' matopt.bas - jack@ord.ca - revised 2 Oct 02 - Liberty Basic v3.01
' matrix optics ray tracing program
' rays traced from an object in H(-) to its image in H'(-)

  Mainwin 80 30
  dim p(10): dim q(10): p(8)=0: p(9)=0
  cls : input "Index of incident medium = "; nleft
  input "Number of Matrices = "; m
  for j=1 TO m
    b11=0
    input "Translation=1 Curved Surface=2 Plane Surface=3 Lens=4, Choice = "; z
    if z=1 then
      input "Displacement (+) = "; d
      b11=1: b12=0-d: b21=0: b22=1: p(9)=p(9)+d
    end if
    if z=2 then
      input "Radius (+/-) = "; d
      input "nright = "; nright
      b11=1: b12=0: b21=(nright-nleft)/(nleft*d): b22=nright/nleft
      nleft=nright
    end if
    if z=3 then
      input "nright = "; nright
      b11=1: b12=0: b21=0: b22=nright/nleft
      nleft=nright
    end if
    if z=4  then
      input "focal length (+/-) = "; f
      b11=1: b12=0: b21=1/f: b22=1
    end if
    if b11=0 then print "Error": STOP
    if j=1 then
      a11=b11: a12=b12: a21=b21: a22=b22
    else
      x11=a11*b11+a12*b21: x12=a11*b12+a12*b22
      x21=a21*b11+a22*b21: x22=a21*b12+a22*b22
      a11=x11: a12=x12: a21=x21: a22=x22
    end if
    print "Matrix "; j; space$(12); b11; space$(15-len(str$(b11))); b12
    print space$(20); b21; space$(15-len(str$(b21))); b22
  next j
  print "O-O' Matrix         "; a11; space$(15-len(str$(a11))); a12
  print space$(20); a21; space$(15-len(str$(a21))); a22
  det=a11*a22-a21*a12
  print "      Determinant = "; det
  if abs(a21)<.000001 then
    print "Telescopic System"
    print "        Angular M = "; 1/a22
  else
    d1=a11/a21: d2=a22/a21: f1=1/a21: f2=f1*det
    print "Positions of the focal points relative to O and O'"
    print space$(15); "OF = "; d1
    print space$(14); "O'F = "; d2
    print "The focal lengths f and f'"
    print space$(16); "f = "; f1
    print space$(15); "f' = "; f2
    print "Positions of the principal points relative to O and O'"
    print space$(15); "OH = "; d1-f1
    print space$(14); "OH' = "; d2-f2
    gosub [plot]
    wait
  end if
  end

[plot]
  'array index 0 to 9: H(-), F, H, N, N', H', F', H'(-), O, O'
  WindowWidth=610     ' pixel scale 0-600
  WindowHeight=189    ' pixel scale 0-160
  UpperLeftX=10: UpperLeftY=10
  open "Ray Tracing" for graphics_nsb as #1   ' no slide bars
  p(0)=0-d1-f1: p(1)=0-d1: p(2)=f1-d1: p(3)=f2-d1
  p(4)=p(9)+d2-f1: p(5)=p(9)+d2-f2: p(6)=p(9)+d2: p(7)=p(9)+d2+f2
  xmin=p(0): xmax=p(0)
  for i=1 to 9
    if p(i)<xmin then xmin=p(i)
    if p(i)>xmax then xmax=p(i)
  next i
  xsc=500/(xmax-xmin)
  for i=0 to 9
    q(i)=50+int((p(i)-xmin)*xsc+.5)
  next i
  #1 "down ; color lightgray ; backcolor lightgray"
  #1 "place "; q(8); " 0": #1 "boxfilled "; q(9); " 160"
  #1 "color black ; line 25 80 575 80"
  #1 "color blue ; line "; q(2); " 5 "; q(2); " 155"
  #1 "line "; q(5); " 5 "; q(5); " 155"
  if q(2)-12>q(8) and q(2)-12<q(9) then #1 "backcolor lightgray" else #1 "backcolor white"
  #1 "place "; q(2)-12; " 15": #1 "\H"
  if q(5)+4>q(8) and q(5)+4<q(9) then #1 "backcolor lightgray" else #1 "backcolor white"
  #1 "place "; q(5)+4; " 15": #1 "\H'"
  #1 "color cyan ; line "; q(0); " 20 "; q(2); " 140"
  #1 "line "; q(5); " 140 "; q(7); " 140"
  #1 "color green ; line "; q(0); " 20 "; q(2); " 20"
  #1 "line "; q(5); " 20 "; q(7); " 140"
  #1 "color yellow ; line "; q(0); " 20 "; q(3); " 80"
  #1 "line "; q(4); " 80 "; q(7); " 140"
  #1 "color red ; line "; q(0); " 20 "; q(0); " 80"
  #1 "line "; q(0); " 20 "; q(0)-2; " 30"
  #1 "line "; q(0); " 20 "; q(0)-1; " 30"
  #1 "line "; q(0); " 20 "; q(0)+1; " 30"
  #1 "line "; q(0); " 20 "; q(0)+2; " 30"
  #1 "line "; q(7); " 140 "; q(7); " 80"
  #1 "line "; q(7); " 140 "; q(7)-2; " 130"
  #1 "line "; q(7); " 140 "; q(7)-1; " 130"
  #1 "line "; q(7); " 140 "; q(7)+1; " 130"
  #1 "line "; q(7); " 140 "; q(7)+2; " 130"
  if q(1)-12>q(8) and q(1)-12<q(9) then #1 "backcolor lightgray" else #1 "backcolor white"
  #1 "place "; q(1)-12; " 95": #1 "\F"
  if q(6)+4>q(8) and q(6)+4<q(9) then #1 "backcolor lightgray" else #1 "backcolor white"
  #1 "place "; q(6)+4; " 75": #1 "\F'"
  if q(3)-12>q(8) and q(3)-12<q(9) then #1 "backcolor lightgray" else #1 "backcolor white"
  #1 "place "; q(3)-12; " 95": #1 "\N"
  if q(4)+4>q(8) and q(4)+4<q(9) then #1 "backcolor lightgray" else #1 "backcolor white"
  #1 "place "; q(4)+4; " 75": #1 "\N'"
  #1 "backcolor red"
  #1 "place "; q(1); " 80": #1 "circlefilled 3"
  #1 "place "; q(3); " 80": #1 "circlefilled 3"
  #1 "place "; q(4); " 80": #1 "circlefilled 3"
  #1 "place "; q(6); " 80": #1 "circlefilled 3"
return