191 Sir D. Brewster on the Phanomena of Thin Plates 



observation*, exhibit at one glance the general phsenomena 

 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 alvva3s 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 incli- 

 nation 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 ic in the preceding 

 formula at an incidence of 70°, we shall find it 66° 25', at 

 which azimuth the inclinations f and <p"' of the planes of polar- 

 ization are W'^ 47', and 49° 53'; but though the sum of these 

 angles is 90°, yet the real inclination of the planes is <p"' — <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 2i° 44' in glass, and to study 

 the phaenon)ena which such pencils exhibit, either in their 

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



But the phtenomena 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 pro- 

 duced by a change in the refractive power of the second sur- 

 face by contact with another refracting surface, and obtain 

 pencils inclined 90° to each other, and therefore exhibiting 

 the white-centred rings. The phoenomena will in this case 

 resemble 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 second surface we 

 can make it fall upon it at a greater angle than the polarizing 

 angle. The phaenomena may be still more varied by inclining 

 the surface of emergence to the surface of incidence t; but as 

 it is not easy to obtain films with faces suitably inclined to 

 each other, it is unnecessary to pursue this branch of the sub- 

 ject any further. 



Such are the phaenomena of ildn and thick plates when 

 viewed by polarized light, or by common light subsequently 

 analysed by a doubly refracting rhomb. But if we use polar- 



* See Pliilosophical Transaclioiis, 1830, pp. 74, 138. 

 t Ibid. p. 147, fig. 3. 



