PROPAGATION OF A PLANE WAVE. 625 



Substituting these* values in equations (34), we get 



/Vr yz yo\ _yp 



^ " ~ " ' 



(35) 



KM -^+ 



These equations have a solution of the form 



Y =r cos (// - qz] cos #*, 

 (36) 



G = r cos (/^ - qz] sin ws. 



The coefficients will be determined by the condition that the 

 differential equations are satisfied for all values of z and of /, which 

 gives 



(37) 



Z? 2 

 7 - = 0. 



The values of F and G are projections on the axes of an 

 electromotive force r cos (// qz\ which makes with the axis of x 

 an angle mz proportional to the thickness. 



643. ROTATION OF THE PLANE OF POLARIZATION. The 

 phenomenon represents then a ray of light, which is propagated 

 along the z axis with a velocity V = -, the period of whose 

 vibration is T = ; the wave length that is, the space traversed 



*. p 2TT 27T 



during a period is A = -- = . 

 q p q ^ 



This ray is rectilinearly polarized ; but the plane of polarization 

 rotates as in an active medium, and the complete rotation is effected 



27T 



in a time T = . 

 m 



s s 



