[ 822 ] 



XC. Note on the Reflexion of Electromagnetic Waves from 

 the Surface of a Moving Mirror. By T. Harris *. 



IN the Philosophical Magazine, October 1914, Mr. Edser 

 published a paper on the " Reflexion of Electromagnetic 

 Waves at the Surface of a Moving Mirror." He shows there 

 that both the amplitude and frequency of electromagnetic 

 waves are altered by the motion of the reflector, and that 

 this alteration in amplitude is responsible for the change in 

 energy density of the reflected waves. 



I should like to point out that the problem has already 

 been discussed by H. A. Lorentz in his 'Theory of Elec- 

 trons,' for the case when both the direction of the waves 

 and the motion of the mirror are along the normal to the 

 mirror. 



It may also, perhaps, be of interest to show that the 

 pressure can be calculated very simply, using the well- 

 known idea that electromagnetic waves possess momentum. 

 Taking, for simplicity, a parallel beam of waves, it can easily 

 be shown that the momentum possessed by unit volume is 



-, where e is the energy density of the waves and c the 



c 



velocity, the direction of the momentum flow being that of 

 the beam. Suppose this beam to be incident normally upon a 

 mirror moving with a velocity v, in a direction opposite to 

 that in which the incident beam is travelling. Let e 7 be the 

 energy density of the reflected waves, which therefore possess 



momentum - per unit volume. Then the momentum received 



c .6 



by the mirror per unit area per second is -(c + v) from the 



incident waves and - (c—v) from the reflected waves as they 



leave the mirror. Hence, we have 



e' € 



p =-(«-*) + -(<? + v), 



where p is the pressure on the mirror. 



The work done by unit area of the mirror per sec. is 

 equal to the difference between the flow of energy away from 

 and up to the unit area per second, hence 



pv = e'(c- v) — e(c -f v), 

 * Communicated by the Author. 



