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.

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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.

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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.

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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?

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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?

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c. How many extra wavelengths does wave 2travel compared to wave 3?

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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.

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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.

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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?

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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?

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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.

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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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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.

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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

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c. How will the screen appear if the aperture diameter is decreased to less than the wavelength of thelight?

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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

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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.

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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.

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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

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