Motion of Electrons in Solids. 783 



given for vibrations polarized in the plane of incidence by 



K/ Ah cos 2 0,' 

 fjL 2 K x cos 2 l ' 



(19) 



and for vibrations polarized perpendicular to the plane of 

 incidence, by 



£K,cos^ 



^ K/ fli cos- ti x v y 



Then if R 12 denotes the coefficient of reflexion of radiation 

 incident at angle Q x in medium (1), it can be shown in the 

 usual way * that 



Rl2 T+^" s | ' 



where | a + ?/5 | denotes the modulus of a + i/3, namely 



V" 2 + /3 2 . 



For the coefficient of reflexion of radiation incident at 

 angle 6 2 m medium (2), we have similarly 



where m 21 i s given by equations similar to (19) and (20), but 

 having K l5 /aj, 6 x interchanged with KJ, /jl 2 ^ 0-2- It is at once 



obvious that ?«2i= ■— , and from this it follows that R 12 =R 21 . 



It should be noticed that in this equation E 12 is evaluated 

 for light incident at an angle # l? but R 21 for light incident 

 at an angle 6 2 . 



15. Let media 1 and 2 be filled with radiation such that the 

 energy per unit volume of radiation of frequency between p and 

 p + dp is E x dp in medium 1 and E 2 dp in medium 2. 



The stream of energy which falls onto the boundary at an 

 angle between Q x and i +d0 l per unit time is 



iEiViCos^sinMMp, 



so that the amount transmitted from medium 1 to medium 2 

 is 



PxVi dp j (1 -R 12 ) cos 6, sin 0, tWi. - . (21) 



Similarly the amount transmitted from 2 to 1 is 



JE S V 2 dp J (l-RaO cos 2 sin 0, rf0 2 . . . (22) 



In a state in which there is an equal exchange of energy 

 * Jeans, ' Electricity and Magnetism,' p. 523. 



