﻿S94 
  Reflexion 
  of 
  Light 
  at 
  an 
  Ideal 
  Plane 
  Mirror, 
  

  

  and 
  magnetic 
  force 
  in 
  the 
  incident 
  and 
  reflected 
  waves 
  are 
  

   obtained 
  by 
  putting 
  * 
  

  

  [ 
  + 
  Ex' 
  diydz' 
  + 
  E/ 
  d^dx' 
  + 
  E/ 
  da^diJ-cE.x' 
  dw'dt' 
  

   -cRy' 
  di/'dt'-cit^dz'df] 
  

   =Exd^dz 
  + 
  'Eydzdx 
  + 
  Ezdxdij 
  + 
  cBixdxdt 
  + 
  cRydydt 
  + 
  cRzdzdt, 
  

  

  where 
  (E^, 
  E^, 
  E^) 
  (Hx, 
  Hy, 
  H^) 
  are 
  the 
  components 
  of 
  the 
  

   electric 
  and 
  magnetic 
  force 
  respectively. 
  

  

  Calculating 
  Ex'', 
  Hx' 
  ... 
  by 
  means 
  of 
  the 
  formulae 
  

  

  we 
  have 
  

  

  c^ 
  — 
  'tj- 
  ^ 
  c^—v^ 
  ' 
  c^ 
  — 
  ■y^ 
  c^ 
  — 
  v^ 
  

  

  These 
  give 
  

  

  E/ 
  + 
  7;H/=-(Ey 
  + 
  ^H,), 
  

   E/-i;H/= 
  -(E.-rHy), 
  

   H/-vE/=-(H^-t;E.), 
  

  

  H/ 
  + 
  i'E/=-(Hz 
  + 
  rE^). 
  

  

  Relative 
  to 
  an 
  observer 
  moving 
  with 
  velocity 
  v 
  the 
  com- 
  

   ponents 
  of 
  the 
  electric 
  and 
  magnetic 
  force 
  are 
  

  

  ^ 
  ^y 
  + 
  vRz 
  E^-^;Hy, 
  

   Ji/A', 
  # 
  - 
  i 
  ^ 
  

  

  H. 
  

  

  

  Hence 
  the 
  above 
  equations 
  indicate 
  that 
  the 
  sum 
  of 
  the 
  

   tangential 
  components 
  of 
  the 
  two 
  vectors 
  in 
  the 
  incident 
  and 
  

   reflected 
  waves 
  is 
  zero 
  at 
  the 
  surface 
  of 
  the 
  mirror. 
  

  

  * 
  See 
  a 
  paper 
  by 
  the 
  author, 
  Proc. 
  London 
  Math. 
  Soc. 
  1909. 
  

  

  