Waves at the Surface of a Moving Mirror, 521 



The average value of E x 2 over the surface of the mirror is 

 equal to a 2 / 2 at each instant. Therefore the average pres- 

 sure p is given by 



2a? (ccos0 + v) 2 /0 . N 



P= Q — 1~ — o — * — (o4; 



1 87TC 2 C 2 — V 



When = 0, (34) reduces to (7). When u=0 



p-S;^ 6 < 35 ) 



11. The problem of reflexion at a perfectly reflecting 

 mirror, which is moving in a direction perpendicular to its 

 plane, has now been completely solved for the case where 

 the electric field of the incident waves is perpendicular to the 

 plane of incidence. The case where the motion of the mirror 

 is tangential, the electric field of the incident waves being- 

 perpendicular to the plane of incidence as before, presents 

 little difficulty. 



In the first place, let the mirror move tangentially from 

 South to North with the velocity v. Then, taking into account 

 the auxiliary forces called into play by the motion of the 

 mirror, the condition that the force on a unit positive charge 

 placed near the mirror and moving with it, must vanish, is 

 expressed by the equation 



Ei + E 2 + -(E^intf-Easinfl')*!), 



... fr.'+'^'+B,.'-'"''^. . (36) 



c c 



The condition that the component of the force exerted on 

 a unit N pole placed near the mirror and moving with it, 

 resolved perpendicular to the surface of the mirror, must 

 vanish, gives 



- (E 2 sin - E 2 sin 0') + \ (E x + E 2 ) = 0, 



.-. t(E 1 (csin^+t?)-E 2 (csin^-i?)=0. . . (37) 



From (36) and (37), 



e + v sin 6 _ c — t?sin0' 

 c sin -r c c sin b' — •«' 



.-. sin 0\c 2 -v 2 )=- sm0(c 2 -v 2 ), 

 and 0'=-0, 



so that the ordinary law of reflexion is obeyed. The reflected 



