﻿Talbot's 
  Fringes 
  and 
  the 
  Echelon 
  Grating. 
  759 
  

  

  a 
  focus 
  by 
  a 
  lens. 
  The 
  first 
  diffraction 
  minima 
  to 
  the 
  right 
  

   and 
  left 
  of 
  the 
  central 
  maximum 
  will 
  lie 
  in 
  directions 
  such 
  

   that 
  the 
  path 
  difference 
  between 
  the 
  disturbances 
  coming 
  

   from 
  the 
  edges 
  of 
  the 
  aperture 
  is 
  a 
  whole 
  wave-length. 
  If 
  

   the 
  right-hand 
  half 
  of 
  tlie 
  aperture 
  is 
  covered 
  with 
  a 
  trans- 
  

   parent 
  plate 
  which 
  retards 
  the 
  wave-train 
  one 
  half 
  wave- 
  

   length, 
  we 
  shall 
  have 
  zero 
  illumination 
  at 
  the 
  centre, 
  and 
  

   two 
  bright 
  maxima 
  of 
  equal 
  intensity 
  in 
  the 
  position 
  pre- 
  

   viously 
  occupied 
  by 
  the 
  first 
  minima. 
  It 
  is 
  clear 
  that 
  the 
  

   path 
  difference 
  for 
  the 
  left-hand 
  maximum 
  is 
  one 
  wave-length, 
  

   and 
  for 
  the 
  right-hand 
  one 
  zero. 
  We 
  may 
  therefore 
  call 
  

   the 
  former 
  the 
  spectrum 
  of 
  the 
  first 
  order, 
  and 
  the 
  latter 
  the 
  

   spectrum 
  of 
  zero 
  order, 
  considering 
  the 
  aperture 
  as 
  a 
  grating 
  

   of 
  two 
  elements. 
  If 
  we 
  consider 
  the 
  change 
  as 
  taking 
  place 
  

   progressively^ 
  starting 
  with 
  a 
  transparent 
  lamina 
  of 
  infinite 
  

   thinness 
  which 
  oraduallv 
  thickens, 
  it 
  is 
  clear 
  that 
  the 
  central 
  

   maximum 
  moves 
  to 
  the 
  right, 
  decreasing 
  in 
  intensity, 
  while 
  

   its 
  neighbouring 
  maximum 
  to 
  the 
  left 
  increases 
  in 
  brightness 
  

   moving 
  in 
  the 
  same 
  direction. 
  When 
  the 
  thickness 
  cor- 
  

   responds 
  to 
  a 
  halt-wave 
  retardation 
  these 
  two 
  maxima 
  are 
  of 
  

   equal 
  intensity, 
  and 
  occupy 
  the 
  positions 
  previously 
  occupied 
  

   by 
  the 
  minima 
  to 
  the 
  right 
  and 
  left 
  of 
  the 
  central 
  maximum. 
  

   If 
  we 
  increase 
  further 
  the 
  thickness 
  of 
  the 
  plate 
  the 
  maxima 
  

   drift 
  further 
  to 
  the 
  right, 
  the 
  left-hand 
  one 
  increasing 
  in 
  

   brilliancy, 
  the 
  right-hand 
  one 
  decreasing. 
  When 
  the 
  re- 
  

   tardation 
  becomes 
  one 
  whole 
  wave-length 
  we 
  again 
  have 
  a 
  

   single 
  bright 
  maximum 
  at 
  the 
  centre, 
  as 
  with 
  the 
  uncovered 
  

   aperture. 
  In 
  this 
  case, 
  however, 
  it 
  is 
  the 
  spectrum 
  of 
  the 
  

   first 
  order 
  which 
  is 
  at 
  the 
  centre. 
  As 
  we 
  o^o 
  on 
  increasino- 
  

   the 
  thickness 
  of 
  the 
  plate 
  the 
  march 
  of 
  the 
  fringes 
  continues, 
  

   new 
  ones 
  coming 
  into 
  view 
  on 
  the 
  left 
  and 
  disappearing 
  on 
  

   the 
  right, 
  and 
  the 
  order 
  of 
  spectrum 
  increasing. 
  The 
  con- 
  

   dition 
  when 
  we 
  have 
  a 
  pair 
  of 
  bright 
  maxima 
  will 
  be 
  recog- 
  

   nized 
  as 
  the 
  condition 
  which 
  obtains 
  when 
  an 
  echelon 
  grating- 
  

   is 
  set 
  for 
  the 
  position 
  of 
  double 
  order, 
  the 
  single 
  order 
  

   position 
  corresponding 
  to 
  the 
  case 
  when 
  we 
  have 
  a 
  single 
  

   bright 
  maximum 
  at 
  the 
  centre. 
  

  

  •Suppose 
  now 
  that 
  we 
  have 
  a 
  thick 
  retarding 
  plate 
  and 
  

   gradually 
  decrease 
  the 
  wave-length 
  of 
  the 
  light 
  which 
  

   illuminates 
  the 
  slit 
  from 
  which 
  the 
  plane 
  waves 
  are 
  coming. 
  

   We 
  shall 
  have 
  the 
  same 
  march 
  of 
  the 
  fringes 
  as 
  before, 
  the 
  

   gradual 
  increase 
  in 
  retardation 
  resulting 
  from 
  the 
  decrease 
  

   in 
  wave-length. 
  If 
  our 
  source 
  emits 
  two 
  wave-trains 
  of 
  

   different 
  wave-length, 
  and 
  the 
  retardation 
  for 
  one 
  of 
  the 
  

   trains 
  is 
  an 
  odd, 
  and 
  for 
  the 
  other 
  an 
  even 
  number 
  of 
  half 
  

   wave-lengths, 
  it 
  is 
  clear 
  that 
  the 
  single 
  and 
  double 
  maxima 
  

  

  