Does Huygens’ principle apply to x,a910kxd44 6ngauqdnv o 6o 3xoe(ehsound waves? To water waves? Explain.

What is the evidence that lka2 g pin*-7 ttclug2 ,ut::uhight is energy?

Why is light sometim 6b4cx:s tv6mnu)tk q6es described as rays and sometimes as waves?

We can hear sounds around corners, but we cannot s7xa+bm rsr ;h-ee around corners; yet both sound and light are waves. Explain the differencex-r 7 ;srhmba+.

If Young’s double-slit experiment t-nz6k5 i: .od39 znerbbnlr/ were submerged in water, how would the fringe pattern be change bolik-zr. nn59/ be3t:zdrn6d?

Monochromatic red light is incident on a double slit, andhzvpmd; -t u7o)7b:pc the interference pattern is viewed on a screen some distance away. Explain how the fringe vbp-cp7 z:; o mt)h7udpattern would change if the red light source is replaced by a blue light source.

Two rays of light fromn,7h km0;i-ka 4xk.cqy38ir0 i qcl fwj67dzu the same source destructively interfere if their path lengths differ by how ,hnmy4 w 837i iqjcf-70uarqz0kdlk;6xc i .kmuch?

Why was the observation q,dz 3(q q9mnssd- h6gof the double-slit interference pattern more convincing evidence for the wave theory of dsn(dq gm- q9,qzhs36light than the observation of diffraction?

Compare a double-slit experimento9tx(cs pqr j.k8h/) ukg:6nm for sound waves to that for light waves. Discuss the similanxs u6r8ch.okqt j9k g /:m()prities and differences.

Why doesn’t the light from the two headlights 9hs6csgw4:g ye,stk -of a distant car produce an interference patterngssh:6c,sew9- ygk 4t?

Suppose white light falls on the two slits of Fig. 24–7, but o /x,26 eng+:oddtklubgt:4uhne slit is covered by a red filterkgl6 o+uxtu: /bdd et42,:hng (700 nm) and the other by a blue filter (450 nm). Describe the pattern on the screen.

When white light passes through a flat piece of win4k :ecqd p01wn 88glvzdow glass, it is not broken down into colors as zpn k8d0eqg :8 1cvw4lit is by a prism. Explain.

For both converging a(gv9gfm7e -ys-j h*k ldd7ss h1ad0at *;b 5send diverging lenses, discuss how the focal length for red light differs from that forhs-a*(*y 0 -mgs 7d7 hes;slk f beg1vtd9ad5j violet light.

A ray of light is refracted through three d2kx: qlr32/2ty rrbtyifferent materials (Fig. 24–55). Rank the materials according to their index of refracti/2k2xt:t b yryrq2 r3lon, least to greatest.

Hold one hand close to your eye and4-jkk ;ww/w9afl e (h l mbgr4+3jgo3u focus on a distant light source through a narrow slit between two fingers. (Adjust your fingers to obtain the best pattern.) Describe the pgugok -l4wkw bel3r+j/jf4w 3h am9;(attern that you see.

What happens to the diffraction p2/ba0 a1d hijbattern of a single slit if the whole apparatus is i2 bab0ah dij1/mmersed in (a) water, (b) a vacuum, instead of in air.

For diffraction by a single slit, what is the effect of inc we isvomo(:w 2w* a475k iau1.j.idvcreasing (a) the slit width, and (b) thueivwmk. :d4oaws cav(5.*i o172ijw e wavelength?

What is the difference in the interference-5 x v/bpr(cea patterns formed (a) by two slits $^{-4}\;cm^2$ apart, (b) by a diffraction grating containing $10^4lines/cm$?

For a diffraction gratpsp q;:f)hy s)ing, what is the advantage of (a) many slits, (b) closely sp);spp) hqf:sy aced slits?

White light strikes (a) a diffraction grating, and (b) a prism.3uofc7w )msq, A rainbow appears on a wall just below the direction of the horizs)3 wuqc7 m,foontal incident beam in each case. What is the color of the top of the rainbow in each case? Explain.

For light consisting of wavelen(s /z mmzi5q8id(6.w /tfivlqgths between 400 nm and 700 nm, incident normally on a diffraction grating.(8 izwzivfq s5qil (mm6 t//d, for what orders (if any) would there be overlap in the observed spectrum? Does your answer depend on the slit spacing?

Why are interference fringes noticeable only for a thin film like a soap rv uqd2xcdg9yvzno ;0 mc -m0:/mk.g8bubble and not fo2dc9 qg 8ugmv0kdzyv ro.nx:0c-m;m/r a thick piece of glass, say?

When a compact disk (CD) is held at an angle in white light, the refle3z1um/1*y*mlub qefx cted light is a full spectrum (Fig. 24–56). Explain. What would you expect to see u/b1eqxy* zuf m1m *l3if monochromatic light was used?

Why are Newton’s rings (Fig. 24–31) closer to*eb*) kba2t (mdquq-y gether farther from the center?

Some coated lenses appear greenlfv1x4p7ysis6)l9 svy4 8p saish yellow when seen by reflected light. What wavelengths do you suppose the coating is designed to transmit xsv9s6ps )p 8fy1ysvl7i la44 completely?

A drop of oil on a pond appears brme ( vzel+lv,6 sms*10a8pqhpight at its edges, where its thickness is much less than the wavelengths of visible light. What can you saype60lelvz1m +vh8q(m a ,*pss about the index of refraction of the oil?

What does polarization tell us ab6gy am/oqtwljpqg* x37 h6:9i* ;grju :+hkdmout the nature of light?

Explain the advantage ofaei t 7 44emywu 68x,:jnl.dqn)ns/k r polarized sunglasses over normal tinted sunglasses.

How can you tell if a pair of sunglassess nw4nhzmd8 o(il9i40 is polarizing or not?

Two polarized sheets rotated at an wqwr61apubblpl v/l (2 hn202angle of 90$^{\circ}\,$ with respect to each other will not let any light through. Three polarized sheets, each rotated at an angle of 45$^{\circ}\,$ with respect to each other, will let some light through. What will happen to unpolarized light if you align four polarized sheets, each rotated at an angle of 30$^{\circ}\,$ with respect to the one in front of it?

What would be the color of the sky if the Earth had no atmosphere(xm, aat9*j pq7u j4ul?

If the Earth’s atmosphere were 50 to ufmo)uucfi zu.18zol7s*4 7imes denser than it is, would sunlight still be white, or would it be som.z l oios1f7o)ufu4uc87uz m *e other color?

  Monochromatic light falling onwd*y89on)c ime +dp d/ two slits 0.016 mm apart produces the fifth-order frinp io/+ddm*)9 dn ec8ywge at an 8.8$^{\circ}\,$ angle. What is the wavelength of the light used?    $ \times10^{-7 }\;m$

  The third-order fringe of 610 nm light6 y5km qy;l.4f0d rhlj is observed at an angle of 18$^{\circ}\,$ when the light falls on two narrow slits. How far apart are the slits?    $\mu m$

  Monochromatic light falls on two very narrow slits 0.048 mgahqs t49 m 1nxls2r,,m apart. Successive fringes on a screen 5.00 m away are 6.5 cm apart near the center of the pattern. Determine the wavelength and frequens,xg4ql1t r 2 hanm,9scy of the light.
$\lambda\;=\;$    $m$
$f$ =    Hz

  A parallel beam of light from a He-Ne laser, with a wavelength 656 nm, fal/ rf ;dzxf:3mc0fj.slls on two very narrow slits 0.060 mm apart. How far apazcjr 0m/ :ff3dslf; .xrt are the fringes in the center of the pattern on a screen 3.6 m away?    cm

  Light of wavelength 680 j:p51/4sqxnn o4s 9ixs qa* lnnm falls on two slits and produces an interference pattern in which the fourth-order fringe is 38 mm from the central fringe on a screen 2.0 m away. Wqi5lsa ox44/9q1n nps x:njs* hat is the separation of the two slits?    mm

  If 720-nm and 660-nm light passes through two slits 0.58 mm apart, hom 7no(sr8i. cnor1m*ww far apart are the second-order fr c 7mn*sw .(oorrn8im1inges for these two wavelengths on a screen 1.0 m away?    mm

  In a double-slit experiment,bg a g;))2b-p o5vonai it is found that blue light of wavelength 460 nm gives a second-order maximum at a certain location on the screen. What wavelength of visible light would have a b)n)aiov5 -2p b;oggaminimum at the same location?    nm

Water waves having pareirhg ( *ah8 :4oaczrcs t).3xallel crests 2.5 cm apart pass through two openings 5.0 cm apart in a board. At a point 2.0 m beyond the board, at what .3:(eccza xi)h *gs 84hrto raangle relative to the “straight-through” direction would there be little or no wave action?

Suppose a thin piece of glass is placed in f mcz8vtrr6wk-( 4hfb 8ront of the lower slit in Fig. 24–7 so that the two waves enter tkbz-v6m4wc88fr( hrthe slits 180$^{\circ}\,$ out of phase (Fig. 24–57). Describe in detail the interference pattern on the screen.
24-7
24-57

  In a double-slit experiment, the third-order maximum fd q q:u8x5r2suor light of wavelength 500 nm is located 12 mm from the central bright spot on a screen 1.6 m from the slits. Light of wavelength 650 nm is then projected through the same slits. How far from the central bright spot will the second-order maximum of thissuru qd8q5 x2: light be located?    mm

  Two narrow slits separated by 1.0 mm are illumb4a5dti kecyd+/ 7xk.inated by 544 nm light. Find the distance between adjacent brigh4kx ekbt7y+a c/. i5ddt fringes on a screen 5.0 m from the slits.    mm

  Light of wavelength 480 nm in air falls on two slits /a0q wby )ng ,1vkox*n$6.00 \times10^{-2 }\;mm$ apart. The slits are immersed in water, as is a viewing screen 40.0 cm away. How far apart are the fringes on the screen?    mm

  A very thin sheet of plasti 0w2s+/izq vxic (n=1.60) covers one slit of a double-slit apparatus illuminated by 640-nm light. The/w0 s +i2xvqiz center point on the screen, instead of being a maximum, is dark. What is the (minimum) thickness of the plastic?    nm

  By what percent, approximately, does the speed of red light (700 gm)p2cie+ +z6bvm tp4nm) exceed that of violet light (400 nm) in silicate flint glass? (See Fig. 24–14.) t)i p4+cmzp 2gbe+ v6m    %

  A light beam strikes a piece of gl0v ie*fj: nsgn4nx5 *mass at a 60.00$^{\circ}\,$ incident angle. The beam contains two wavelengths, 450.0 nm and 700.0 nm, for which the index of refraction of the glass is 1.4820 and 1.4742, respectively. What is the angle between the two refracted beams?    $^{\circ}\,$

  A parallel beam of light con4lvxi3lsq :f) taining two wavelengths, $\lambda_1\;=\;450\;nm$ and $\lambda_2\;=\;650\;nm$, enters the silicate flint glass of an equilateral prism as shown in Fig. 24–58. At what angle does each beam leave the prism (give angle with normal to the face)?
$\theta_{d1}$    $^{\circ}\,$ from the normal
$\theta_{d2}$    $^{\circ}\,$ from the normal

  If 580-nm light falls on a slit 0.0440 mm wide, what is tha uj *3s5aewa1fyl.0 sdng-gl 1j3 ng/e full angular width of the centrag l.5*sfan1 1ej a/ nl0 jyw3ag3dsu-gl diffraction peak?    $^{\circ}\,$

  Monochromatic light fa.2/s i,upciouz:ky*e lls on a slit that is $ 2.60\times10^{ -3}\;mm$ wide. If the angle between the first dark fringes on either side of the central maximum is 35.0$^{\circ}\,$ (dark fringe to dark fringe), what is the wavelength of the light used?    nm

  Light of wavelength 520 nm falls on ayvfb)fm up 9l(s q(g-: slit that is $ 3.20\times10^{ -3}\;mm$ wide. Estimate how far the first brightish diffraction fringe is from the strong central maximum if the screen is 10.0 m away.    m

  A single slit 1.0 mm wide is illuminateu8pa 8p 8bzcv,d by 450-nm light. What is the width of the central maximum (in cm) in the diffraction pattern on a scrua 8vz8p,bp 8ceen 5.0 m away?    cm

  Monochromatic light of:.kdnr51 lofr wavelength 653 nm falls on a slit. If the angle between the first bright fringes on either skdl o5.r1r: fnide of the central maximum is 32$^{\circ}\,$, estimate the slit width.    $\mu m$

  How wide is the central diffraction peak on a screen 2.30 m behind a by du suxd+:dlrcn:d +u,8;n(-r5 cw l0.0348-mm-wide slit illuminated cuwuu;d(rr +l,:nx -+yn5d8 sldc:bd by 589-nm light?    cm

  When blue light of wavelength 440 nm falls on a singb ,u1zjw0.c v28 ncpbyle slit, the first dark bandpc 08 vbw12, jyn.zucbs on either side of center are separated by 55.0$^{\circ}\,$. Determine the width of the slit.    $ \times10^{-7 }\;m$

  When violet light of wavelength 415 nm falls on a syl ldu(9w d:;ningle slit, it creates a central diffraction peak that is n;ylw:dul(d9 9.20 cm wide on a screen that is 2.55 m away. How wide is the slit?    mm

  If a slit diffracts 65f64q bgkl9mv 6p29 nj g+d7asc0-nm light so that the diffraction maximum is 4.0 cm wide on a screen 1.50 m away, what will be the width of the diffraction maximum for li 9492vfgjbag ds7 l+m66q nckpght of wavelength 420 nm?    cm

For a given wavelengtfm9;3jxn peh50f d qv7h $\lambda$, what is the maximum slit width for which there will be no diffraction minima?

  At what angle will 560-nm light produce a second-order maximum when fallinftb;f;z.jg59ue*u wp g on a grating whose slits .z*g;wf;bu5 fj9ue tpare $1.45 \times10^{-3 }\;cm$ apart?    $^{\circ}\,$

  A $3500-line/cm$ grating produces a third-order fringe at a 28.0$^{\circ}\,$ angle. What wavelength of light is being used?    nm

  How many lines per centimeter does adtr(nw amh;7 nzm(ftk,cv 8 ), grating have if the third-order occurs at an,zctm,v k((7m )wf8nt;r dhan 18.0$^{\circ}\,$ angle for 630-nm light?    $ \times10^{3 }\,lines/cm$

  A grating has $8300\;lines/cm$. How many complete spectral orders can be seen (400 nm to 700 nm) when it is illuminated by white light?   

  The first-order line of 589-nm light falling on a f7o)s/0vd */;r bm1h8s itmbch0mbindiffraction grating is observed ats;*s0 /ho) 7 fmbmh mibrd/0ctb 8v1ni a 15.5$^{\circ}\,$ angle. How far apart are the slits?    $\mu m$
At what angle will the third order be observed?

  A diffraction grating hassel lnj r,0dx8r1p*l6 $ 6.0\times10^{ 5}\;lines/m$. Find the angular spread in the second-order spectrum between red light of wavelength $ 7.0\times10^{-7 }\;m$ and blue light of wavelength $ 4.5\times10^{-7 }\;m$.    $^{\circ}\,$

  Light falling normallw c4tj. bzj(9,r geqt5y on a $9700-line/cm$ grating is revealed to contain three lines in the first-order spectrum at angles of 31.2$^{\circ}\,$, 36.4$^{\circ}\,$, and 47.5$^{\circ}\,$. What wavelengths are these?
$\lambda_{31.2}$    nm
$\lambda_{36.4}$    nm
$\lambda_{47.5}$    nm

  What is the highest spectral order that can 6b5ne+dtum8af. c 4ahbe seen if a grating with 6000 lines per cm is illuminated with 633 a h8a+nfe4ubtdc6m .5-nm laser light? Assume normal incidence.   

  Two (and only two) full spectral orders can be seen on either side+wrh84i c-xhkd tzg iu);pg e 3utc991 of the central maximum when white light is sent through a diffraction gra;h 3cd9p rc9t )wx4itukgei-z1uh 8+gting. What is the maximum number of lines per cm for the grating?    $ \times10^{ 3}\;lines/cm$

  White light containing wavelengths from 410 nm to 750 nm falls on a c c/ 6sdrzus3j,itk8 wm5i9b5grating with 3 k6i twi5 b8,/ cjz5susm9crd$8500\;lines/cm$ How wide is the first-order spectrum on a screen 2.30 m away?    m

  A He-Ne gas laser which produces monochromatic light of a x60dcp3it4+9lgz lye known wavelength $\lambda\;=\;6.328\times10^{-7 }\;m$ is used to calibrate a reflection grating in a spectroscope. The first-order diffraction line is found at an angle of 21.5$^{\circ}\,$ to the incident beam. How many lines per meter are there on the grating?    $ \times10^{ 5}\;lines/m$

  Two first-order spectrum qvc pe y32d)-y d.v/i0ktw nl3q7mg(vlines are measured by a $9500-line/cm$ spectroscope at angles, on each side of center, of +26$^{\circ}\,$ 38$^\prime$,+41$^{\circ}\,$ 08$^\prime$ and -26$^{\circ}\,$48$^\prime$,-41$^{\circ}\,$ 19$^\prime$. What are the wavelengths?
$\lambda_{26.72^{\circ}}\;=\;$    nm
$\lambda_{41.23^{\circ}}\;=\;$    nm

  If a soap bubble is 120 nm thick, what wavelength is most strongly reflected aij3c(5 g9l 0hd(ka4 k(wp kwtit the center of the outer surf 3(wl4at5gp dk i9w0 (kk(hijcace when illuminated normally by white light? Assume that $n\;=\;1.34$. $\lambda$ =    nm ,which is an    -  

  How far apart are the dark fr rxawc,ib8g 8.inges in Example 24–8 if the glass plates are each 26.5 cm long bi 8c.wr,agx8?    cm

  What is the smallest thickness of nehp:kc5++2e(9kp5aiv,5dka j azcc a soap film $(n\;=\;1.42)$ that would appear black if illuminated with 480-nm light? Assume there is air on both sides of the soap film. $t_min$    nm

  A lens appears greenish ,0:p uz7sfjl4 i2yc s x8sdz;yyellow ($\lambda\;=\;570\;mm$ is strongest) when white light reflects from it. What minimum thickness of coating $(n=1.25)$ do you think is used on such a glass $(n=1.52)$ lens, and why? $t_{min}$    nm

  A total of 31 bright ae2 :xamn)li7)jltg / wnd 31 dark Newton’s rings (not counting the dark spot at the center) are observed when 550-nm light falls normally on a planoconvex lens resting on a flat glass surface (Fig. 24–31).i/lej)) mwl :g 27txan How much thicker is the center than the edges?    $\mu m$

  A fine metal foil separates one end of two pieces of optically flat zp+b8t rm;1.qo7jtee glass, as in Fig. 24–33. When light of wavelength 670 nm is incident normally, 28 dark lines arebzpqe . t;8t+o1r 7ejm observed (with one at each end). How thick is the foil?    $\mu m$

  How thick (minimum) should the air layer be between two f kmj11kkp1)erqi*xinj/ s9: qlat glass surfaces if the glass is to appear bright when 450-nm light is incident normal1:*jp1nkij9r mks)/ ixk1 eqqly?    nm
What if the glass is to appear dark?    nm

  vA piece of material, suspected ofxwf q+k,l :f*h being a stolen diamond $(n=2.42)$ is submerged in oil of refractive index 1.43 and illuminated by unpolarized light. It is found that the reflected light is completely polarized at an angle of 59$^{\circ}\,$. Is it diamond? ----待选择----yesno 

  A thin film of alcohof;n1bt a/eq- bl $(n=1.36)$ lies on a flat glass plate $(n=1.51)$. When monochromatic light, whose wavelength can be changed, is incident normally, the reflected light is a minimum for $\lambda\;=\;512\;nm$ and a maximum for $\lambda\;=\;640\;nm$ What is the minimum thickness of the film?    nm

  When a Newton’s ring apparatus (Fig. 24–31) is immersb5d h4m17en two1m:ffed in a liquid, the diameter of t4tfm w7be1h15mnf :dohe eighth dark ring decreases from 2.92 cm to 2.48 cm. What is the refractive index of the liquid?   

  What is the wavelengthc *;1kaspkft s36xy8/ilrs1 x-e lgj, of the light entering an interferometer if 644 bright fringe*81/i j ckklxtrp ,;fsax g3-l1eyss6s are counted when the movable mirror moves 0.225 mm?    nm

  A micrometer is connected to the movable mirror of an intew w*o+z792 apeig)ckjj c )p0lrferometer. When the micrometer is tightened down on a thin metal foa0cc 7l9po)*ww gpjjz+e) ki2il, the net number of bright fringes that move, compared to the empty micrometer, is 272. What is the thickness of the foil? The wavelength of light used is 589 nm.    $\mu m$

  How far must the mir 0p;gol.c-aa fror $M_1$ in a Michelson interferometer be moved if 850 fringes of 589-nm light are to pass by a reference line?    mm

  One of the beams of an interferometer (Fig. 24–59) passes through a small gn u 2c*b02l1faa5et xjlass container containing a cavity 1.30 cm deep. When a gas is allowed to slowly fill the container, a total of 236 dark fringes are counted to move past a refe a2e a0 x5tncub1f2lj*rence line. The light used has a wavelength of 610 nm. Calculate the index of refraction of the gas, assuming that the interferometer is in vacuum. $n_{gas}$

  

  Two polarizers are orie7 akm. om-pd0lnted at 65$^{\circ}\,$ to one another. Unpolarized light falls on them. What fraction of the light intensity is transmitted?   

  What is Brewster’s anglr1s0q jf7ni:;k. kxu ne for an air–glass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s angle for a diamond submerged in water9fsz 1l3mq/mz if the light is hittingl m1z9q /z3sfm the diamond $(n=2.42)$ while traveling in the water? $\theta_{p}$    $^{\circ}\,$

  Two Polaroids are aligned so that the light passing tsx r y+u)*n6ap,qwm6g i j4.tdhrough them is a maximum. At what angle should one of them b* ,pwxqr64g6ymt)s.inaudj+ e placed so that the intensity is subsequently reduced by half?    $^{\circ}\,$

  At what angle should the axes of two Polaroiunh 5(jvycc 58ds be placed so as to reduce the intensiccn5jv 8hy (u5ty of the incident unpolarized light to
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are o+ gmwfq*+dj( yriented at 40$^{\circ}\,$ to each other and plane-polarized light is incident on them. If only 15% of the light gets through both of them, what was the initial polarization direction of the incident light?    $^{\circ}\,$

  Two polarizers are oriented at 38.0r436cowy awdvcur 9o 4o:yq 48$^{\circ}\,$ to one another. Light polarized at a 19.0$^{\circ}\,$ angle to each polarizer passes through both. What percent reduction in intensity takes place?    %

  What would Brewster’s angle be for reflectionta5q 1zevybd9*sj(4rp g/f d -s off the surface of water for light coming from beneath the surface? Compare to tts5pz -yad 9*vbq41r/g(e jdfhe angle for total internal reflection, and to Brewster’s angle from above the surface.
If the light is coming from water to air, $\theta_{p}$    $^{\circ}\,$For the refraction at the critical angle from water to air $\theta_c$   $^{\circ}$ If the light is coming from air to water $\theta_p'$   $^{\circ}$

  Unpolarized light passes through fi-ugrn2dh76. g h;xk l;,sw qdyve successive Polaroid sheets, each of whose axis make.gkg6u ;hr w,nqys7d2h;d -l xs a 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength e:a)h b7y7x hsov-)ic$ 5.0\times10^{7 }\;m$ passes through two parallel slits and falls on a screen 4.0 m away. Adjacent bright bands of the interference pattern are 2.0 cm apart.
(a) Find the distance between the slits.    mm
(b) The same two slits are next illuminated by light of a different wavelength, and the fifth-order minimum for this light occurs at the same point on the screen as the fourth-order minimum for the previous light. What is the wavelength of the second source of light? $\lambda_2$    $ \times10^{-7 }\;m$

  Television and radio waves reflecting from mountains or airplanes can intely fj6e, pzpk1.wn) .frfere with the dikzl1.jpp y6 fne .,)fwrect signal from the station.
(a) What kind of interference will occur when 75-MHz television signals arrive at a receiver directly from a distant station, and are reflected from a nearby airplane 118 m directly above the receiver? Assume $\frac{1}{2}\;\lambda$ change in phase of the signal upon reflection.  ----待选择----constructivedestructive 
(b) What kind of interference will occur if the plane is 22 m closer to the receiver?  ----待选择----constructivedestructive 

  Red light from three separate sources :;c9 bi.vp 9iy:oto tzpasses through a diffraction grating with bo99i.cit z:vt yo:p;$ 3.00\times10^{5 }\;lines/m.$ The wavelengths of the three lines are $ 6.56\times10^{-7 }\;m$ (hydrogen), $ 6.50\times10^{ -7}\;m$ (neon), and $6.97 \times10^{ -7}\;m$ (argon). Calculate the angles for the first-order diffraction lines of each of these sources. $\theta_{h}$    $^{\circ}\,$ $\theta_{n}$    $^{\circ}\,$ $\theta_{a}$    $^{\circ}\,$

  Light of wavelength 590 nm passes through two narrow slits 0.60 :hzy. v/ i-b pojev8s63ge4m9xa , vuomm apart. The screeneujiox v,8g9.zvsp4ye6:bmv 3oh- a/ is 1.70 m away. A second source of unknown wavelength produces its second-order fringe 1.33 mm closer to the central maximum than the 590-nm light. What is the wavelength of the unknown light? $\lambda_2$    nm

A radio station operating at 102.1 MHz broadcasts from two i u8lt99i1agdd dentical antennae at the same elevation but separated by an 8.0-m horizontal distance d, Fig. 24–60. A maximum signal is found along the midline, perpendicular to d at i1da tl9 8udg9its midpoint and extending horizontally in both directions. If the midline is taken as 0$^{\circ}\,$, at what other angle(s) $\theta$ is a maximum signal detected? A minimum signal? Assume all measurements are made much farther than 8.0 m from the antenna towers.

  A teacher stands well back from an outside doorway 0.88 m wide, and blow-1dn(-awrtm9 s ye cndk j k0xx,j,,s4s a whistle of frequency 750 Hz. Ignoring reflections, estimate at what angle(s) it is not yksj ndkats4w9c xjnx ,-e (-,,r0dm1possible to hear the whistle clearly on the playground outside the doorway.    $^{\circ}\,$ either side of the normal.

If parallel light falls on a singf ej)x vqy3a32le slit of width D at a 30$^{\circ}\,$ angle to the normal, describe the diffraction pattern.

  The wings of a certain beetle have a series of pvc0 qgkv 2*elv4zl g55arallel lines across them. When normally incident 460-nm light is refle5kzv c04v llgv2g q5*ected from the wing, the wing appears bright when viewed at an angle of 51$^{\circ}\,$. How far apart are the lines?    nm

  How many lines per cfyqw o7(i 2(rql27nnkw,on 1t60 wkk xentimeter must a grating have if there is to be no second-orde lnn7t6w(0o fkykrq 2 n 1qwx(,i2wko7r spectrum for any visible wavelength?   $ lines/cm$

Show that the second- and third-order spectra of white light produced bc+x o zcw)y/6ky a diffraction grating always overlap. What )c+6kzx oyc/w wavelengths overlap exactly?

  When yellow sodium li)enzi6fkd2r 9 ght, $\lambda\;=\;$ falls on a diffraction grating, its first-order peak on a screen 60.0 cm away falls 3.32 cm from the central peak. Another source produces a line 3.71 cm from the central peak. What is the wavelength of the new source? How many $lines/cm$ are on the grating?
   nm
  $ lines/cm$

  Light is incident on a diffraction grating uh+vd nqh2 -s2with and the pattern is viewed on a screen 2.5 m from the grating. The inciden2nh q 2-uvs+hdt light beam consists of two wavelengths, $\lambda_1\;=\; 4.6\times10^{ -7}\;m$ and $\lambda_2\;=\; 6.5\times10^{ -7}\;m$. Calculate the linear distance between the first-order bright fringes of these two wavelengths on the screen.    m

What is the index of refractio5e;dx l(ad-n/ 3zoswd n of a clear material if a minimum of 150 nm thickness of it, when laid on glass, is needed to reduce reflection to nearly zero when light of 600 nm is incident normalx ddoes-3/a n(lzw;d5ly upon it? Do you have a choice for an answer?

  Monochromatic light of variable wavel v3vb8 p4( 8:t)+knxasr/7klpjywskf ength is incident normally on a thin sheet of plastic film in air. The reflected b+/k4f x38 nkrwj7ytp vkva(s :lp)8slight is a minimum only for $\lambda\;=\;512nm$ and $\lambda\;=\;640nm$ in the visible spectrum. What is the thickness of the film $(n=1.58)$? [Hint: Assume successive values of m.]    nm

  Compare the minimum thickness needed for an anti-reflective cm6 +kvr:pip lo6hf4babfxey )2 l5u51oating $(n=1.38)$ applied to a glass lens in order to eliminate
(a) blue (450 nm),    nm
(b) red (700 nm) reflections for light at normal incidence.    nm

  What is the minimum (non-zero) thickness for the air layer betweqi6su4ef:x 0sdb c;5s )o.dmeen two flat glass surfaces if the glass is to appear dark when 640-nm light is incidd.do:;fi 50 4)csq bexsmus 6eent normally?    nm
What if the glass is to appear bright?    nm

Suppose you viewed the light transmitted throo2ue qw6l9 b la4ck y)+u .jjy x*sdc*ac,1mj*ugh a thin film layered on a flat piece of glass. Draw a diagram, similar to Fig.a *+by2cuc*dx u l jj9, j*6keo. q1lms)4awyc 24–30 or 24–36, and describe the conditions required for maxima and minima. Consider all possible values of index of refraction. Discuss the relative size of the minima compared to the maxima and to zero.
24-30
24-36

  At what angle above the horizon is the Sun when light reflecting o/i renxa+y4d, e7 quys-mp.8s ff a smooth lake is polarized most strongly?s/u yx 4 na.yes,+d-rp7ime q8    $^{\circ}\,$

  At what angle should the axes of two Polaroids be place i69n ba;vk,z(rd4.afdag a 1id so as to reduce the intensity of the incident unpo rg n9a6afzk4 ;a1,.di(avi dblarized light by an additional factor (after the first Polaroid cuts it in half) of
(a) 4,    $^{\circ}\,$
(b) 10,    $^{\circ}\,$
(c) 100?    $^{\circ}\,$

  Unpolarized light falls on two polarizer sheets whose o8.y )arbe67bsypb( 3lm(d tj transmission axes are at right angles. A third polarizer is placed between the first two so thadrj7a3(m)byb 6olp(.btsy e8t its axis makes a 62$^{\circ}\,$ angle with the axis of the first polarizer.
(a) What fraction of the incident light intensity is transmitted?    $I_0$
(b) What if the third polarizer is in front of the other two?

Four polarizers are placed in succession with their axes vertit*xc1 g4pbd h,cal, at 30$^{\circ}\,$ to the vertical, at 60$^{\circ}\,$ to the vertical, and at 90° to the vertical.
(a) Calculate what fraction of the incident unpolarized light is transmitted by the four polarizers.
(b) Can the transmitted light be decreased by removing one of the polarizers? If so, which one?
(c) Can the transmitted light intensity be extinguished by removing polarizers? If so, which one(s)?

  A laser beam passes throu gyen52 u(og4fj)oad/gh a slit of width 1.0 cm and is pointed at the Moon, which is approximately 380,000 km from the Earth. Assume the laser emits waves of wavelength 630 nm (/d4uo5(fyg2 e)na gojthe red light of a He-Ne laser). Estimate the width of the beam when it reaches the Moon.    km

  A series of polarizers are eachiv5h4.xe(cx-it+z1(bkf e+rs sxj h- / , maxy placed at a 10$^{\circ}\,$ interval from the previous polarizer. Unpolarized light is incident on this series of polarizers. How many polarizers does the light have to go through before it is $\frac{1}{4}$ of its original intensity?   

  A thin film of soap vfx:1 x)g dc/ sm15kk0lv7so px 1e0zl$(n=1.34)$ coats a piece of flat glass $(n=1.52)$ .How thick is the film if it reflects 643-nm red light most strongly when illuminated normally by white light?    nm

  Consider two antennas radiating 6.0-MHz radio waves in phase jp9rugs k0ob;g uv5 zg1r(;7qqk.n+gwith each other. They qp. 0; gz7k 1ogg qnur(v g+su59bjk;rare located at points $S_1$ and $S_2$, separated by a distance $d\;=\;175m$, Fig. 24–61. What are the first three points on the y axis where there will be destructive interference? (Destructive interference in this case means that a radio receiver placed at that point would pick up no signal).    m    m    m

  A parallel beam of light containing two wavelengths, 4balf 97 . 4+fwk+wyqup20 nm and 650 nm, enters a silicate flint glass equwp4aq7b9+yl+.ff kw uilateral prism (Fig. 24–58).
(a) What is the angle between the two beams leaving the prism?    $^{\circ}\,$
(b) Repeat part (a) for a diffraction grating with    $^{\circ}\,$

  A Lucite planoconvex lens has ) o.b5 hv r4eqmwn;11+ rmsqdbone flat surface and one with $R\;=\;18.4\,cm$ It is used to view an object, located 66.0 cm away from the lens, which is a mixture of red and yellow. The index of refraction of the Lucite is 1.5106 for red light and 1.5226 for yellow light. What are the locations of the red and yellow images formed by the lens? [Hint: See Section 23–10.]
$d_{i-red}$    cm
$d_{i-yellow}$    cm