262 Polarizing Prisms for the Ultraviolet. 



III. The Glan-Foucault Prism. 



This is a square-ended prism cut so that the optic axis lies 

 in the plane of division. I£ this axis is taken at right-angles 

 to the paper the sections o£ the wave-surfaces are both circles 

 and the conditions for transmission may be determined at 

 once from the values of the critical angle corresponding to 

 /x and fji e . We have therefore for the extraordinary rays : 



X=6708 c = 42°21' a = 47°39' 



\=4047 c = 41°54' * = 48° 6' 



\ = 2144. c=39°52'. a = 50°8 / . 



Also, for the ordinary rays as already determined under I. : 



\ = 6708 A = 4047 \=2144 



/3 = 52° 48'. /3=53°30'. £=57° 12'. 



Taking the dividing plane at 50° 17' to the line of vision, we 

 obtain the following values for the internal diameter of the 

 beam : — 



X = 6708. I X = 4047. i X = 2144. 



5°9' = (2 3r+2°38'). | 5°24' = (3°13'+2 ir). | 7° 4' = (6° 55' +9'). 



Theoretically the values thus derived for the internal 

 angular diameter of the beam are not quite exact owing to a 

 small variation in the refractive index when the direction of 

 the ray varies through a few degrees ; also they refer only to 

 a plane containing the optic axis and perpendicular to the end 

 face, i. e. } to a principal plane of section. They are, however, 

 sufficiently exact for ordinary experimental adjustments. 

 The external angle allowable will be somewhat greater than 

 the internal angle, — approximately 1*56 times as great, and 

 hence if the external beam does not exceed in angular 

 diameter the values given for the internal beam there will be 

 a safe margin for complete polarization. 



The angular diameter of the polarized beam can be much 

 increased by the use of a suitable cement for the two halves 

 of the prism. Canada-balsam is inadmissible in ultraviolet 

 work, as even in thin films it arrests all rays beyond \3400, 

 but liquids such as castor-oil and glycerine can be used. 

 It is hoped to deal with the cemented prisms in a later 

 paper when the necessary experimental data have been 

 determined. 



