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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 75 "8/24/95  rotpol.mws      (
 CW and CCW rotating vectors added and animated) " }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 89 "a) Show that two counter-
rotating circular polarizations yield a linearly polarized beam." }}
{PARA 0 "" 0 "" {TEXT -1 165 "b) Show that when the two counter-rotati
ng beams travel thround a thickness x of material at different wavelen
gths, the plane of linearly polarized light is rotated." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 8 "Remarks." }}{PARA 0 "
" 0 "" {TEXT -1 191 "Circular polarizations give linear polarization o
riented horizontally when  x=0.  But different wavelengths give a phas
e shift when x>0 so that we get a rotation of the plane of polarizatio
n." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 114 "By
 plotting at different colors and thicknesses, then combining and disp
laying, a more flexible animation is done." }}{PARA 2 "" 0 "" {TEXT 
-1 1 "\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 22 "kval:=2*Pi/wavelength;" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 26 "Two different values of k:" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "k[2]:=subs(wavelength=11/
10,kval);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "k[1]:=subs(wav
elength=1,kval);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 101 "Distance x t
ravelled through the medium with different wavelengths. (Change x and \+
restart from here.)" }}{PARA 2 "" 0 "" {TEXT -1 1 "\n" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 8 "x:=1/80;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 23 "
clockwise rotating wave" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "Qx1:=5.0
*cos(k[1]*x+3*t+phi[1]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 
"Qy1:=5.0*sin(k[1]*x+3*t+phi[1]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
30 "counterclockwise rotating wave" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
32 "Qx2:=5.0*cos(k[2]*x-3*t+phi[2]);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 32 "Qy2:=5.0*sin(k[2]*x-3*t+phi[2]);" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 36 "NN:=40; # of pieces in the animation" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "Phases of the waves" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 10 "phi[1]:=0;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 10 "phi[2]:=0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
22 "for i from 0 to NN  do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "t:=i/
10;   #  t = time" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "g.(i):=plot([[
0,0],[Qx1,Qy1]],color='red',thickness=3):" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 56 "h.(i):=plot([[0,0],[Qx2,Qy2]],color='blue',thickness=
3):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "j.(i):=plot([[0,0],[Qx1+Qx2,
Qy1+Qy2]],color=black,thickness=5):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
36 "s.(i):=display(\{g.(i),h.(i),j.(i)\}):" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 3 "od:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 75 "animation \+
of CW, CCW, and their sum - looks very nice when run continuously" }}
{PARA 0 "" 0 "" {TEXT -1 70 "Go back and reset the x value to see a 'r
otated' plane of polarization" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "di
splay([s.(0..NN)],insequence=true);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{MARK "15 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }