420 Prof. Jakob Kunz : An Elementary Theory of the 



scattered in any direction is proportional to E s 2 and therefore 

 proportional to sin 2 $. 



The energy dE contained in a ring of volume 



dr=2irr sin SrdS.l 



due to the oscillating doublet 



E s 2 

 is equal to dE = -5— dr 



07T 



equal to dE = ^E 2 (t^* g V*£ S -^2irr 2 sin $dd, 



where V= -t>-R 3 is the volume of the scattering sphere. 



The energy E^ in a spherical shell of unit thickness is 

 therefore 



4 



E 2 V 2 /£-l 



or 



(— -Y 



= 3tt 



but the electric energy E 2 per unit volume of the primary 



E 2 

 beam is equal to E x = — hence 



For the light scattered by N particles per unit volume, 

 arranged in random order so that energies may be summed 

 without considering phase differences, we should have 



r^Sfe 1 ) 2 *' • • • • (6) 



an expression first given by Lord Rayleigh by a different 

 method. The energy radiated from a layer of thickness dz 

 and of unit area is therefore 



E x - 47r \*\k + 2J 



or E! = E e- 



hz 



VV/v-lV. 



^toJ 1 



