﻿obtained 
  with 
  Glass 
  Wedges. 
  435 
  

  

  point 
  on 
  the 
  piece 
  for 
  a 
  given 
  displacement. 
  The 
  alteration 
  

   in 
  thickness 
  of 
  the 
  sheet 
  is 
  \/2cosr 
  for 
  each 
  fringe 
  that 
  

   passes 
  the 
  point. 
  

  

  The 
  Fringes 
  in 
  White 
  Light. 
  — 
  In 
  general 
  the 
  central 
  

   fringe 
  of 
  the 
  system 
  is 
  not 
  in 
  the 
  field 
  of 
  view, 
  but 
  its 
  

   position 
  may 
  easily 
  be 
  found 
  by 
  applying 
  the 
  observation 
  of 
  

   § 
  2. 
  The 
  coloured 
  fringes 
  exhibit 
  in 
  an 
  interesting 
  way 
  the 
  

   effect 
  of 
  multiple 
  reflexions 
  in 
  the 
  film. 
  The 
  multiple 
  re- 
  

   flexions 
  which 
  occur 
  in 
  Newton's 
  rings 
  may 
  be 
  looked 
  on 
  as 
  

   giving 
  separate 
  systems 
  of 
  fringes 
  which 
  are 
  all 
  superposed 
  

   on 
  each 
  other, 
  the 
  observed 
  colours 
  being 
  the 
  resultant 
  effect 
  

   of 
  them 
  all. 
  In 
  the 
  wedge 
  fringes 
  similar 
  multiple 
  reflexions 
  

   at 
  the 
  air-film 
  occur, 
  but 
  unlike 
  the 
  Newton's 
  rings, 
  the 
  

   individual 
  systems 
  may 
  be 
  completely 
  separated 
  from 
  each 
  

   other. 
  Without 
  analysing 
  the 
  effects 
  in 
  detail, 
  we 
  can 
  see 
  

   that 
  a 
  ray 
  which 
  has 
  been 
  reflected 
  from 
  the 
  non-adjacent 
  

   face 
  of 
  plate 
  i. 
  can 
  interfere 
  with 
  any 
  ray 
  which 
  has 
  passed 
  

   through 
  plate 
  ii., 
  and 
  has 
  also 
  been 
  reflected 
  any 
  even 
  

   number 
  of 
  times 
  at 
  the 
  air-film, 
  and 
  vice 
  versa. 
  Hence, 
  if 
  

   pi 
  and 
  p 
  2 
  are 
  the 
  optical 
  paths 
  through 
  plates 
  i. 
  and 
  ii. 
  in 
  

   any 
  place, 
  and 
  / 
  that 
  of 
  the 
  air-film, 
  interference-systems 
  

   will 
  be 
  produced 
  the 
  centres 
  of 
  which 
  are 
  at 
  such 
  places 
  that 
  

  

  p 
  1 
  + 
  2nf=p 
  2 
  + 
  2mf, 
  

  

  -n 
  and 
  m 
  being 
  any 
  whole 
  numbers. 
  The 
  system 
  n 
  = 
  m 
  has 
  

   its 
  centre 
  at 
  the 
  point 
  of 
  the 
  wedges 
  where 
  pi=p 
  2 
  , 
  the 
  

   systems 
  n 
  = 
  m 
  + 
  l 
  at 
  the 
  points 
  where 
  P]=P2 
  + 
  %fi 
  an 
  d 
  so 
  on. 
  

   When 
  the 
  film 
  is 
  very 
  thin 
  the 
  systems 
  are 
  all 
  superposed 
  

   on 
  each 
  other, 
  giving 
  a 
  complex 
  set 
  of 
  coloured 
  fringes, 
  but 
  

   on 
  slightly 
  separating* 
  the 
  plates 
  this 
  splits 
  up 
  into 
  the 
  

   different 
  systems, 
  one 
  of 
  which 
  remains 
  fixed, 
  while 
  the 
  others 
  

   move 
  off 
  to 
  right 
  and 
  left 
  with 
  different 
  velocities 
  until 
  they 
  

   are 
  quite 
  separated. 
  

  

  The 
  system 
  of 
  fringes 
  which 
  remains 
  stationar}^ 
  can 
  be 
  

   kept 
  in 
  the 
  field 
  of 
  view 
  even 
  if 
  the 
  plates 
  are 
  separated 
  by 
  

   several 
  centimetres, 
  so 
  long 
  as 
  they 
  are 
  kept 
  parallel 
  to 
  each 
  

   other, 
  and 
  are 
  in 
  fact 
  the 
  fringes 
  which 
  are 
  used 
  in 
  the 
  well- 
  

  

  * 
  More 
  simply 
  by 
  tilting 
  one 
  plate 
  on 
  the 
  other 
  perpendicular 
  to 
  the 
  

   plane 
  of 
  incidence. 
  By 
  then 
  tilting 
  in 
  the 
  plane 
  of 
  incidence, 
  each 
  of 
  

   the 
  previously 
  formed 
  systems 
  again 
  splits 
  up 
  into 
  two, 
  which 
  move 
  off 
  

   the 
  field 
  in 
  opposite 
  directions. 
  The 
  effect 
  is 
  very 
  beautiful 
  in 
  practice, 
  

   as 
  many 
  as 
  a 
  dozen 
  sets 
  of 
  coloured 
  fringes 
  often 
  being 
  in 
  the 
  field 
  at 
  the 
  

   same 
  time. 
  The 
  second 
  separation 
  is 
  due 
  to 
  each 
  of 
  the 
  previous 
  systems 
  

   being 
  really 
  the 
  superposed 
  effect 
  of 
  two 
  systems, 
  one 
  on 
  each 
  surface 
  of 
  

   the 
  air-film. 
  The 
  simplest 
  form 
  of 
  each 
  system 
  is 
  illustrated 
  in 
  fig. 
  1 
  

   and 
  fig. 
  4 
  respectively. 
  The 
  interfering 
  rays 
  which 
  form 
  them 
  pass 
  through 
  

   the 
  air-film 
  in 
  different 
  places 
  (e. 
  g. 
  at 
  A 
  and 
  D, 
  fig. 
  1, 
  and 
  conversely, 
  at 
  

   D 
  and 
  B, 
  fig. 
  4), 
  and 
  consequently 
  if 
  the 
  film 
  is 
  not 
  plane 
  parallel, 
  their 
  

   centres 
  appear 
  at 
  different 
  places 
  on 
  the 
  plates. 
  

  

  2 
  G2 
  

  

  