Polarizing Prisms for the Ultraviolet. 259 



wave-lengths in the ultraviolet have been determined by 

 Gifford. (Proc. Hoy. Soc. 1902, 1904). For pur present 

 purpose it is sufficient to consider a few typical values. 

 We shall select the values for A = 6708 and \ = 4047 near 

 the ends of the visible spectrum ; and \= 2144 as the limit 

 of the ultraviolet spectrum to be considered. The results 

 are shown in the following table : — 



X. 



/V 



/V 



f*o 2 - 



He 2 - 



9. 



r. 



a. 



6708 



1-6537 



1-4843 



2-736 



2-202 



21° 39' 



•663 



48° 38' 



4047 



1-6813 



1-4969 



2-825 



2-240 



21° 21' 



•6565 



49° 31' 



2144 



1-8459 



1-5600 



3-408 



2-434 



19° 24' 



•627 



51° 30' 



(b) The ordinary ray. In the square-ended prism the 

 ordinary ray enters without deviation. Hence the limiting 

 position of the dividing plane for total reflexion is determined 

 at once from the value of the critical angle (c). 



Thus - = sinc and /8=(90°-c). 



Taking the same wave-lengths as before : — 



\ = 6708 

 X=4047 

 X = 2144. 



c = 37°12' 

 c=36 Q 30' 



c = 32°48'. 



/3 = 52°48' 

 /5 = 53° 30' 

 0=57° 12'. 



It will be seen that if the dividing plane is inclined to the 

 line of vision at an angle less than 51° 30' the extraordinary 

 ray will not be transmitted at X = 2144, whereas if the angle 

 be greater than 52° 48' the ordinary ray at \ = 6708 will be 

 transmitted and this part of the light will not be plane- 

 polarized. If the plane of section be at 52° the whole beam 

 will be plane-polarized, provided its angular diameter within 

 the crystal does not exceed the following values for the three 



wave-lengths under discussion :- 



X=6708. 

 4° 10' =(0° 48' +3° 22' 



3°59' 



X = 4047. 



= (l°30'+2°29'). 



X = 2144. 

 I 5°42' = (5°12'+30'). 



(The figures within the brackets represent the deviations 

 on opposite sides of the two internal lines of vision.) 



It will be seen, therefore, that it the visible as well as the 

 ultraviolet portions are to be polarized, the transmitted 

 pencils must be almost parallel. 



S2 



