186 Sir D. Brewster on the Phcenomena of Thin Plates 



Wlien m and ot' are thus related, the 'white-centred rings 

 will just disappear when i = 90°, the light being then incident 

 on the second surface at its polarizing angle. But if we use 

 a film of still less refractive power in relation to the second 

 body, the refracted rays will fall on the second surface at an 

 angle greater than the polarizing angle (/ being still 90°), and 

 consequently the black-centred rings "mil reappear, and there 

 will be some angle of incidence I on the film, less than 90°, 

 at which the angle of refraction i' will be equal to the polari- 

 zing angle of tlie second surface. This angle will be found 

 from the expression 



. , in m' 



sui 1 = — 



vm^ + m'^ 



When vi = 7u' no rings whatever will be formed, as no light is 

 reflected at the common surface; but if ?« = ?«' only for a par- 

 ticular colour in the spectrum of each substance, and if these 

 indices differ considerably for another colour, rings will be 

 formed in which that colour predominates, in which ?« > m', 

 or m < m'. This takes place in a remarkable manner with 

 oil of cassia ai-n\ fint glass, in Avhich 7n = ?n' for the red rays, 

 but tn > m for the blue rays. The consequence of this is, that 

 a quantity of blue light is reflected from the separating surface 

 of the oil and the glass; and hence if a sufficiently thin film 

 of oil of cassia is laid upon the glass, blue would greatly pre- 

 dominate in the system of rings. 



Hitherto the azimuth of the polarized light has been 90°, 

 or perpendicular to the plane of reflexion. Let us now sup- 

 pose that its azimuth is gradually changed from 90° to 0° by 

 the rotation of the polarizing surface or crystal. 



At all azimuths, from 90^ to 0°, the rings with the black 

 circumference are seen, between the angles of 0^ and 53° 11', 

 and at the incidence of 53° 11'. But at incidences between 

 53° 11' and 90°, in the case of the iriscope, very interesting 

 phaenomena appear. We shall first describe what takes place 

 at 56° 45', the polarizing angle of the black glass. At this 

 angle none of the polarized light is reflected when the azimuth 

 is 90°, and the rings with the wliitc circumference are beauti- 

 fully seen on the dark ground of the glass, which now reflects 

 no light. As the azimuth is changed to 87°, 88°, &c., the 

 black glass reflects a little light, and the two surfaces of the 

 film a little more light, the rings gradually become fainter 

 and fainter, till at an azimuth of about 79° O' they disappear 

 exactly as they did at 53° 1 1', and in the azimuth 90°. When 

 this disappearance takes place, the light reflected from the glass 

 seems to be exactly equal to the light reflected from both sur- 



