520 Mr. A. E. Oxley on an Apparatus for the 



Using equations (2) and (3) we see that the phase- 

 difference produced at a single reflexion between the com- 

 ponents polarized parallel and perpendicular to the plane of 

 incidence, is given by 6 — 6\ where 



e ~ sin (yjr4-7]i) 



2 . sin 2 (i/r— tjl) 



2 sin (^ — ^0 sin (yjr + rji) 



cos 2-v/r . cosh 2r\ -f 1 . sin 2-^ . sinh 2^ — 1 

 cosh 2r) — cos 2i/r 



= cos 0-0' + « sin 6-9'. 



Writing 6-6' = A, 



, cos 2yjr . cosh 2ri — 1 /iN 



cos A = cos 6-6' = fro rVr • • • • ( 4 ) 



cosh 2rj — cosh 2t/t 



Since from (1) smyjr = fi . cosh rj, we have, using (4), 



0f /2sin 2 ^ \ 

 COS 2-KJrl g-2- — 1 j 



o • 2 , ^ = cos A (40 



„- r - — 1 — cos 2^ 



P r 



Writing a?=cos 2i/r, 



.-. x{l— jj?— x)— /* 2 =(1 -# — 1-Hb . //) . cos A, 

 or 



x 2 -x{l-fi 2 +(l+tf) .cos A}+ cosA + ^ 2 (l-cosA) = 



. - • (5) 

 If the beam of plane-polarized light incident normally upon 

 the surface of the rhomb, be vibrating in a plane inclined at 

 45° to a principal section of the rhomb, a phase-difference 

 amounting to A will be produced between the components, 

 and their amplitudes will be equal. 



Now taking //,= ——(glass to air) and A = -^*, we find 



on substitution that x 2 and therefore cos 2 2-v/r is real. 

 Moreover, both values of yjr are real, one being about 75° 



I 7T TV 



* A may be of the form -p +2«7r+m — where n is any integer and 

 m is either 1 or 0. 



