516 The Electromagnetic Theory of Light [OH. xviu 



On comparing the results obtained from the electromagnetic theory of 

 light, with those obtained from physical optics, it is found that the wave of 

 light which we have been examining is a plane-polarised ray whose plane of 

 polarisation is the plane containing the magnetic force and the direction of 

 propagation. Thus the magnetic force is in the plane of polarisation, while 

 the electric force is at right angles to this plane. 



Conditions at a Boundary between two different media. 



593. Let us now consider what happens when a wave meets a boundary 

 between two different dielectric media 1, 2. Let the suffix 1 refer to quanti- 

 ties evaluated in the first medium, and the suffix 2 to quantities evaluated in 

 the second medium. For simplicity let us suppose the boundary to coincide 

 with the plane of yz. 



At the boundary, the conditions to be satisfied are ( 137, 467): 



(1) the tangential components of electric force must be continuous, 



(2) the normal components of electric polarisation must be continuous, 



(3) the tangential components of magnetic force must be continuous, 



(4) the normal components of magnetic induction must be continuous. 

 Analytically, these conditions are expressed by the equations 



K.X^K.X,, Y,= F 2 , Z, = Z 2 (550), 



/>t 1 a 1 = ^ 2 a 2 , & = &, 71 = 72 (551). 



It will be at once seen that these six equations are not independent : if 

 the last two of equations (550) are satisfied, then the first of equations (551) 

 is necessarily satisfied also as a consequence of the relation 



_pda == dZ_dY 

 C dt~ dy dz 



being satisfied in each medium, while similarly, if the last two of equations 

 (551) are satisfied, then the first of equations (550) is necessarily satisfied. 

 Thus there are only four independent conditions to be satisfied at the 

 boundary, and each of these must be satisfied for all values of y, z and t. 



Refraction of a Wave polarised in plane of incidence. 



594. Let us now imagine a wave of light to be propagated through 

 medium (1), and to meet the boundary, this wave being supposed polarised in 

 the plane of incidence. Let the boundary, as before, be the plane of yz, and 

 let the plane of incidence be supposed to be the plane of xy. Since the 

 wave is supposed to be polarised in the plane of incidence, the magnetic 



