﻿88 
  Mr. 
  Nalinimohan 
  JBasu 
  on 
  the 
  Diffraction 
  of 
  

  

  Also, 
  x' 
  = 
  dtnn20 
  + 
  a(cos0 
  sec 
  20 
  — 
  1). 
  

  

  These 
  two 
  relations 
  may, 
  to 
  a 
  close 
  approximation, 
  be 
  written 
  

   in 
  the 
  form 
  

  

  B'=2d0 
  2 
  + 
  2a0\ 
  

  

  and 
  x' 
  = 
  2d0 
  + 
  3a0 
  2 
  /2. 
  

  

  Putting 
  d 
  = 
  0, 
  we 
  get 
  the 
  formula 
  already 
  deduced 
  (see 
  

   paragraph 
  9 
  above) 
  for 
  the 
  fringes 
  at 
  the 
  edge 
  of 
  the 
  

   cylinder. 
  On 
  the 
  other 
  hand, 
  if 
  d 
  be 
  greater 
  than 
  a, 
  we 
  

   may, 
  to 
  a 
  sufficient 
  approximation, 
  write 
  

  

  h 
  f 
  =2dd\ 
  

   and 
  x' 
  = 
  2d0, 
  

  

  and 
  the 
  positions 
  of 
  the 
  points 
  at 
  which 
  the 
  direct 
  and 
  the 
  

   reflected 
  rays 
  are 
  in 
  opposite 
  phases 
  are 
  given 
  by 
  the 
  formula 
  

  

  x' 
  =\/2nd\. 
  

  

  13. 
  But, 
  as 
  remarked 
  above, 
  the 
  simple 
  formula 
  x' 
  = 
  V2ndk 
  

   also 
  gives 
  the 
  approximate 
  positions 
  of 
  the 
  minima 
  in 
  the 
  

   diffraction-fringes 
  at 
  a 
  considerable 
  distance 
  from 
  the 
  cylinder, 
  

   where 
  the 
  effect 
  of 
  the 
  reflected 
  rays 
  is 
  negligible. 
  It 
  is 
  thus 
  

   seen 
  that 
  the 
  formulae 
  

  

  n\ 
  = 
  2d0 
  2 
  + 
  2a0'\ 
  1 
  

   and 
  x' 
  = 
  2d0 
  + 
  3a0 
  2 
  /2,\ 
  

  

  suffice 
  to 
  give 
  the 
  approximate 
  positions 
  of 
  the 
  minima 
  of 
  

   illumination 
  at 
  the 
  edge 
  of 
  the 
  cylinder 
  (at 
  which 
  point 
  the 
  

   fringes 
  are 
  due 
  to 
  simple 
  interference 
  of 
  the 
  direct 
  and 
  the 
  

   reflected 
  rays) 
  and 
  also 
  at 
  a 
  considerable 
  distance 
  from 
  it 
  

   (in 
  which 
  case 
  they 
  are 
  due 
  only 
  to 
  the 
  diffraction 
  of 
  the 
  

   incident 
  light). 
  A 
  priori, 
  therefore, 
  it 
  would 
  seem 
  probable 
  

   that 
  the 
  formulae 
  would 
  hold 
  good 
  also 
  at 
  intermediate 
  

   points, 
  that 
  is 
  for 
  all 
  values 
  of 
  d. 
  That 
  this 
  is 
  the 
  result 
  

   actually 
  to 
  be 
  expected 
  may 
  be 
  shown 
  by 
  considering 
  the 
  

   effect 
  due 
  to 
  the 
  reflected 
  rays 
  at 
  various 
  points 
  in 
  the 
  plane 
  

   of 
  observation. 
  The 
  reflected 
  wave-front 
  is 
  the 
  involute 
  of 
  

   the 
  virtual 
  caustic 
  (see 
  fig. 
  3 
  below). 
  At 
  the 
  edge 
  C, 
  the 
  radius 
  

   of 
  curvature 
  of 
  the 
  wave-front 
  is 
  zero, 
  and 
  increases 
  rapidly 
  

   as 
  we 
  move 
  outwards 
  from 
  the 
  edge 
  of 
  the 
  cylinder. 
  The 
  

   reflected 
  rays 
  accordingly 
  suffer 
  the 
  most 
  rapid 
  attenuation 
  

  

  