718 Sir J. J. Thomson on some Optical Effects 



Changes produced by the Electrons on the 

 type of Polarization. 



We see from equation (1) that i£ the electrons acquire 

 from the primary wave a finite average velocity in any 

 direction, secondary waves with the electric force in that 

 direction will be emitted. Thus unless the displacement of 

 the electrons due to the electric force in the primary wave 

 is in the direction of that force, the electric force in the 

 secondary waves will not be in the same direction as that 

 in the primary, and the mixture of primary and secondary 

 waves will differ in the state of the polarization from the 

 primary light. The change may be one or other of two 

 types : (1) the mixed light may differ from the primary by 

 being elliptically polarized; or (2) it may still be plane 

 polarized, but the plane of polarization may be rotated. 



Y the force in the scattered light is by equation (1) 

 proportional to dy/dt : hence, if y is in the same phase as Z, 

 the force in the primary light, dy/dt and therefore Y will 

 differ in phase from Z by a quarter of a period, so that the 

 mixture of primary and scattered light will be elliptically 

 polarized. Jf, however, dy/dt is in the same phase as Z, 

 Y and Z will be in the same phase and the mixture of 

 scattered and primary light will be plane polarized, though 

 the plane of polarization will not coincide with that of the 

 primary light. 



Unless the electrons in an atom are distributed in an 

 exceptionally symmetrical way, a force parallel to z will 

 produce a displacement parallel to y, but in cases similar to 

 that discussed on page 716 the y displacement will be in 

 the same phase as Z, and dy/dt will differ in phase from Z 

 by a quarter of a period and the light will be elliptically 

 polarized, The amount of ellipticity in the polarization 

 will depend upon the orientation of the atoms or molecules, 

 and in non-crystalline substances there may be as many 

 molecules producing a positive effect as there are producing 

 a negative one, so that the aggregate effect may be nil and 

 the light will continue to be plane polarized. Thus in the 

 case considered on page 716 the displacement parallel to y 

 produced by the force Z is 



£(cos sin cj> cos -yjr + cos (/> sin yjr) 



+ w(— cos sin cj> sin i|r + cos $ cos ^/r) + f (sin sin 0) r 



where 6 and </> have the same values as before, and yjr is the 

 angle between ZC and ZX. Substituting the values of 



