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Wave Optics22.1 Light and Optics22.2 The lnterference of LightL
The figure shows the Iight intensity recorded by a piece of
film
in an interference experiment. Notice that the light
intensitycomes "full on" at the edges of each maximum, so this is
not theintensity that would be recorded in Young's
double-slitexperiment.a. Draw a graph of light intensity versus
position on the film.
Your graph shor-rld l-rave the sarre horizontal scale as
the"photograph" above it.
b. Is it possible to tell, from the information given, what
thewavelength of the light is? If so, what is it? If not, why
not?
N o o\\o wo'.\J ^"eJ *o knovlIfhc dirto^.c {o thQ. fi\*',.
2. The graph shows the light intensity on the viewing screen
duringa double-slit interference experiment. liltersjtva. Draw the
"photograph" that would be recorded if a piece of
film were placed at the position of the screen. Your"photograph"
should have the same horizontal scale as thegraph above it. Be as
accurate as you can. Let the white ofthe paper be the brightest
intensity and a very heary pencilshading be the darkest.
b. Three positions on the screen are marked as A, B, and C.Draw
history graphs showing the displacement of the lightwave at each of
these three positions as a function of time.Show three cycles, and
use the same vertical scale on allthree.
Intcnsily
Positirxr
t.;:l,!l!:l):.1
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,iIji!I
't
Photograph
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22-1
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22-2 cHAPTER 22 . Wave Optics
3. The figure below is a dor"rble-slit experiment seen looking
down on the experiment from above.Although we usually see the light
intensity only on a viewing screen, we can use smoke or dust tomake
the light visible as it propagates between the slits and the
screen. Assuming that the space inthe figure is filled with smoke,
what kind of light and dark pattern would you see as you look
down?Draw the pattern on the figure by shading areas that would
appear dark and leaving the white of thepaper for areas that would
appear bright.
The figure shows the viewing screen in a double-slit experiment.
FringeC is the central maximum. For questions a--c, will the fringe
spacingincrease, decrease, or stay the same? Give an explanation
for each.a. The distance to the screen is increased.
ABCDE
utlr*tse po.e otcd.
The frinSesSirne*-
wilI bu.o",.,,," w\ora widelyY'tT
b. The spacing between the slits is increased.
no fri'^1es *,\\ bu.o*u v1^ofq clo5qty sgoced.si,nO = \^I-?-
c. The wavelength of the light is increased.
The frinle-5 *lll be.o*o vtAof o-S\nO = '^lT-
d. Suppose the wavelength of the light is 500 nm. How much
farther is it from the dot in the center offringe E to the more
distant slit than it is from the dot to the nearer slit?
Eg.t" f11"1e -
Sr o* C rcpresc.rnl5 d.n aldl{i o!^q\ poth larytl^0f \.
ThJ""fore, *o *h ..rte. # ftiyrqe E rcqrli rcs cr\po.tl lo^gth
Jiffnno*.o of l.\ = tiGl J
widely scpor*lcJ. ot!o
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Two slits
Vicwing scrccn
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Wave Optics ' cHAPTER 22 22'3
22.3 The Diffraction Grating5. The figure shows four slits in a
diffraction grating. A set of Huygens
wavelets is spreading out from each slit. Four wave paths,
numbered 1 to 4,are shown leaving the slits at angle 0r.The dashed
lines are drawnperpendicular to the paths of the waves'a. Use a
colored pencil or heavy shading to show on the figure the extra
distance traveled by wave 1 that is not traveled by wave 2.
b. How many extra wavelengths does wave 1 travei compared to
wave 2?
wovclctf"o
^t.is o\^ewo.vctc.'^oth.)
c. How many extra wavelengths does wave 2travel compared to wave
3?
O nc wavc,\c^St\^
d. As these four waves combine at some large distance from the
grating, will they interfereconstructively, destructively, or in
between? Explain'
Co*struc{ivclv. T^. ootl. \o*qt\^ diffqrehcos or"e oll
itejur*.^\l,i p\os of '+ho s"J" *nvoli^gJ6 ( A t- -- t^ I) .
e. Suppose the wavelength of the light is doubled. (Imagine
erasing every other wave front in thepicture.) Would the
interference at angle Q then be constructive, destructive, or in
between?Explain. Your explanation should be based on the figure,
not on some equation.
\e- oq*\^ \o*q\\'l .liffcr.^."s \^tou\A {h"^ corrsspl.*4 toono I
\^at f r^ri.uc\orn5th so *h" i*cc $e.re\^ce wor,tld
bedos{ro.}i.re.
f. Suppose the slit spacing is doubled. (lmagine closing every
other slit in the picture). Would theinterference at angle 01 then
be constructive, destructive, or in between? Again, base
yourexplanation on the figure.
Explain how you can tell from the figure.
One wcve,lav,q+h, Eo'c\n 5s\^^'icirctere,presots +ri* cftst of a
wevo'il"o di.*q,n(s bctrlrer,n^ rdqve {rou*S
TS *he slil Soocinq, \Nqre, Jo*blod, *hqnn lheIi{ro"=^*'*+"6-:
".;iJ
incrco*sj' +.o t* oa!\,1 11^* i^\*$oJ"^.c rnrou\d bc
cons*rt^cTr-w .
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224 c:n,+prt;r< 22 . Wave Optics
6. These are the same slits as in Exercise 5. Waves with the
same wavelength are spreading out on theright side.a. Draw four
paths, starting at the slits, at an angle d2 such that the wave
along each path travels
fwo wavelengths farther than the next wave. Also draw dashed
lines at right angles to the traveldirection. Your picture should
look much like the figure of Exercise 5, but with the waves
travelingat a different angle. Use a ruler!
b. Do the same for four paths at angle Q2suchthat each wave
travels one-half wavelength farther thanthe next wave.
' l1,i,o"'L';:L'Jf:ffiJJ[:[il: ffl^'f"Tffi::"?il].#:iiii;IlJ' *
il H r t #the same spacing d between adjacent slits?
a. Would the number of fringes on the screen increase, decrease,
or stay # * il # t ryjthe same?S*oy s the savns .
b, Would the fringe spacing increase, decreasel or stay the
same?
Sta.1s +h" sq,u^e.
c. Would the width of each fringe increase, decrease, or stay
the same?
bo.r*ros, Th" {ringes be..o^o nq,rr0\^rq.f.d. Would the
brightness of each fringe increase, decrease, or stay the same?
a
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Wave Optics . CHAPTER 22 22-5
22.4 Single-Slit Diffraction8. Plane waves of light are incident
on two narrow,
closely-spaced slits. The graph shows the lightintensity seen on
a screen behind the slits.a. Draw a graph on the axes below to show
the light rnr,
intensity on the screen if the right slit is blocked,allowing
light to go only through the left slit.
b. Explain why the graph will look this way.
Jhn 5i*.{c sll} Jiff"o.lio,^ rnrpotlerr. ?onloi*s o brood
"r^lnolYvtcxivnu,vv\. Thq, nq,r.rowur *wo S\i+i r^ls{"fcrc,,ncc
pol}orrr Ji sagrpoar.su.rhe.n o\nt, sll\ is cowr.qd.(N.+o +hot *ho
qroph is not
-dro*^'{; +ho sqrqc
-i^"i"{ii+t scclc.)
9. This is the light intensity on a viewing screen behind a slit
ofwidth a. The light's wavelength is 2. Is )' < q, I = a, ).
> q,or is it not possible to tell? Explain.
lX. ql Ssvo"o.l se.s*ndq,.y rnalirnlo' ,6G..
-For o.sivlOp = pf , +tre lirstr.,rinivna. f"o* *h" or^tr"\
rnnoxiwtu.n'rrequircs sirn O, = +, nhi & r^nust be'lo-ss *l"qn
l.
10. This is the light intensity on a viewing screen behind a
rectangularopening in a screen. Is the shape ofthe opening
ITJExplain.
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It^e v\o.rrowcr *hq. openinq in o. ger.iit'*lor di"et{io^,il
3#il ii; 'i;*l,o li-+u'" l:iht i^ *ho*
'
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22-G cseprcn 22 ' Wave Optics
I 1 The graph shows the light intensity on a screen behind
a0.2-mm-wide slit illuminated by light with a 500 nmwavelength.a.
Draw a picture in the box of how a photograph taken
at this location would look. Use the same horizontalscale, so
that your picture aligns with the graph above'Let the white ofthe
paper represent the brightestintensity and the darkest you can draw
with a pencilor pen be the least intensitY.
b. Using the same horizontal scale as in part a, drawgraphs
showing the light intensity ifi. ). = 250 nm, a = 0.2 mm.ii. )" =
1000 nm, a = 0.2 mm.iii. ),= 500 nm, a = 0.1 mm.
22.5 Gi rcu lar-Apertu re Diffraction12. This is the light
intensity on a viewing screen behind a circular apefiure.
a. If the wavelength of the light is increased, will the width
of the centralmaximum increase, decrease, or stay the same?
Explain.
Th" -rdt\n i^gegcsCS.
0. = 1e3) so o,"\ Db. If the diameter of the aperture is
increased, will the width of the central maximum increase,
decrease, or stay the same? ExPlain.-The
*il+\. 4".r,o5"5.0 , A".roosos \"rit\ i'vrcreasing D.
c. How will the screen appear if the aperture diameter is
decreased to less than the wavelength of thelight?
\A".i{or,".r\y 3rq). No nninimo. *o*ld aPPcqr.
incrLc\se,i hli+h 1.E
=Etr.)
AOdo
T,\ = 2.5{l nrra = 0.2 mrl
.I = 500 nma = 0.1 nrnr
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Wave Optics . cHAPTER 22 22-7
22.6 lnterferometers13. The figure shows a tr-rbe through which
sound waves
with 2 = 4 cm travel from left to right. Each wavedivides at the
first junction and recombines at thesecond. The dots and triangles
show the positions ofthewave crests at t = 0 s
-rather like a very simple wave
front diagram.a. Do the recombined waves interfere
constructively or
destructively? Explain. l=4crn 8cmCons{ruc{ivo\, Thq pathare *U;
sq,\
^s of +ha. o\,i.onslf\^cllvo.tv. I vr( DqTvln^,.^l+'r pla. oS
+\^s *ov"J",.nalJ
, r^t
lc^r{h diffc..rcrrcc is o.nn i1}e3cr"$h'. T^e wo.va- cre.s+
gosiliol.sp"*.
b. How much extradistance does the upper wave travel? I 6. c
t"uHow many wavelengths is this extra distance? I
c. Below are tubes with Z = 9 cm and L =10 cm. Use dots to show
the wave crest positions at / = 0 sfor the wave taking the lower
path. Use triangles to show the wave crests at / = 0 s for the
wavetaking the upper path. The wavelength is 7 = 4 cm. Assume that
the first crest is at the left edge ofthe tube, as in the figure
above.
Ecm 8 cnr
How many extra wavelengths does the upper wave travel inlhe L= 9
cm tube? Ll ' 5What kind of interference does the L =9 cm tube
produce? D*Sffu"fiveHow many extra wavelengths does the upper wave
travel in the I = 10 cm tube? 5What kind of interference does the L
=10 cm tube produce? C'outStf,^"tit'c
8 crn 8 crl
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22-8 cneprex22 . Wave Optics
14. A Michelson interferometer has been adjusted to produce a
bright spot at the center of the interferencepattern.a. Suppose the
wavelength of the light is halved, Is the center of the pattern now
bright or dark, or is it
not possible to say? Explain.
Thu cs\^*e.r of *he oo,$hrn*o oppur, ihe pat\r
lev,ql}6u'r,^l{ip\ns b{ }h. wo{e,le,^;+\.p"t[.l.n qths \{ill now
li$eri ^to.fcisnce. .
will slill b" b"ight. Fo," " b';Sht spo{cqn on\1 difftc b1
ttt$'n .mIf the. *^u.lc''5\\'is hJud.' thett e-, whi"h ; s{ill
cons{ruc}ivc
b. Suppose the wavelength of the light doubled to twice its
original value. Is the center of the patternnow bright or dark, or
is it not possible to say? Explain.
T+ is .
iynpossibk +o sqy. Pce,vio\^slyr*h. po*hlc",qil.s diff.crJ tvT
i''tc5oc vn.^llil.L--of \hc ',n,o,uol."gl\n. ff .'+h.,1.
-[tcqoris
".1-4tlne.,'. *he p*+\ .hff."sr.,c. is now qn odd rn*^lfido i{
^h^lf
'
wcvoln^gt\ , w\.rch woulA- .",^sQ, lcs{".^.hno ir.{erfcrohca.
or
o. d"ck spot. I{ 'Uo- *'r,*caqr wcs e{gy1. }hgn +l.e pc}hswil\
sli I t 'd,ffo. \ *,^ i,"l+c.+r -*t+i'ple o{ h. u,^.1c1.r,5{\q^A
th" ce-rn*ur wiit 1* brigft,
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