' dif3.bas - jackord@kw.igs.net - 16 Oct 06 - Liberty Basic v4.02
' The diffraction grating: 1, 3, or 5 slits of width w=2 microns
'   with a separation between slits of w, 2w, or 3w (at a separation of w
'   the pattern is that of a single slit of width n*w)
' The intensity pattern is that viewed on a screen 1 m from the grating
'   with one pixel representing 1 mm in the x direction
' The wavelengths are red C, yellow D, green E, and blue F
' A line plot (in magenta) of the analytic intensity expression for red light
'   is superimposed for the case of 3 slits spaced 2w apart

' Initialize Window
  nomainwin
  button#1, "Plot", [q1], UL, 126, 2, 40, 20
  WindowWidth=490     ' Pixel Scale 0-480
  WindowHeight=269    ' Pixel Scale 0-240
  UpperLeftX=10: UpperLeftY=10
  dim a$(3): a$(0)="d=w": a$(1)="d=2w": a$(2)="d=3w"
  dim b$(3): b$(0)="n=1": b$(1)="n=3": b$(2)="n=5"
  combobox#1.chd, a$(, [waitHere], 2, 2, 60, 60
  combobox#1.chn, b$(, [waitHere], 64, 2, 60, 60
  open "Diffraction Grating" for graphics_nsb as #1
  #1 "trapclose [quit]"
  dim la(4)
    la(0)=.6563/1000: la(1)=.589/1000                      ' Red C, Yellow D
    la(2)=.5269/1000: la(3)=.4861/1000                     ' Green E, Blue F
  dim c$(4)
    c$(0)="red": c$(1)="yellow": c$(2)="green": c$(3)="blue"
  #1.chd "selectindex 2"
  #1.chn "selectindex 2"
  #1 "cls ; down ; color black ; backcolor white"

[waitHere]
  wait

[q1]
goto [plot]

[plot]
  #1.chd "selectionindex?": input#1.chd, nd                ' Slit spacing
  #1.chn "selectionindex?": input#1.chn, n: n=2*n-1        ' Slit number
  #1 "cls ; down ; color black ; backcolor white"
  pi=4*atn(1): w=.002: x0=240: z=1000: zz=z*z
  nw=5
  for j=0-int(n/2) to int(n/2)                             ' Show slit pattern
    for i=0-int(nw/2) to int(nw/2)
      x1=x0+j*nd*nw+i
      #1 "line "; x1; " 10 "; x1; " 30"
    next i
  next j
  nw=141                                                   ' Use 141 point model
  sy=200/(n*n*nw*nw)
  for nl=0 to 3                                            ' Wavelength loop
    #1 "color "; c$(nl)
    for nx=0 to 240                                        ' Screen loop
      r0=sqr(zz+nx*nx): sr=0: si=0                         ' Algorithm C
      for j=0-int(n/2) to int(n/2)                         ' Slit number loop
        for i=0-int(nw/2) to int(nw/2)                     ' Slit loop
          xg=(j*nd*nw+i)*w/nw
          t=2*pi*nx*xg/r0/la(nl): a=.5*(1+z/r0)*sqr(z/r0)
          sr=sr+a*cos(t): si=si+a*sin(t)
        next i
      next j
      x2=240-int(sy*(sr*sr+si*si))
      if x2<240 then                                       ' Plot Intensity
        #1 "line "; x0+nx; " "; x2; " "; x0+nx; " 240"
        #1 "line "; x0-nx; " "; x2; " "; x0-nx; " 240"
      end if
    next nx
  next nl
  if n=3 and nd=2 then                                     ' If d=2w and 3 slits
    #1 "color darkred"                                     ' Dark red curve
    x1=40
    for nx=1 to 240
      t=atn(nx/z)                                          ' Analytic calculation
      p0=2*pi*w*sin(t)/la(0)
      p0=sin(p0/2)/(p0/2)
      p1=2*pi*nd*w*sin(t)/la(0)
      p1=sin(n*p1/2)/sin(p1/2)
      x2=240-int(200*p0*p0*p1*p1/n/n)
      if x1<240 or x2<240 then
        #1 "line "; x0+nx-1; " "; x1; " "; x0+nx; " "; x2  ' Analytic curve
        #1 "line "; x0-nx+1; " "; x1; " "; x0-nx; " "; x2
      end if
      x1=x2
    next nx
  end if
goto [waitHere]

[quit]
  close #1
end