of these phenomena occur will, 

 however, depend upon the assumption made with regard to the behaviour of the 

 ether-molecules in the film between the two bodies. Conversely, observations of 

 such phenomena might throw light on the assumption to be made. 



The above equation for (f> is, however, too general to admit of a solution ; all 

 information must thus be gained from an examination of 

 special cases; I have chosen the following one for the 

 preseut purjjose, since it appears to be of particular interest. 

 Let one (if the principal planes of the given crystal be taken 

 as reflecting surface, and let the plane of incidence lie in 

 one of tlie other two, as indicated in the annexed figure. 

 ( y .:: reflecting plane, .r y incident plane) 



The above equation for ^ then reduces to 



sin (^ - (^^,) cos (^ + 0^,) - tan e^ sin -(^^ =0 ; . . . (2) 



its derlvalion, into which I cannot enter here, requires considerable care, chiefly 

 on account of the appearance of indeterminate forms. 

 Explicitly, it can be written 



/■■■]/'•• - (A- - W) sin "4>'] cos (^ = B ^v- - A? sin '(f, [u= + (A'^ - B-) sin ^^J, . (3) 



wliere A, B, C are three medium constants of the dimensions of a velocity, and v 

 the velocity of propagation of electromagnetic disturbances in air. 

 For isotropic insulators, i.e. A=^B=C', this equation for 4> becomes 



V 



' Of also P. Volkmann,T(;/'/6's«w^d!re iiher die Theorie des Lichtes, p. 341. 



