Polarizing Prisms for the Ultraviolet. 257 



data as were available the limiting values of the angles of 

 inclination of the air-film for transmitting polarized beams of 

 short wave-length. The results, as they may be of interest 

 to others working in the same department of optics, are for 

 three special cases given in the present note. These are, 

 namely : — 



I. A "square-ended" Foucault, the end faces being per- 

 pendicular to the line of vision, and to the planes containing 

 this line and the optic axis. 



II. An ordinary Foucault, the end faces being the natural 

 ends of the crystal. 



III. A Glan- Foucault prism. 



The angles of a natural crystal of spar are indicated in 

 fig. 1, which represents a principal section-plane. We shall 



Fig-.]. 



denote the inclination of the dividing plane AB to the line of 

 vision by a or yS according as we are dealing with the extra- 

 ordinary or ordinary ray respectively. 



Let //,o= the ordinary index of refraction for light of wave 

 length \ ; 

 /x e = the extraordinary index of refraction for light of 



wave-length X ; 

 a = the semi-major axis and b = the semi-minor axis of 

 the elliptic section of the extraordinary wave-sheet ; 

 r = the radius-vector of the ellipse in the direction of 



the ray within the crystal ; 

 # = the inclination of r to the major axis in the plane 



containing the optic axis ; 

 $ = the inclination of the tangent plane (at the point 

 where r meets the ellipsoid) to the major axis. 



Then, if the velocity of light in air be denoted by unity, 

 we have 



_ 1 _ 1 # velocity in air _ 1 



" 0— £' a' ray velocity along r r' 



Phil. Mag. S. 0. Vol. 28. No. 164. Aug. 1914. S 



