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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 103 "Wave Packet Problem      \+
                                                                  RAYt
race.mws" }}{PARA 0 "" 0 "" {TEXT -1 103 "2D Paraxial Ray Trace       \+
                                                                ABW 7/
21/95" }}{PARA 0 "" 0 "" {TEXT -1 81 "Learning objectives: Visualize p
ropagation of multiple rays through simple system" }}{PARA 0 "" 0 "" 
{TEXT -1 80 "                                    Physical intuition re
garding image formation" }}{PARA 0 "" 0 "" {TEXT -1 37 "              \+
                       " }}{PARA 0 "" 0 "" {TEXT -1 37 "              \+
                       " }}{PARA 0 "" 0 "" {TEXT -1 62 "MAPLE: linalg[
matrix], evalm, &*,  for..from..to..do..od, plot" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 45 "Procedure traces five ray
s through two lenses" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 24 "Definition of Variables:" }}{PARA 0 "" 0 "" {TEXT -1 
29 "x = position along optic axis" }}{PARA 0 "" 0 "" {TEXT -1 24 "f = \+
focal length of lens" }}{PARA 0 "" 0 "" {TEXT -1 27 "L = distance betw
een lenses" }}{PARA 0 "" 0 "" {TEXT -1 28 "y1 = initial height of ray \+
1" }}{PARA 0 "" 0 "" {TEXT -1 35 "phi1 = initial inclination of ray 1
" }}{PARA 0 "" 0 "" {TEXT -1 23 "x0 = start of ray trace" }}{PARA 0 "
" 0 "" {TEXT -1 23 "xmax = end of ray trace" }}{PARA 0 "" 0 "" {TEXT 
-1 88 "r[i][y[i],phi[i]] = vector with components of height (y) and an
gle (phi) of ray number i" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 2 "" 0 "" {TEXT -1 1 "\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linal
g):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "##Calculate separations need
ed for calculations" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "L1:=
x1-x0:L2:=x2-x1:L3:=xmax-x2:" }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 1 "\n
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "## Calculate matrices that prop
agate rays" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "m1:=matrix(2,
2,[1,L1,0,1]): #translate ray from object to first lens" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "m2:=matrix(2,2,[1,0,-1/f1,1]): #ben
d ray at first lens" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "m3:=
matrix(2,2,[1,L2,0,1]): #translate from first lens to second lens" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "m4:=matrix(2,2,[1,0,-1/f2,1]
): #bend ray at second lens" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
54 "m5:=matrix(2,2,[1,L3,0,1]): #translate to end of trace" }}}{EXCHG 
{PARA 2 "" 0 "" {TEXT -1 1 "\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "#
# Define and propagate [height, angle] coordinates for rays" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "for i from 1 to 5" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 7 "     do" }}{PARA 2 "" 0 "" {TEXT -1 1 "\n
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "            r0[i]:=matrix(2,1,[
y[i],phi[i]]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "            r1[i]
:=evalm(m1&*r0[i]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "            \+
r2[i]:=evalm(m2&*r1[i]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "       \+
     r3[i]:=evalm(m3&*r2[i]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "  \+
         r4[i]:=evalm(m4&*r3[i]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
35 "           r5[i]:=evalm(m5&*r4[i]):" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 9 "      od:" }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 1 "\n" }}{PARA 0 
"> " 0 "" {MPLTEXT 1 0 46 "## Calculate the (x,y) coordinates of each \+
ray" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "for i from 1 to 5" }
}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "    do" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 98 "        ray[i]:=[[x0,y[i]],[x1,r1[i][1,1]],[x2,r3[i][
1,1]],[xmax,r5[i][1,1]]]; #x,y pairs for rays" }}{PARA 2 "" 0 "" 
{TEXT -1 1 "\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "    od;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "############### Input Numeri
cal Values for Particular System ###########" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "#s
tart and end points of plot" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
16 "x0:=0: xmax:=35:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "#de
scribe the position and focal length of each lens" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 27 "x1:=10:   f1:=5:    #lens 1" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "x2:=25:   f2:=15:  #lens 2" }}}
{EXCHG {PARA 2 "" 0 "" {TEXT -1 1 "\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 49 "#specify the initial height and angle of each ray" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 111 " y[1]:=1:phi[1]:=0:   y[2]:=1:phi[
2]:=0.5:   y[3]:=1:phi[3]:=-.5:  y[4]:=1:phi[4]:=0.25: y[5]:=1:phi[5]:
=-0.25:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "plot(\{ray[1],ra
y[2],ray[3],ray[4],ray[5]\},x=15..xmax, title=`Paraxial Ray Trace`);" 
}}}}{MARK "14 0 0" 1 }{VIEWOPTS 1 1 0 1 1 1803 }