Production of Circularly Polarized Light. 527 



On a simple interpolation we obtain ^ = 73" 48 / *6. Tfcera-* 

 fore f = 2(^-^=57° 37'-2. 



These values give a phase-difference between the com- 



77" 



ponents on emergence equivalent to -~, for the D x line, and 



the emergent beam will be circularly polarized. 



Since (f) = T3° 48'*6, the colour effect as calculated from 

 equation (6) for a single reflexion will be nearly the same as 

 for a single reflexion in the Bi-rhomb, for which (£ = 74° 38'*2. 

 There are two such reflexions, and the colour effect is 

 2.dA — +0*102, so far as they are concerned. Fur the 



. C- F 



reflexion at angle of incidence <f>' , the value of dA = +0*18. 



C— F 

 Hence the total colour effect is a little less than that for an 

 ordinary Fresnel's rhomb. 



For an aperture of S cms. (S is the breadth of the beam 

 of light) the length of the Bi-trapezoid will be 2 . S . tan %, 

 where % is the acute angle of the trapezoid. Also the 

 greatest breadth of the trapezoid is AB = 



S (cot ^ — tan 2%). 



If ^=75°, S = l cm., the length in the direction of the 

 incident light is I'D cms., approx. i.e., half the length of the 

 previous form. CD is then about 1*7 cms. 



Ihe Azimuth of the Incident Vibration. 



With (£ = 73°48'*6 the phase-difference for the three re- 

 flexions, between the components polarized parallel and 



77* 



perpendicular to the plane of incidence, is exactly — for 

 sodium light, /i being 1*5035. 



Since, however, the component polarized parallel to the 

 plane of incidence is more copiously reflected on crossing the 

 joint than the perpendicular component is, the usual azimuth 

 (viz. 45°) would produce elliptically polaiized light, the 

 major axis of the ellipse being parallel to CD (fig. 3). By 

 adjusting the azimuth, the transmitted ben m can be made 

 circularly polarized. The new azimuth can be found in two 

 w r ays. 



(1) Experimentally. — Using a Babinet's compensator or 

 the Bi-rhomb (which produces circularly polaiized light, 

 since here the beam crosses the joint normally) we can 

 analyse the light transmitted by the Bi-trapezoid, and adjust 



