178 TRANSVERSAL VIBRATIONS : 



result from a consideration of the formula, and to show 

 that a similar change must take place in the rings formed 

 between two transparent -substances of different refractive 

 powers, as the incidence passes the polarizing angle of either 

 substance. 



(190) When a polarized ray undergoes reflexion, the 

 reflected light is still polarized, but its plane of polarization 

 is changed, the amount of the change depending on the in- 

 cidence. When the angle of incidence is nothing, or the 

 ray perpendicular to the reflecting surface, the new plane of 

 polarization is inclined to the plane of incidence by the same 

 angle as the old, but on the opposite side. As the angle of in- 

 cidence increases, the plane of polarization of the reflected ray 

 approaches the plane of incidence, and finally coincides with 

 it, when the incidence reaches the polarizing angle. As the 

 angle of incidence still further increases, the plane of polariza- 

 tion of the reflected ray crosses the plane of incidence, and 

 therefore lies on the same side of it with the original plane ; 

 and the two planes of polarization finally coincide, when the 

 angle of incidence is 90. 



The azimuth of the plane of polarization of the reflected 

 ray may be deduced from the theory we have been consider- 

 ing. For, let the vibration of the incident ray, a, be re- 

 solved into two, one in the plane of incidence, and the other 

 in the perpendicular plane. If a denote the angle which it 

 makes with the plane of incidence, these resolved portions 

 are a cos a, and a sin a. After reflexion they become,* re- 

 spectively, 



sin (i-r) - tan (i-r) t 



- a cos a _ : _ -, a sin a - - ; 

 sin (i + r) tan (i+r) 



* In order to explain the facts above mentioned, the values of v and v' 

 (184, 5) must be affected with opposite signs; and there are other phenomena 



