﻿Elliptic 
  Polarization. 
  

   Table 
  II.— 
  cos^ 
  2a 
  < 
  tan2 
  2/3. 
  

  

  0<a<7r/4. 
  

  

  201 
  

  

  tan 
  R. 
  

  

  tan 
  2(0 
  -o). 
  

  

  Siu 
  ly. 
  

  

  

   cot 
  2a 
  

  

  sin 
  2/3 
  cot 
  "^ 
  

  

  tan" 
  23 
  

   sin 
  2a 
  cos 
  2a 
  

  

  —tan 
  2a 
  

  

  — 
  sin 
  2/3 
  tan 
  ^ 
  

  

  

   — 
  tan 
  4a 
  

  

  -tan 
  2a 
  

  

  

  

  —tan 
  4a 
  

  

  -tan 
  2a 
  

  

  

  

  TT 
  

  

  2-" 
  

  

  i„2ftan-l^) 
  

   \ 
  COS 
  2a 
  / 
  

  

  sin 
  2a 
  COS 
  2/3 
  cot 
  T 
  

  

  ^/^ 
  , 
  tan2/3\ 
  

   n 
  2| 
  tan-1 
  ^ 
  1 
  

  

  cos 
  'la 
  

  

  TT 
  — 
  a 
  

  

  TT 
  

  

  v+a 
  

  

  

  

  —sin 
  2a 
  cos 
  2/3 
  tan 
  ^ 
  

   

  

  7r/4<a<7r/-- 
  

  

  tan 
  R. 
  

  

  tan 
  2(0 
  -a). 
  

  

  0. 
  sin 
  2y. 
  

  

  1. 
  

   2. 
  

   3. 
  

  

  4. 
  

   5. 
  

   6. 
  

  

  7. 
  

  

  

  

  sin 
  2/3 
  cot 
  ^^ 
  

  

  -tan 
  2a 
  

  

  tan" 
  23 
  

  

  sin 
  2a 
  cos 
  '2a 
  

  

  -sin 
  2/3 
  tan 
  "^ 
  

  

  cot 
  2a 
  

   

  

  

  

  -tan 
  2a 
  

  

  —tan 
  4a 
  

  

  

  

  — 
  tan 
  2a 
  

  

  — 
  tan 
  4a 
  

  

  

  

  a 
  

  

  5 
  sin 
  2a 
  cos 
  2i8 
  cot 
  f^ 
  

  

  T-a 
  

  

  5 
  + 
  a 
  sin2ftan-l^'^"7^\ 
  

   :^ 
  V 
  cos 
  2a 
  / 
  

  

  IT 
  — 
  sin 
  2a 
  cos 
  2/3 
  tan 
  ^ 
  

  

  ^'-« 
  sin2(tan-l*-2'5N 
  

   \ 
  COS 
  i:a 
  / 
  

   TT+a 
  

  

  5. 
  The 
  transition 
  from 
  one 
  of 
  these 
  cases 
  to 
  the 
  other 
  

   occurs 
  when 
  cos^ 
  2ci= 
  tan^ 
  2/3, 
  and 
  then 
  

  

  t 
  9(^/9- 
  >) 
  ^ 
  ^ 
  tan 
  R(l 
  -- 
  tan 
  2a 
  t 
  an 
  E) 
  2 
  tan 
  R 
  

  

  ^^"^ 
  ""^ 
  l-tan2 
  2atan2R 
  ~ 
  1+ 
  tan2a 
  tanK^ 
  

  

  In 
  this 
  case 
  increases 
  from 
  a 
  to 
  a 
  + 
  7r/2, 
  as 
  R 
  increases 
  

   from 
  to 
  TT 
  : 
  the 
  light 
  is 
  circularly 
  polarized 
  when 
  

   tan 
  R= 
  cot 
  2a, 
  and 
  while 
  for 
  values 
  of 
  R 
  less 
  than 
  that 
  

   given 
  hy 
  this 
  equation 
  gives 
  the 
  plane 
  of 
  maximum 
  

   polarization, 
  for 
  greater 
  values 
  it 
  determines 
  the 
  plane 
  of 
  

   minimum 
  polarization*. 
  

  

  * 
  When 
  tanR= 
  cot 
  2a, 
  tan2(^— 
  a) 
  of 
  course 
  becomes 
  indeterminate, 
  

   but 
  it 
  is 
  easy 
  to 
  see 
  that 
  the 
  change 
  from 
  determining 
  the 
  plar.e 
  of 
  

   maximum 
  polarization 
  to 
  giving 
  that 
  of 
  minimum 
  polarization, 
  or 
  vice 
  

   versa, 
  occurs 
  as 
  passes 
  through 
  the 
  values 
  (2n+l)7r/4. 
  

  

  