39,8 Sir J. J. Thomson on the Scattering of 



scattered light, OZ the direction of the electric force in 

 the incident light ; IZ is always equal to tt/2. 



The intensity of the scattered light is, as we have just 

 seen, proportional to 



2f+ (g-f) sin* 0. 



cos — cos PZ = sin (f> cos yfr. 



If </> = PI, ^ = PIZ. 



Hence the intensity of the scattered light is pro- 

 portional to 



/+#-(#-/) sin2 # cos2 ^- 



If the light is not polarized and all values of ty are 

 equally probable, the mean value of cos 2 -^ is 1/2. So that 

 the intensity of the scattered light is 



Since g is greater than / the intensity is greatest when 

 <£ = 0, when it is equal tof+g, and least when $ = 7r/2, when 

 it is equal to i(3f+g) ; since / is positive the minimum 

 intensity is always greater than (f+g)/2, and thus always 

 greater than half the maximum energy. For the sym- 

 metrical atom /=0 and the minimum intensity of the 

 scattered light is one-half the maximum. 



Another point of difference between the scattering of 

 light by symmetrical and unsymmetrical atoms occurs 

 when the distances between the scattering atoms are small 

 compared with the wave-length of the light. With sym- 

 metrical atoms or isolated electrons the scattered light 

 reaching a point P will be in the same phase from which- 

 ever atom it may proceed ; so that if there are N atoms 

 the intensity of the magnetic force will be proportional 

 to N and the intensity of the scattered light will be 

 proportional to N 2 . In the case of unsymmetrical atoms, 

 though they may be packed close together, the phase of 



