PKOCEEDINGS 



OF THE 



AMERICAN ACADEMY 



OF 



ARTS AND SCIENCES. 



VOL. IX. 

 PAPERS READ BEFORE THE ACADEMY. 



I. 



APPLICATIONS OF FRESNEL'S FORMULA FOR THE 

 REFLECTION OF LIGHT. 



By Edward C. Pickering. 



Read, Oct. 14, 18T3. 



Part I. Theoretical. 



One of the most beautiful applications of the Undulatory Theory was 

 made by Fresnel, in deducing a formula for computing the amount 

 of light reflected by the surface of a transparent medium. He showed 

 that if the light was polarized in the plane of incidence, that the 

 amount reflected would be ^ = %ji~^y while, if polarized in a 

 plane perpendicular to it, the proportion would be ^ = ^^"g" ('—'•) 



t and r representing the angles of incidence and refraction respectively. 

 Natural light may be regarded as composed of two equal beams polar- 

 ized at right angles, hence the amount reflected H = )y (A ~\- B) 



~ 2 l^sin'^ (i + r) r tang-'((+r)J' ^ formula which may be applied to 

 any special case, by substituting proper values for i and r. The value 

 of A evidently increases as ^ varies from 0° to 90°. That of B, on 

 the other hand, diminishes from 0° until ^ + r = 90°, when it equals 0, 

 or at this angle, which is that of total polarization, all of the ray B is 

 transmitted, all the reflected beam being polarized in the plane of inci- 

 dence. When i = 90°, A .-= 1, B= 1, hence all the light is reflected. 

 When the light, instead of passing from the rare to the dense 

 medium, goes in the other direction, the same amount of li^ht is 



VOL. I. 1 ° 



