1 81 Sir D. Brewster on the Pluvnomeua of Thin Plates 



the circumference, like the portion sliovvn at EF, fig. 1 ; and 

 when they are seen at incidences between 53° 11' and 90 , 

 they are 'white in the circumference, like the portion shown at 

 CD, fig. 1 . 



If the rings of vapour are formed upon a polished surface 

 o^Jiuor spar, additional phaenomena 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 refrac- 

 tive powers of water and fluor spar is such, that at an inci- 

 dence of 78° 4' upon the surface of the vapour, the light inci- 

 dent on the spar will be reflected at the polarizing angle of 

 the united media. Thus if ??« = r437, the refractive index of 

 fluor spar, and ?»' = 1*336, the refractive index of water, then 



— , = l*07]6, the refractive index of the united media, or of 

 m' 



their separating surface. The polarizing angle for this sur- 

 face will therefore be an angle whose tangent is 1'0756 or 

 47° 5', and the angle of incidence on the first surface of the 

 watery 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° 11', because the pencil incident on the 

 spar will not be reflected. At incidences greater than 78° 4' the 

 system of rings with the black circumference will again appear 

 as at incidences below 53° 11', and will be visible up to 90^ 

 of incidence, the interfering pencils being nov/ both reflected 

 at angles above the jxolarizing angle of the surfaces which 

 reflect them. 



This experiment with vapour and fluor spar I have not 

 made; and it may be difficult to see the rings at such an 

 oblique incidence. If the rings are formed by soap upon 

 plate glass, or by alcohol upon Jliior spar, the second disap- 

 pearance of the rings may be seen : 



Plate glass m _ TSIO _ ,.„,p.. 

 soap m' ~" 1"487 "" 

 Polarizing angle at second surface of the soap 45° 26' 

 Angle of incidence on the first surface . . . 71° 45' 



Fluor spar m _ 1*437 _ 

 alcohol" m' ~ 1*370 " 



Polarizing angle at second surface of alcohol 46° 22' 

 Angle of incidence on the first surface . . 82° 32' 



If we call »j, m' the indices of refraction of the two sub- 

 stances, viz. the flm and the surface upon which it rests, m 

 being the larger index, then a ray incident at 90° will fall 



