106 On the Direction of the Vibrations of a Polarised Ray. 



abrupt change of condensation caused by a break of continuity 

 of the circumstances of the fluid. So far as the sudden retarda- 

 tion acts in the direction of the axis of the wave-ray, it produces 

 reflexion, but no polarization, because this action is symmetrical 

 with respect to the axis. Reflexion also takes place by a sudden 

 retardation of the transverse vibrations, because such retardation 

 causes a sudden increment of condensation or rarefaction along 

 the axis and contiguous parts. (The eff'ect of transverse action 

 is considered in a communication to the Philosophical Magazine 

 for February 1853, under Proposition XIII.) If the transverse 

 vibrations be resolved in directions perpendicular and parallel to 

 the plane of refraction, no polarization appears if the retardations 

 of the two sets of vibrations are equal. Polarization is in pro- 

 portion to the difference of the retardations, because, if such dif- 

 ference exists, the action on the wave-ray is not symmetrical 

 about its axis. The platie of polarization is coincident with the 

 plane of refraction, because the retarding action is symmetrical 

 about this plane. 



These preliminaries being admitted, it may next be shown 

 that polarization must be produced in every case of reflexion by 

 oblique incidence. For the transverse vibrations perpendicular 

 to the plane of refraction are suddenly impeded at the surface 

 of the medium, without any opposite action in this direction, 

 because, as we have seen, d^ before refraction is the same as d\ 

 after. As this is the case for every value of ^, this set of vibra- 

 tions always gives rise to reflexion. The other set of transverse 

 vibrations are also impeded, so far as the action of the medium 

 is concerned ; but simultaneously with the increase of condensa- 

 tion or rarefaction by this action, a decrement is caused by the 

 change of d^ into the greater value d'^, and the consequent dis- 

 persion of the condensation or rarefaction over a larger space. 

 The reflexion is due to the excess of the former action above the 

 other. Hence the transverse vibrations of the reflected wave-ray 

 perpendicular to the plane of reflexion, since they suff"er no such 

 diminution, are greater than those parallel to that plane ; that 

 is, the reflected ray is j)artialhj polarized. 



In the particular case in which tan^ = /Lt, it has been shown 

 that s' = 5. In this case the medium has no tendency to check 

 either the longitudinal vibrations, or the transverse vibrations in 

 the plane of reflexion. Consequently there is no reflexion of 

 transverse vibrations in this plane, and the reflected ray is com- 

 pletely polarized. If this completely polarized ray be received 

 at the same angle of incidence on the same substance, the plane 

 of refraction being turned through 90°, as there will be no action 

 to check either the direct or the transverse vibrations, there will 

 be no reflexion whatever, as is known to be the fact. 



