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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 26 "Computer Intensive Physic
s" }}{PARA 18 "" 0 "" {TEXT -1 23 "Physics 212E: Fall 1997" }}}{EXCHG 
{PARA 19 "" 0 "" {TEXT -1 16 "Steven R. Dunbar" }}{PARA 19 "" 0 "" 
{TEXT -1 40 "Department of Mathematics and Statistics" }}{PARA 19 "" 
0 "" {TEXT -1 30 "University of Nebraska-Lincoln" }}{PARA 19 "" 0 "" 
{TEXT -1 23 "Lincoln, NE, USA  68588" }}{PARA 19 "" 0 "" {TEXT -1 20 "
sdunbar@math.unl.edu" }}{PARA 0 "" 0 "" {TEXT -1 32 "http://www.math.u
nl.edu/~sdunbar" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 35 "LENGTH:  Lecture-lab demo
nstration." }}{PARA 0 "" 0 "" {TEXT -1 47 "AUDIENCE:  Student use in c
omputer lab setting." }}{PARA 0 "" 0 "" {TEXT -1 21 "SOFTWARE: Maple V
 R 4" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 113 "
FUTURE: Add in a figure of the Young's two-slit experiment, together w
ith distances marked for the section below." }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 177 "Figure out how to go from the \+
sum of two sines to the product of a sine-cosine, so that from superpo
sition can get to the traditionally derived form of the interference p
attern." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
35 "HISTORY:  Created December 10, 1997" }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{PARA 0 "" 0 "" {TEXT -1 14 "REFERENCES:   " }}{PARA 0 "" 0 "" 
{TEXT 256 31 "Geometrical and Physical Optics" }{TEXT -1 46 ", 2nd ed.
  Longhurst, Longman 1967, pages 6-9." }}{PARA 0 "" 0 "" {TEXT 257 7 "
Physics" }{TEXT -1 19 ", Tipler, 1068-1076" }}{SECT 0 {PARA 3 "" 0 "" 
{TEXT -1 18 "History and Set-Up" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 381 "In the famous experiment designed by
 Thomas Young in 1801 in which he demonstrated the wave nature of ligh
t, two light sources are produced by illuminating two parallel slits w
ith a single source of light.  Each slit is very narrow.  In Young's e
xperiment each slit acts as a line source.  A pattern is observed on a
 screen far from the slits, which are separated by a distance of " }
{TEXT 258 1 "d" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 150 "F
requently, it is necessary to find the total illumination at a point, \+
when waves from a number of sources arrive at the same time.  Accordin
g to the " }{TEXT 259 26 "Principle of Superposition" }{TEXT -1 69 ", \+
the resultant illumination is simply the sum of the separate waves." }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 181 "Let E1 be the light wave electric fi
eld from source 1 at some point P on the screen. Likewise, let E2 be t
he light wave electric field from source 2 at some point P on the scre
en.  " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 147 
"Note that the two sources have the same magnitude and the same freque
ncy, since they come from the same source, but they may have different
 phases." }}{PARA 0 "" 0 "" {TEXT -1 3 "   " }}}}{SECT 0 {PARA 3 "" 0 
"" {TEXT -1 41 "First Investigation of Phase Interference" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "restart;    # clear all variables" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "E1 := A*sin(omega*t - del
ta1);\nE2 := A*sin(omega*t - delta2);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "E := E1 + E2;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
200 "Since the magnitude of the sources, and the frequency of the sour
ces is the same, and only the phases differ, we may as well fix a magn
itude, and frequency, and investigate only the phase difference. " }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "omega := 2*Pi;\ndelta1 := 0;
\nA := 1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "subs( delta2 =
 2, [E1, E2, E]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "\nplot
( subs( delta2 = 2, [E1, E2, E]), t=0..4, color=[red,blue,green]); " }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 102 "Take a sequence of phase differ
ence values, and investigate the resulting superposition of the  waves
." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 138 "This suggests taking a fixe
d time t, and looking at the magnitude of the superposition at that ti
me as a function of the phase difference:" }}{PARA 0 "" 0 "" {TEXT 
260 30 "Question 1:  Make such a plot:" }{TEXT -1 1 " " }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "plot( subs( ,  ), delta2= ..  );" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT 261 10 "Question 2" }{TEXT -1 3 ":  " }
{TEXT 262 94 "What is the form of the magnitude of the superposition a
s a function of the phase difference? " }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 43 "Intensity is the square of the magnitude.  " }}{PARA 0 "
" 0 "" {TEXT 263 11 "Question 3:" }{TEXT -1 2 "  " }{TEXT 264 56 "Plot
 the intensity as a function of the phase difference" }{TEXT -1 1 "." 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 3 "" 
0 "" {TEXT -1 41 "The Phase Difference from the Two Sources" }}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 36 "The distance between the slits is d." }}
{PARA 0 "" 0 "" {TEXT -1 48 "The distance from the slits to the screee
n is l." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
96 "Consider a point at a distance x along the screen, measured from t
he midpoint between the slits." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "l1 := \nl2 := " }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "distance_diff := " }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 33 "taylor( distance_diff, d = 0, 3);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "convert(\", polynom);  # ign
ore the higher-order terms" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
12 "simplify(\");" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 110 "Now using t
his information, for a given x, calculate the phase difference in the \+
two paths from the two slits." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 128 
"Finally, using the information from the previous section, calculate w
here the brightest intensity lines will occur on the screen" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 218 "Example:  Two narrow sl
its are separted by 1.5 mm and are illuminated by sodium light of wave
length 589 nm.  Interference fringes are observed on a screen  3 m awa
y.  Find the spacing betwent the fringes on the screen." }}}{SECT 1 
{PARA 3 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
33 "restart;    # clear all variables" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 61 "E1 := A*sin(omega*t - delta1);\nE2 := A*sin(omega*t -
 delta2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "E := E1 + E2;
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "delta := delta1 - delta
2;\nEtest := 2*A*cos( delta/2) * sin(omega*t - delta/2); " }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
37 "expand(E, trig);\nexpand(Etest, trig);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}}}{MARK "17 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }