526 Reflexion of Electromagnetic Waves, 



Now let the mirror move vertically upwards with velocity v. 

 As before, we have 



E 1 cos^ + E 2 cos^ = 0, 



which leads to the result just obtained. 



Thus, tangential motion of the mirror produces no effect on 

 the reflected waves, whatever may be the direction of the 

 electric field of the waves. 



Pressure exerted by Diffuse Radiation on an 

 Advancing Mirror. 



15. Now let it be supposed that plane waves, travelling 

 indiscriminately in all possible directions, are reflected from 

 a perfectly conducting mirror which is advancing to meet 

 them with a velocity v. Choose any point in front of the 

 mirror, and let n plane wave-trains, each of amplitude a, be 

 passing through the point towards the mirror. From the 

 chosen point draw a unit vector pointing along the direction 

 in which each wave-train is advancing ; the remote ends of 

 these vectors will be distributed uniformly over the surface 

 of a hemisphere of unit radius described about the point. 

 From the point drop a perpendicular on to the mirror, and 

 let 6 be the angle that any vector makes with this line. 

 Then the number of vectors inclined to this line at angles 

 lying between 6 and 6 + d6 is 



n 



n- lir sin 6d6 = n sin Odd. 



LIT 



This gives the number of wave- trains incident on the 

 mirror at angles between 6 and 6 + dd, and each of these 

 wave-trains exerts an average pressure given by (44) , what- 

 ever may be the direction of the electric field of these waves. 

 Then the total average pressure exerted by the n wave-trains 

 is equal to 



W 1 p 



8ttc 2 'c 2 -v 2 ] 

 •Jo 



{ccos0 + v) 2 sindd0 



1 2na 2 (c + v) ? ' — v* 

 3c'Snx 2 ' c 2 -v 2 



1 W ( c +vy+(c + v)v 



3'8tTC 2 ' C l — V % 



3 Sttc 2 



f c+2v v 2 ~] 



\c-v + c 2 -v 2 j ' 



