AND TRANSMITTED BY THIN PLATES. 1G1 



When the incident light is polarized perpendicularly to the plane 

 of incidence, the signs of u and w 2 depend on the incidence, as well 

 as on the relative refractive densities of the media. When the 

 angle of incidence is less than the polarizing angle at either .sur- 

 face, the sign of u, or of 2 , is the same as in the case of light 

 polarized in the plane of incidence ; when it is greater, the sign is 

 opposite. Accordingly, when the incidences at both surfaces are 

 less than their respective polarizing angles, the character of the 

 rings will be the same as for light polarized in the plane of inci- 

 dence. And the same thing is true when the incidences at both 

 surfaces are greater than their respective polarizing angles ; for 

 in this case the signs of u and w 2 are changed simultaneously. But 

 when the incidence at one surface is less, and at the other greater, 

 than their respective polarizing angles, one of the quantities, u and 

 w 2 , changes sign, and the other does not ; and the character of the 

 rings will be the opposite to that presented when the light is 

 polarized in the plane of incidence. 



It follows, then, that when the refractive density of the plate 

 is greater or less than those of the two media, the rings will be 

 dark -centred at the lower and higher incidences, and bright-centred 

 at the intermediate incidences. This phenomenon was observed 

 by Arago, and explained by Mr. Airy. On the other hand, when 

 the refractive density of the plate is intermediate to those of the 

 two media (the light being still polarized in the perpendicular 

 plane), the rings will be bright-centred at the lower and higher 

 incidences, and dark-centred at the intermediate incidences. This 

 latter case has not been hitherto noticed. 



At the polarizing angles of either surface, u = 0, or u = 0, and 

 the rings vanish. 



7. Now let the incident light be polarized in any plane, inclined 

 at the angle y to the plane of incidence ; and let the amplitude of 

 the incident vibration (= 1) be resolved into two, cos y and sin 7, 

 in the plane of incidence and in the perpendicular plane, respec- 

 tively. Let v and i\ denote the values of u and v, in the case of 

 light polarized in the plane of incidence ; w and r 2 the correspond- 

 ing values for light polarized perpendicularly ; then the intensities 

 of the light in the two reflected pencils are 



E* + 2cf, cos Q + t ./ ., r u? + 2M-tf> cos a + f^ h)2 



~ l + - + rY CCS ~ 7 ' " 1 + Stfw, cos a 4 tftf 



