THERMODYNAMICS OF RADIATION. 



339 



Doppler's principle the wave-length of the reflected train is altered. Sup- 

 pose that the reflecting surface B is moving with velocity u away from the 

 source A (Fig. 192). Consider first a normal pencil. It will appear, 

 when reflected, to come from a source A', as far behind B as A is in 



2u 



B 



FIG. 192. 



front, so that A' is moving back with velocity 2u and the waves, which 

 in the incident beam fill a length U equal to the velocity of radiation, 

 fill in the reflected train a length U + 2u. Hence if A, is the wave-length 

 in the incident train, A.' that in the reflected, 



or if A.' = X + d\ 



U 



If the train is inclined at 9 to the normal, then (Fig. 193) the reflected 

 train may be supposed to come from A', the image of the source A in the 



2u A' 



Fro. 193. 



reflecting surface B, and again A' is moving back with velocity 2u. But 

 this only increases the length of the reflected p.ith by 2cos#. Hence 

 the waves originally in U will be now spread over U + 2wcos0 and 



