due to the Scattering of Light by Electrons. 719 



£> Vi f given on page 716, we find that the displacement 

 parallel to y is 



m \ n 2 — 





2 sin 6 sin -^ (cos 6 sin </> cos \|r-f- cos </> sin yjr) 

 sin # cos yjr( — cos # sin <£ sin i/r -f cos (f) cos ^) 



— :r. cos 6 sin # sin </> > 



« 3 2 -p 



I£ there is no order in the arrangement of the atoms or 

 molecules, we see that the average value of each term is 

 zero, so that the light would not be elliptically polarized. 



Magnetic Rotation of the Plane of Polarization. 



An important case when an electric force acting on an 

 electron may produce motion at right angles to itself is 

 when the electrons are exposed to a magnetic field parallel 

 to the direction of propagation of the light. Let H be the 

 magnitude of the magnetic force, y and z the displacements 

 of the electron parallel to y and z respectively, Z the electric 

 force in the light wave. The equations of motion of the 

 electron will be of the form 



J2 * N du 



Ze + Re^ 



dt 





Hence, neglecting terms in H 2 , we find if Z varies as € ipt , 

 dy _ ZfW _ 

 dt ~ m 2 (n 2 -p 2 ) 2 ' 



We see from equation (1) that this involves the production 

 of a wave in which the electric force is parallel to y, and 

 that Y the magnitude of this force for a slab of thickness D 

 is given by the equation 



Y=-2,r^i>^ 



dt 



2 



H.Z. 



(n 2 -p 2 ) 2 



In traversing the distance D the plane of polarization is 

 twisted through the angle Y/Z, or 



2 ™^ r ' S , H.D. 



nrc (n 2 — p 2 ) 2 



