Polarizing Prisms for the Ultraviolet. 261 



If OP is the natural end of the crystal, 

 A=19°8'; B = 44°37'. 

 Hence from (4), (1), and (2) we can determine <f>, 0, and r. 



The limiting angle for the transmission of the extraordinary 

 ray is given by : — 



velocity of light in air _ P'B/ 

 velocity of ray in spar Q'B/ 



sin (0 + tfO . 



1 



i. e. - 



sinClSO -^ ^'-^-*)' 

 sin (0 + 0) 



(5) 



r sin (153° 45' -<£- a)' 



from which a may be found. 



Substituting the numerical values we obtain the results 

 shown below : — 



X. 



/V 



/v 



t- 



e. 



r. a. 



6708 



1-6537 



1-4843 



57 r 0' 



27°37'0" 



•6569 



55° 54' 



4047 



1-6813 



1-4969 



56° 51' 30" 



27° 21' 30" 



•6503 



56° 35' 



2144 



1-8459 



1-5600 



56° 11' 20" 



25° 33' 15" 



•6184 



59° 40' 



(h) Ordinary rays. The angle of incidence is 19° 8'. If 

 8 is the deviation of the ray from the line of vision and c the 

 critical angle, the limiting angle of inclination /3 of the 

 section plane is found from 



0=8 + (9O°-c). 



Hence we obtain : — 



X,= 6708 



\ = 4047 

 X-2144. 



8=7° 43' 



8= 7° 54' 



£=60° 31' 

 /3=61°24' 

 S = 8° 55'. /3=r.W } V 



The values of a and /3 show that the angular diameters of 

 the transmitted pencils must be small if the light is to be 

 completely polarized ; also, if the inclination of the section- 

 plane is less than 56° 35 ; no ultraviolet light will be trans- 

 mitted. Taking the obliquity of the air-film as 59°, the 

 internal rays may diverge to the extent shown by the following 

 figures : — 



A = 6708. I A=4047. i A = 2144. 



.4° 37' = (1° 31' 4- 3° 6') I 4°49' = (2°24 / +2 25'). | no axial transmission. 



With the dividing plane inclined at G0° the values are : — 



4°37=(31' + 4°6'). | 4° 49' = (1° 24' +3° 25'). | 6 o 27' = (6°7'+20'). 



