414 WRIGHT— POLARIZED LIGHT IN THE 



Therefore 



2qoEp^=(qo-\-qi) cos 8"i, 2q^Es^={q^ ^q^) sin h^; 



2go^^i=C^i — (?o) cos 81, 2q^Rs^={q^ — q^) sin \. 

 Similarly 



2go£/'2=(^o + go) cos~8o, 2q^Ep._=(q,,^q.,) sin S", ; 



2qQRpn={'q2 — ^0) cos S.,, 2q,,Rsn={qQ — g,) sin 82. 



On substituting these values in equation (19), we obtain 



2go(22 - qi) tan 5i tan 62 - [(go - Si) (go + 22) tan 5i 



i?5 ~ (go ~ g2) (g + gi) tan ^2] tan e 



Rp (go - g2)(go + gi) tan 5i - (go - gi)(go + g2) tan ^2 



- 2go(g2 — gi) tan e 



(19') 



The right-hand side of this equation is complex ; therefore, plane 

 polarized light incident on a crystal plate of an absorbing crystal gen- 

 erally becomes on reflection elliptically polarized. The equations 

 are, however, so complicated, that progress is best made by the solu- 

 tion of a few simple cases in which the crystallographic symmetry 

 relations prescribe certain types of vibration. 



For the special case that the plane of incidence is a plane of sym- 

 metry the equations become noticeably simpler ; this assumption is 

 valid for isotropic, uniaxial, and certain sections of orthorhombic 

 crystals because in these the positions of the principal axes of the 

 polarization and absorption surfaces of reference coincide as they 

 are fixed by the symmetry relations. In general these axes do not 

 coincide and the surface of reference can be represented only by the 

 use of complex quantities. On the assumption that the plane of in- 

 cidence is a plane of symmetry let 9 be the angle between the Z' axis 

 (normal to the plate) and the Z principal axis. The equations de- 

 fining the complex polarization constants then obtain 



aii = a-^i -j- ^"^11 = ^' cos- 6 -\-'c~ sin- 6, 



a'20 = aoo + ib^n = h-, 



0,33 = ^33 -{- ibss = «' sin- 6 -\-c' cos" 6, 



O03 = ao3 4- i&23 = o» 



