54 



SIR DAVID BREWSTER ON THE PHENOMENA OF THIN PLATES 



The results in this Table, which may be considered as those of observation*, exhibit 

 at one glance the general phenomena at all angles of incidence and azimuth. 



The two interfering pencils are in every case reflected at angles either both above 

 or both below the polarizing angle, and hence their planes of polarization are always 

 on the same side of the plane of reflexion and in the same quadrant, and consequently 

 they never can be at right angles to each other so as to prevent interference. For 

 the same reason the inclination of the planes never can exceed 90°, so as to produce 

 the complementary white-centred rings, in conformity with the law previously given. 



If, for example, we compute the value of x in the preceding formula at an inci- 

 dence of 70°, we shall find it Q&° 25', at which azimuth the inclinations <p and ^"' of 

 the planes of polarization are 40° 47', and 49° 53' ; but though the sum of these an- 

 gles is 90°, yet the real inclination of the planes is (p'" — ^ = 9° 6'. 



This property of parallel transparent films, of giving by reflexion pencils polarized 

 in planes at various inclinations, when the incident light is polarized in different 

 azimuths, enables us to obtain two pencils of polarized light, inclined at any angle, 

 varying from 0° to 21° 44' in glass, and to study the phenomena which such pencils 

 exhibit, either in their mutual action, or in their relations to other properties of light. 



But the phenomena become more varied and interesting when the second surface 

 of the plate is inclined to the first. In this way we may produce effects analogous to 

 those produced by a change in the refractive power of the second surface by contact 

 with another refracting surface, and obtain pencils inclined 90° to each other, and 

 therefore exhibiting the white-centred rings. The phenomena will in this case re- 

 semble those of a film of oil upon water. 



When the refractive index of a parallel film exceeds 1*508, the ray is incident on 

 the second surface at an angle less than the polarizing angle ; but by inclining the 



* See Philosophical Transactions, 1830, pp. 74, 138. 



