174 TRANSVERSAL VIBRATIONS ! 



(185) In the case of light polarized perpendicularly to the 

 plane of incidence, the vibrations are all in the plane of inci- 

 dence ; and, since they are also perpendicular to the rays 

 themselves, the condition given by the first principle is 



(1 + 0') cos i = w' cos r ; 



the other conditions remaining the same as in the former case. 

 Eliminating, as before, we have 



1 - v _ sin i cos i 

 1 + v sin r cos r 

 "Whence 



^^ /= tanfc'-r) ^ = sin 2 i 



tan (i + r)' sin (i+ r) cos (i - r)' 



(186) The intensity of the light is measured by the vis viva, 

 or by the mass of the ether put in motion, multiplied by the 

 square of the amplitude of the vibration. Hence, for light 

 polarized in the plane of incidence, the intensities of the inci- 

 dent, reflected, and refracted rays will be m, mv z , and w'p 2 , 

 respectively ; or, if we take the intensity of the incident 

 light as unity, 



1, v*, and 1 - v 2 ; 



since, by the law of the vis viva, m (1 - v 2 ) = m'w n . Simi- 

 larly, for light polarized in the perpendicular plane, the in- 

 tensities in the three pencils are 



1, v /2 , and 1-V 2 . 



(187) Confining our attention for the present to the re- 

 flected vibration, it will be easily seen that, for light polar- 

 ized in the plane of incidence, the value of the amplitude v, 

 and consequently the intensity of the light, increases with 



