412 



WRIGHT— POLARIZED LIGHT IN THE 



The computation of these four quantities from the equations is exceed- 

 ingly complicated. The introduction of " uniradial azimuths " facilitates the 

 solution considerably. Thus for a certain value of e such as «,, all of the 

 refracted light takes the path D (Dj^i, Z>o:=o), while for another azimuth 

 of the incident plane polarized wave, {D^^i, Z?i = o) and all of the light is 

 refracted along D^. The values of the uniradial azimuths are given by the 

 equations 



sin^ r-tan 5 



tan p = — cos {i + r) tan 6 

 tan e = cos {i — r) tan 5 



sin {i — r) cos 5 

 sin^ ?-tan s 



(i6) 



sin {i + r) cos 5 



in which T is the angle between the wave normal and the ray direction of the 

 refracted wave. 



Let the values of E and R, computed under the assumption that D^^^o, 



Dt^i, be £„ R^; similarly for £)i = o, Z). = i, let the values be E., Rn. 

 Since equations (15) and (15^) are linear in D^ and D.,, we find on sub- 

 stituting therein first Z), = 0, Z?i = i and then Dj =: 0, D.^i, and indicating 

 by subscripts, i or 2, in each case the proper uniradial azimuth, multiplying 

 the equations thus obtained by D^ and D^ respectively and then adding 



[ (E, cos ej), + £„ cos e,A) — {R, cos Sjj^ + ^^cos S,A) ] cos i _ 



= Z), cos Sj cosTi -\- Dn cos S.. cosn; 

 therefore 



E cos e = Ep= E, cos e, A + E., cos ej)._ = Ep,D, + Ep.3, 

 R cos Pz=Rp = R, cos pj5, + R., cos pjj. = Rp,D, + Rp.3. 



Similarly 



(17) 



E sin e=^Es ^= Ej sin e^D^ -\- £0 sin (..D. = Es^D^ -\- Es.D., 

 'R sin p = Rs — R, sin p,D^-j-R. sin p,5, = Rs,D^ + ^.y.A;, 

 in which 



E^h = -Eft sin e,^, Ep,, — E,^ cos e,, ; Rs,^ — R,, sin e^„ Rp,^ = Rj^ cos e,,. 



If the amplitude and polarization azimuth of the incident wave be given 

 and hence Esi, Ep^, 5^, and r,,, the corresponding values of the reflected wave 

 can be computed from equations (17) and put into the form 



(Ep,Es,—Ep,Es,)Rs,= (Rs,Es,—Rs,Es,)Ep—(Rs,Ep,—Rs,Ep,)Es, 

 (Ep,Es,—Ep,Es,)Rp = (Rp,Es,—Rp,Es,)Ep— (Rp,Ep,—Rp,Ep,)Es, 



(18) 



which is deduced by eliminating D, and D._. from equations (17). The values 

 oi Rs and Rp are complex. _ 



If the incident wave be plane-polarized the complex values of Rs/En, 

 Rp/Ep, and Rs/Rp show that phase differences exist between the three waves 

 and that therefore the reflected wave is in general elliptically polarized. If 



