Waves at the Surface of a Moving Mirror. 525 



This, however, is not the only force exerted on the mirror. 

 The electric field (E x sin 9 + E 2 sin $') , normal to the surface 

 o£ the mirror, exerts a tension equal to 



q — 2 (E x sin -f E 2 sin 0') 2 per unit area, 



OTTC 



and from (38) and (28) 



1 L E x sin 6 J 



so that the tension is equal to 



The net opposing pressure exerted on the advancing mirror 



is therefore equal to 



2JV / (c + rcosfl) 2 _ . ~\ _ 2E1 2 (ccosfl + 7;) 2 

 47TC 2 L c 2 -?; 2 * J-W c 2 -r 2 » 



which is equal to the pressure that is exerted when the 

 electric field of the incident waves is perpendicular to the 

 plane of incidence. 



Averaging the value of Ex 2 over the surface of the mirror, 

 we find that the mean pressure p opposing the advance of 

 the mirror is given by the equation 



2a 2 \ccos0 + v) 2 /AA , 



P=o — "--^ 2—- • • • ( 44 ) 



14. For the sake of completeness, the case of reflexion 

 from a mirror that moves tangentially with a velocity v may 

 be briefly considered. 



First, let the mirror move from South to North. Then the 

 tangential electric force is unaffected by the motion, and in 

 order that it may vanish, we have 



EiCOsfl + EjCOsfl'rrO. .... (45) 



Writing a = in (13) and (14), and substituting the values 

 of E x and E 2 in (45), we obtain 



a cos 6 . cos \m(y sin 6 + ct) \ + a'cos#' cos {m'(ysin — ct) J=0. 



This equation can only be satisfied for all values of y and t, 

 when 



a cosd + a f cos ! = 0, 



m sin 6= —)>i' sin 6', 



mc = m'c, 



.-. sin 0'= — sin 0, and 0' = -0. 



Then a' = — a. 



