WHEN EXPOSED TO POLARIZED LIGHT. 47 



m! 

 Values of m'. Values of , , - , or m. 



V m'* — 1 



1-800 1-202 



1-700 1-236 



1-600 1-281 



1-554 1-307 



1-508 1-336 



1-500 1-341 



1-400 1-428 



1-336 1-508 



1-307 1-554 



The limits, therefore, between which the second disappearance of the rings can take 

 place are 1-554, the index for quartz and Jiint glass, and 1*307, the index for ice. 

 But though the range is very limited, it nevertheless includes a considerable variety 

 of solid and fluid bodies. I have omitted the indices of Tabasheer, and the fluids 

 produced by the compression of gaseous bodies, because, though their refractive 

 powers are beneath 1*307, they cannot be used in the present inquiry. 



When m and m' are thus related, the white centred rings will j ust 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 {i being still 90°), and consequently the black centred rings will 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 polarizing angle of the second surface. This 

 angle will be found from the expression 



sin I = 



mm; 



When m = m' no rings whatever will be formed, as no light is reflected at the com- 

 mon surface ; but if m = m! only for a particular colour in the spectrum of each sub- 

 stance, and if these indices differ considerably for another colour, rings will be formed 

 in which that colour predominates, in which m > W, or m <: m'. This takes place in a 

 remarkable manner with oil of cassia and Jlint glass, in which m = m' for the red 

 rays, but m > 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 predo- 

 minate 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 suppose 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 inci- 



