﻿•432 
  Dr. 
  S. 
  R. 
  Milner 
  on 
  Interference 
  Fringes 
  

  

  glass, 
  while 
  the 
  Newton's 
  rings 
  move 
  rapidly 
  across 
  the 
  field. 
  

   This 
  statement 
  requires 
  a 
  little 
  modification, 
  as 
  will 
  be 
  seen 
  

   later, 
  in 
  consequence 
  o£ 
  multiple 
  reflexions, 
  but 
  the 
  move- 
  

   ment 
  of 
  the 
  fringes 
  due 
  to 
  this 
  cause 
  is 
  limited 
  to 
  half 
  a 
  

   fringe 
  width. 
  

  

  2. 
  Determination 
  of 
  Central 
  Fringe. 
  — 
  The 
  position 
  of 
  the 
  

   central 
  fringe 
  of 
  the 
  system, 
  i. 
  e. 
  that 
  which 
  corresponds 
  to 
  

   equal 
  paths 
  in 
  the 
  two 
  plates, 
  is 
  independent 
  of 
  the 
  angle 
  of 
  

   incidence 
  of 
  the 
  light, 
  but 
  this 
  is 
  not 
  the 
  case 
  with 
  any 
  other 
  

   fringe. 
  Consider 
  the 
  interference 
  of 
  any 
  two 
  rays, 
  ABODE 
  

   and 
  AGDF 
  (fig. 
  4), 
  one 
  in 
  each 
  plate, 
  each 
  of 
  which 
  passes 
  

  

  through 
  the 
  point 
  D 
  and 
  falls 
  on 
  the 
  pupil 
  of 
  the 
  eye 
  at 
  EF. 
  

   Let 
  r 
  and 
  r 
  + 
  dr 
  be 
  the 
  angles 
  which 
  they 
  make 
  with 
  the 
  normals 
  

   to 
  the 
  plates 
  (HAB 
  and 
  HAG 
  in 
  the 
  figure, 
  in 
  reality 
  the 
  

   angles 
  of 
  refraction 
  in 
  the 
  glass) 
  and 
  z 
  1 
  and 
  z 
  2 
  the 
  thicknesses 
  

   of 
  the 
  plates 
  at 
  the 
  points 
  C 
  and 
  G. 
  If 
  the 
  waves 
  start 
  in 
  

   the 
  same 
  phase 
  from 
  the 
  point 
  A, 
  the 
  relative 
  retardation 
  8 
  

   at 
  the 
  point 
  D 
  will 
  be 
  

  

  8 
  = 
  

  

  2^4- 
  AH 
  2£ 
  2 
  + 
  AH 
  

  

  cos 
  r 
  cos 
  (r 
  -+- 
  dr) 
  

  

  2Qsi-r 
  2 
  ) 
  2r 
  2 
  + 
  AH 
  . 
  , 
  

  

  = 
  s 
  — 
  sin 
  r 
  dr. 
  

  

  cos 
  r 
  cos 
  r 
  

  

  But 
  by 
  the 
  geometry 
  of 
  the 
  figure 
  

  

  HD==(2^ 
  + 
  AH)taur 
  = 
  (2^ 
  + 
  AH)tan(r 
  + 
  Jr), 
  

   and 
  on 
  expansion 
  this 
  equation 
  gives 
  

  

  (2.~ 
  2 
  +AH 
  ) 
  s 
  . 
  n 
  r 
  dr= 
  2(^-3.) 
  r 
  

   cos^ 
  r 
  cos 
  r 
  

  

  and 
  consequently 
  

  

  8=2(z 
  1 
  —z 
  2 
  ) 
  cosr 
  (1) 
  

  

  Since 
  S 
  is 
  independent 
  of 
  the 
  position 
  of 
  the 
  starting-point 
  

   of 
  the 
  two 
  rays, 
  it 
  follows 
  that 
  the 
  fringes 
  will 
  be 
  seen 
  by 
  

   focussing 
  the 
  eye 
  on 
  the 
  air-film, 
  whatever 
  be 
  the 
  position 
  

   or 
  size 
  of 
  the 
  source 
  of 
  light. 
  The 
  fringes 
  thus 
  appear 
  fixed 
  

  

  