96 JAMIN ON METALLIC REFLEXION. 



angle CAB; in this case, the restored ray will be polarized on 

 the same side of the plane of incidence as the incident ray. 



If the multiple is uneven, the component vibrations have a 

 final difference of route equal to a semi-undulation ; they are 

 discordant, and the restored vibration will take place in the angle 

 B' A' C, or C A B'. The direction of its polarization therefore 

 will be changed. 



Thus, for angles which, after (m) reflexions, will give between 

 the principal rays differences of phase equal to 

 2X 4A 6X 

 ' ~2' '¥' ~2~' 



the restored ray will be polarized to the right of the plane of in- 

 cidence, if the incident ray was polarized to the right. 

 But if the differences are 



A 3 A 5 X 



2' ~2~' ~2~' 



the plane of restored polarization will be the left of the plane of 

 incidence. 



Therefore, for the angle nearest to 0°, the polarization will be 

 restored to the left ; for that which comes next, to the right ; and 

 so on alternately to the last. 



It is as well to remark, that these two data, the angle which 

 restores the polarization, and the direction of the azimuth of the 

 restored ray, depend absolutely only on the difference of phase 

 of the rays polarized in the principal planes. We shall soon see 

 that the azimuth of the restored ray depends only on their in- 

 tensity. 



3rd. The incident ray being still polarized in the azimuth of 

 (90°— c), it is decomposed into two others whose amplitudes are 

 cos a and sin a ; after the first reflexion they become 

 I cos a, vibration in the plane of incidence, 

 J sin a, vibration perpendicular. 

 A second reflexion will cause them to undergo proportional 

 changes ; they will become 



I^ cos a, 3^ sin a. 

 They will be finally, after (m) reflexions, 



I"* cos a, and J"' sin a. 

 And if the polarization is restored at a certain incidence, the 

 cotangent of the azimuth of vibration, or which comes to the 

 same thing, the tangent of the azimuth of restored vibration, will 



