WHEN EXPOSED TO POLARIZED LIGHT. 45 



from the second surface was, that the light reflected from it was not incident at its 

 polarizing angle. 



I have elsewhere shown*, that when a film of water is laid upon glass whose re- 

 fractive index is above 1*508, there is no angle of incidence upon the first surface of 

 the film which will allow the refracted ray to fall upon the glass at the polarizing 

 angle; and hence at every angle of incidence on the film, the refracted light is re- 

 flected from the glass at angles less than the polarizing angle of the united media, or 



less than an angle whose tangent is equal to ^, m being the refractive index of the 



glass, and m' that of the water. When the refractive index of the glass is 1'508, the 

 angle of incidence on the film must be 90° exactly, in order that the refracted ray 



may fall upon the glass at the polarizing angle whose tangent is equal to ^ 



Now as the portion of the coloured rings at C D, fig. 2., is formed by the interference 

 of two pencils, C A, D E B, fig. 3., one of which, C A, is reflected at an angle, P C A, 

 above the polarizing angle of water, and the other, E B, at an angle below or less than 

 that angle ; while the portion E F, fig. 2., is formed by the interference of two pencils, 

 which are both reflected at angles below or less than that angle, we may suppose that 

 in the formation of the rings with a white circumference, analogous to those with 

 a white centre, there is a loss of half an undulation, while that loss takes place in 

 the interference of common light, or of two pencils reflected on the same side of the 

 polarizing angle. 



When the rings are seen at angles between 0° of incidence and 53° 11', the polar- 

 izing angle of water, they are black in the circumference, like the portion shown at 

 E F, fig. 2. ; and when they are seen at incidences between 53° 1 1' and 90°, they are 

 white in the circumference, like the portion shown at C D, fig. 2. 



If the rings of vapour are formed upon a polished surface oi Jluor spar, additional 

 phenomena will be exhibited. At all incidences, from 0° to about 78°, rings of the same 

 character will be seen as already described ; but the ratio of the refractive powers of 

 water and fluor spar is such, that at an incidence of 78° 4' upon the surface of the 

 vapour, the light incident on the spar will be reflected at the polarizing angle of the 

 united media. Thus if m = 1*437, the refractive index of fluor spar, and m! — 1*336, the 



refractive index of water, then ^ = 1*0716, the refractive index of the united media, 



or of their separating surface. The polarizing angle for this surface will therefore be 

 an angle whose tangent is 1*0756 or 47° 5', and the angle of incidence on the fii-st 

 surface of the watei-y film corresponding to the angle of refraction 47° 5', which is 

 the angle of incidence on the second surface, is 78°'4. 



At an incidence of 78° 4', therefore, the rings will disappear altogether, as at 53° 1 1', 

 because the pencil incident on the spar will not be reflected. At incidences greater 



* Philosophical Transactions, 1815, p. 138. 



