tan A 



522 Mr. A. E. Oxley on am Apparatus for the 



From equation (4') we have 



/2sin 2 ^ 1 ■ X . /2sin 2 ^ T \ i 



I 2 T — 1 — cos 2-v/r I. cos A = cos2\/rf — 2— ^ — lf-*l| 



and differentiatino- logarithmically. 



rfA _ 4 sin 2 ijr r cos2i/r __ 1 



Vyu, jST~ \ co?^(2 sin 2 i/r- /x 2 )^ 2 2sin 2 ^-/r ? (l4 cos 2^) 



_ 2 sin 2 f f 1 1 



a 1 . _ , ll 2 cos 2 yjr sin 2 ilr — u 2 . CO* 2 ilr 

 \siir y— - -— - . ' ' r 



7 cos Jyjr 



Hence for given A ( say A= -— J. and for all values of u, 



as \lr varies from to . , - T - varies from to 

 4: a fji 



11 1 1 2 x tt 



,eot-. 





M 



1.2 2/ 



tan 



77T " 



"8 



/* 



(1 



Here 



M<1, 





then 













r/A 



9 



V 



. cot 



7T 





<y- 



-1) 



8 



*7T 7^ /7 /A 



As -vlr increases from T to _» — m). Now for total reflexion, 

 T ± 2 dp 



yjr must be greater than the critical angle. For a variation 

 in. X corresponding to an increase in v by ^^, the variation in 

 phase SA is greatest in the neighbourhood of the critical 



7T 



angle; while SA-^0 for such a variation in A, as 1 J r- * > o- 



Hence in so far as this effect is concerned large angles of 

 incidence are desirable. In this respect the new arrange- 

 ment has a further advantage over the Fresnel rhomb, for 

 although the two reflexions in the latter are replaced by four 

 reflexions in the former, yet the total colour effect, if we 

 choose the larger value of yjr, is only half that of a Fresnel 

 rhomb. The colour effect is examined below. 



Uviol glass was chosen as the most suitable material for 

 the Bi-rhomb (as this form of the apparatus is called) since 



