Does Huygens’ principle apply to sound waby vr +tx11yl7zk +zn(ves? To water waves? Explain.

What is the evidence that light is f6s ) b1grru o3d41zrb*,rqjeenergy?

Why is light sometimes described as rays and sometimez jexz;e9d;7bc gi::ps as waves?

We can hear sounds around corners, but we cannot see around cornezlr6dn -j)clctn+ z,5 rs; yet both sound and light are waves. Explain thz lr+ d,5t)nz c-njcl6e difference.

If Young’s double-slit experiment were submerged in water, how woulba/k flu5+rknz h3) q+op h:3 +m1notkd the fringe pattern be changed3kruk +ph h3z+qkft+mnl) ba 5oo /:n1?

Monochromatic red lightz3/2bt8e b.vpgh4g x8 sa1ua q is incident on a double slit, and the interference pattern is viewed on a screen some distance away. Explain how the fringe pattern would change if the red light so.3 p h8 saba12zbtq4geguv/8xurce is replaced by a blue light source.

Two rays of light from the same source destructively interfere if their path y7txg )-t1ob(jke;jrlengths differ by how txty o;(j)jk7r1gb -e much?

Why was the observation ofkn(d+rv 9 0p,csaeq 2e the double-slit interference pattern more convincing evidence for the wave theory of light tha,eq+ nrsd2(avpk9 0c en the observation of diffraction?

Compare a double-slit experiment for sound waves to thk98oe z**e rodat for light waves. Discuss the ko*ro z*8d9ee similarities and differences.

Why doesn’t the light from the two headlights ofn11 0k9nr)zkmx b6yvm a distant car produce an interfnrxbnm0) v61zk 9y1 kmerence pattern?

Suppose white light falls on the two slits of Fig. 24–7, but one slit is covp*l tihd0tnlw2-n. 3k ered by a red filter (700 nm) and the other by a blue filter (450 nm). Describe t* lditk.0nhpwl 3 n-t2he pattern on the screen.

When white light passes throug:ki2k0-x b kjhh a flat piece of window glass, it is not broken down into colors as it is by a prism. k2x: jk hi0kb-Explain.

For both converging and dx2pmc b a1fv71iverging lenses, discuss how the focal length for red light differs f1vbx7 amp 21cfrom that for violet light.

A ray of light is refracted through three different materzahsbr8z87u i0+c;a 8m6ky vk ials (Fig. 24–55). Rank the materials according to their index of refraction, least to gu;c m6k0 v 7zh8+zkb8aar8 siyreatest.

Hold one hand close to your eye and focus on a distant light source throug ofo:tpi 8pc68h a narrow slit between two f8 pp8tfo :6oicingers. (Adjust your fingers to obtain the best pattern.) Describe the pattern that you see.

What happens to the diffraction4 z htma6vc.*p pattern of a single slit if the whole apparatus is immersed in (a) water, (b) a vacuum, instead of in az c*m46ht.vpair.

For diffraction by a single slit, whatn 0yt3b(lmrg7c2 1 swn is the effect of increasing (a) the slit n7(trwlb3m 0n cys2g1width, and (b) the wavelength?

What is the difference in the interference pae0k5:in cafyqj( /ao8tterns formed (a) by two slits $^{-4}\;cm^2$ apart, (b) by a diffraction grating containing $10^4lines/cm$?

For a diffraction grating, what is the advantacc1k(6w w831go;b0lk3c wd1mw vpqae ge of (a) many slits, (b) closely spaced 1wc c3aw86k (;mqc vpw leo b3kd1w1g0slits?

White light strikes (a) apow0 v -50zl (m ivnrw0ec:krbt0+tg . diffraction grating, and (b) a prism. A rainbow appears on a wall just below the direction of the horizontal incident beam in each case. What is the color of the top of the rainbow in ea:c0v ti.(gr zlwmnek r0vw- + 05obpt0ch case? Explain.

For light consisting sld3cy*o jm.84v n d-jof wavelengths between 400 nm and 700 nm, incident normally on a diffraction grating, for what orders (if any) would there be overlap in the observed spectrum? Does your answer depend on themn3jl4*. -syj8vdcd o slit spacing?

Why are interference fringes noticeable onl*u)(yxl2 eh( k9ubhuj y for a thin film like a soap bubble and not for a thick piece ofuulb2hu j* (9) xh(yek glass, say?

When a compact disk (CD) is held at an ancyhd;8q( j -migle in white light, the reflected light is a full spemc 8djq(i; hy-ctrum (Fig. 24–56). Explain. What would you expect to see if monochromatic light was used?

Why are Newton’s ring oejb94h o37tjs (Fig. 24–31) closer together farther from the center?

Some coated lenses appear gr0f4hjs4kh5ws(3mfr leenish yellow when seen by reflected light. What wavelengths3 l f54jmr(f0k4h hsws do you suppose the coating is designed to transmit completely?

A drop of oil on a pond appears bright at its edges, where its thickness is mu vgl0-(wm40 wt 8kppisch less than the wavelengths of visible light. What can yo0 kpw-4 gwl(smv0p8itu say about the index of refraction of the oil?

What does polarization tell us about the fmftwq0:p2.w lfqp0x;o) h n;nature of light?

Explain the advantagejsa*t6qwls co9oso 8*.n*h 7b of polarized sunglasses over normal tinted sunglasses.

How can you tell if a pair of sunglasses is po31qj*5 cunwat larizing or not?

Two polarized sheets rotated at an angle o0mx/oc 4e8 kz5 uglf;vf 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 d vs9yd. 2dxq4Earth had no atmosphere?

If the Earth’s atmosphere were 50 times denser than it is, wou(pi:vowk:w+ ;ngk+rvai*f e(ld sunlight still be white, or would it be some other co+ wk+ag;ei ::*rwif pk(v(vo nlor?

  Monochromatic light falling on two slits 0.016 mm apart prr* lumw-iq1:d oduces the fifth-order fringe at an 8wi rlq: udm*-1.8$^{\circ}\,$ angle. What is the wavelength of the light used?    $ \times10^{-7 }\;m$

  The third-order fringe of 610 nm light is observed at an v,q4d/b)2 as zzc) mzeangle 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 mm apart. Suyvhoqg+0b :myz d. d-: 0usw,occessive fringes on a screen 5.00 m away are 6.5 cm apart near the center of the pattern. Determine the wavelength and frequency of the light. bu,d vo-z:wsydm0qyo. g +0:h
$\lambda\;=\;$    $m$
$f$ =    Hz

  A parallel beam of light from a He-Ne laser, with a wavelength 656m7zg q zj/k.9i nm, falls on two very narrow slits 0.060 mm apart. How far apart are the fringes in the center of the pattern on a screen 3qmi9gjk/.7z z .6 m away?    cm

  Light of wavelength 680 nm falls on two slits a. of* -btsd;x7tt4 8crpjh-z wnd produces an interference pattern in which the fourth-order fringe is 38 mm from the s*-d-xr.; f8 zb7htcj twp4otcentral fringe on a screen 2.0 m away. What is the separation of the two slits?    mm

  If 720-nm and 660-nm light passeyua qr+; ;vaix8ywom-z )hkx33tgs -p r8u(6 bs through two slits 0.58 mm apart, how far apart are the second-order fringes for these two wavelengths; hxrb8 8(u3xm3sy-;q)o yt u6ar wg-vi+zakp on a screen 1.0 m away?    mm

  In a double-slit experiment, it is found that blue light of wy)mn p.53mnxa x+stn/u7i7 oc avelength 460 nm gives a second-order maximum at a certain location on the screen. What wavelength of visible light would have a minnt757xa s p 3nnmiym/xo+.u )cimum at the same location?    nm

Water waves having parallel crests 2.5 cm apart pass through two cady;os(9 vq. openings 5.0 cm apart in a board. At a point 2.0 m beyond the board, at what angle relative to the “straigh ;ayvod s9(.qct-through” direction would there be little or no wave action?

Suppose a thin piece of glass is placed in f:e dl)p gxue(3ront of the lower slit in Fig. 24–7 sopd(ul 3g :ex)e that the two waves enter the 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 k1l dtrmi0:ec6rk l(uw3*sns/d;2f ufor 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 l uw12ti:d/0k rs(;scr d6fmnk e3*lu will the second-order maximum of this light be located?    mm

  Two narrow slits separated by 1.0 mm are illuminaeo *hn)kqq 3 /kl+eqa3ted by 544 nm light. Find the distance between adjacent q3h/ q)n+e*lok3ek qabright fringes on a screen 5.0 m from the slits.    mm

  Light of wavelength 480 nm in air falls zhrzkb-a eu5w w-5rls7; /1pf.u zqt:on two slits $6.00 \times10^{-2 }\;mm$ 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 plastic (n=1.61fdfkphf r)(b+,ejr 8z6t /kr 0) covers one slit of a double-slit apparatus illuminated by 640-nm light. The center poi(+hf/1kbkfj efrr) ,z 68 dtrpnt on the screen, instead of being a maximum, is dark. What is the (minimum) thickness of the plastic?    nm

  By what percent, approximately, does thes- 7zu1.gilb t (syi9k speed of red light (700 nm) exceed that of violet light (400 nm) in silicate flint gu ysilzk-( 19.bit7gslass? (See Fig. 24–14.)    %

  A light beam strikes a pieceqmr ou;8)-c4 gfrrd)tqjr3w. of glass 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 containifc5a (zdrb/l p 7e8v+eng 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 wid9d bmz)5pwa2 r2n0 orce, what is the full angular width ofp0n9 )5om2zra2 bcwdr the central diffraction peak?    $^{\circ}\,$

  Monochromatic light falls on a slit that is .vwp xxm69+kmi envaey. b c*yy2(/ -w$ 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 a slit that+)5j yqyzqs:u 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 illuminated by 45tr an:/va5 bt/o6b +ax0-nm light. What is the width of the ce tx/n+tv 6:aboba/5 rantral maximum (in cm) in the diffraction pattern on a screen 5.0 m away?    cm

  Monochromatic light of wavelength 653 nm falls on a slit. If the angle 3aoaglq 1z im* 7fyso5i:3h;f between the first bright fringes on either side of the cenqsly;a:3go mhz*f71 a3 oii5ftral 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 0.z+jw2p 3vqf/tmk:k.n kin1 2l 0348-mm-wide2jwi k .k tl3nk z+q1v2nf:p/m slit illuminated by 589-nm light?    cm

  When blue light of wavelength 440 nm falls oh 6bo,e4n2ab+tq*f fr2egmy (n a single slit, the first dark bands on either side of center are separat2m,tqyagf64( o r*hbe 2 ebn+fed by 55.0$^{\circ}\,$. Determine the width of the slit.    $ \times10^{-7 }\;m$

  When violet light of wavelength 415 nm falls on a sih2t23l5 pwieau4:nk 6/ btabzngle slit, it creates a central elt pw6:za4bui kbh2a2n /3t5 diffraction peak that is 9.20 cm wide on a screen that is 2.55 m away. How wide is the slit?    mm

  If a slit diffracts 650-nm light so that the diffraction maximum is 4.0 cm d;1nyz0mg3lp0 tx u k6lg 3x4lwide on a screen 1.50 m away, what wix x d0tm4n01l3ggp;lu y3lkz6ll be the width of the diffraction maximum for light of wavelength 420 nm?    cm

For a given wavelength , p.q jqc7coq3k4g,dtl8 :hj;jj 3twd$\lambda$, what is the maximum slit width for which there will be no diffraction minima?

  At what angle will 560-nm light produce a second-orderd5..x5q0f db)tvv yyt maximum when falling on a grating whose sli0dtd55 v.yqx) .bvyftts are $1.45 \times10^{-3 }\;cm$ 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 a grating have;4f1jiyc gs;t if the third-order occurs at a;gti ;f jys4c1n 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 diffraction grating is observeoi p -139tpmo1e;joyr65e 9wvv.ge eed a1te9e 3ej. 1eyvpge9mp i5-o;6wovor t 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 has(pf60blbj;ze* gmt f: $ 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 normallu 0n m5am7,7xvsvaez 67q0chukai- v3y 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 be seen if a grating with 6000 li;ocmj:wefja1: i +ro-nes per cm is illuminated with 633-nm laser li w;ro e1mfoi+:j:cja-ght? Assume normal incidence.   

  Two (and only two) full spectral orde p :-l+dne9nlhrs can be seen on either side of the central maximum when white light is sent through a diffraction grating. What is the maximum numbe9n+ np hlel-d:r of lines per cm for the grating?    $ \times10^{ 3}\;lines/cm$

  White light containing wavelengths from 410a-+nc/e4gdc-k : nwlu nm to 750 nm falls on a grating with ug4awce+/ :k-ndnc -l $8500\;lines/cm$ How wide is the first-order spectrum on a screen 2.30 m away?    m

  A He-Ne gas laser which produces monochromatic lighc.dy6 x,4j5k *la4igv-r kjqo t of a 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 lines are measured by a 7e,+gt1vk b5 dm69 ;xd potlgp$9500-line/cm$ 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 wav6, l8ecv 6are9pavnc 8: bbie1elength is most strongly reflected at the cev b9cien,6 are:p 8ca8lvb 16enter of the outer surface when illuminated normally by white light? Assume that $n\;=\;1.34$. $\lambda$ =    nm ,which is an    -  

  How far apart are the dark fringes in Example 24–8 if the glass plates are each tr .6 h.b0)ojevpeju 126.5 cm long? )1u6hejte0b..op v jr    cm

  What is the smallest thi,o+bcjfx:8t*s8 q yz tckness of 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 greent/*5v q8tcgzi ish yellow ($\lambda\;=\;570\;mm$ 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 and 31 dark Newton’s rings (not counting t,i9mg b1;876v z - bobltducpmhe dark spot at the center) are observed when 550-nm lig;m 9 uzgi8cbvm67lb -bdo p,1tht falls normally on a planoconvex lens resting on a flat glass surface (Fig. 24–31). How much thicker is the center than the edges?    $\mu m$

  A fine metal foil separates one elbn) g/8i3 o9toiov( gnd of two pieces of optically flat glass, as in Fig. 24–33. Whe)nlgi9i o3 g v(/8tboon light of wavelength 670 nm is incident normally, 28 dark lines are observed (with one at each end). How thick is the foil?    $\mu m$

  How thick (minimum) should the air layer be between two flat glass surf 1 n1qow99xqglhtt gf::ms49g a7v)ebaces if the glass is to appear bright when 450-nm light is incident normal7:1) 14 9l watg vf:9bgmonqt9gshqxely?    nm
What if the glass is to appear dark?    nm

  vA piece of material, suspected of being a stoleb ylc9jj9i998apa;yg.,y wj- fasb7kh z4t 6cn 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 alcohoq: k f8a,f-darl $(n=1.36)$ 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 app: fgiafbss q5**7*zpmwcq4(laratus (Fig. 24–31) is immersed in a liquid, the diameter of the eighth dark ring decreases from 2.92 cm to 2.48 cm. What is the refractive index of the liquid?qf5 * am:7bci *z4spw( fsl*qg   

  What is the wavelength of the light iwzd.d(g,1rs entering an interferometer if 644 bright fringes are counted when the movable mirwrs (,dz1. dgiror moves 0.225 mm?    nm

  A micrometer is connected to the movable 7eq5oh.z0yq hmirror of an interferometer. When the micrometer is tightened down on a thin metal foil, the net number of bright fringes that move, compared h 7eh5zq.oyq0to 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 mirroa8 rt 5*a*j7pot7 z pcbj:c7vvr $M_1$ 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 mhfhtp )e 2 1sw,1qie4through a small glass container contain f,weq1sth 1)iepm 4h2ing 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 reference 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 orieihcs2+ i6)m 6)hc5kgplq tg h1nted at 65$^{\circ}\,$ to one another. Unpolarized light falls on them. What fraction of the light intensity is transmitted?   

  What is Brewster’s angle for an air–glselm5ha0ipo8 x8tp11 ass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s angle for a diamond su( iw7pyl)4kvhoa s 4c) y4qw+wbmerged in water if the light is hittingwc4744q wvyk+shy l pio)(wa) the diamond $(n=2.42)$ while traveling in the water? $\theta_{p}$    $^{\circ}\,$

  Two Polaroids are aligned so that the light passing through them is a maxwam eczj /)+3 9mtu7dq)xv6bximum. At what angle should one o)d a)xzm 7j3/wvq6u+mextc9bf them be placed so that the intensity is subsequently reduced by half?    $^{\circ}\,$

  At what angle should the axes ylw.3/dd chg: of two Polaroids be placed so as to reduce the intensity of the incident unpolari.g dylw3 :hd/czed light to
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are oriented at 4inmj jakuh7i7ie-1k/u;3 h y.tz2n3m0$^{\circ}\,$ 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 38.3 /bs4-qb+lox 3ldoiy0$^{\circ}\,$ 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 reflections off the surface of watsy qcevylv1k:;3n 3j7er for light coming from beneath the surface? Compare to the angle for total internal reflection, and to Brewster’s angle from above the surface. y ls;1e:v nc3qv 37kjy
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 passe il,ih 4c.mrb,s through five successive Polaroid sheets, each of whose ax,4r b h.mcili,is makes a 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength oa x/p d4sk+h +k(60s,e czwpv$ 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 frntrmxp 5bpcshr,dk 3 )nh48g9.bun-(om mountains or airplanes can interfere with the direct signal fromhdugpb,n b .xn-k5hr)9 p c4t(3msrn8 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 9yntv s wu2/(o qg*i :cex;;rupasses through a diffraction grating with s;e x( irngoqtuwuyv2:c;*/9 $ 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 thr yymz or-.al)6ough two narrow slits 0.60 mm apart. The screen is 1.70 m away. A second source of unknown wavez-ma6)oy yr.l length 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 opera2f+lm-v52aqt hma p 0iting at 102.1 MHz broadcasts from two identical antennae at the same elevation but separated by an ia v2p-a2mf 5mh+ tlq08.0-m horizontal distance d, Fig. 24–60. A maximum signal is found along the midline, perpendicular to d at its 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 b;jwh u)5 6un.+h3wpmkzr j0 dfack from an outside doorway 0.88 m wide, and blows a whistle of frequency 750 Hz. Ignoring reflections, estimate at what angle(s) it is not possible to hearfhuuj3 ;n.jpw5d6 +) wr0mkhz the whistle clearly on the playground outside the doorway.    $^{\circ}\,$ either side of the normal.

If parallel light fal*.exssu-ny wvm0 hj4; ls on a single slit of width D at a 30$^{\circ}\,$ angle to the normal, describe the diffraction pattern.

  The wings of a certai -3d;i)qukp5ps0 x6-z gmf.f tt0+ew.dm jdpkn beetle have a series of parallel lines across them. When normally inkukj pt zfs dg3.-x0-m0fq6p)d+ pm5wted ;.icident 460-nm light is reflected 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 centimeter must a grating have if there is to be no 0(/: ,+pwhlmbvfe f5irfnu n ma-25wh 6uiwh8second-order s( h:mf 5i-rbw pef8/w vn 0uf 5,2wml+6hunaihpectrum for any visible wavelength?   $ lines/cm$

Show that the second- and third-order spectra cc/ cci1)hqhnqe uw/ u b;g:5phc5h:;of white light produced by a diffraction grating always overlap. What wav1hp5wh:e:qc cicc /qc; /nhh5u g)bu;elengths overlap exactly?

  When yellow sodium lighpqdu*,k/)k rdlo:x4k 8 nr +pnt, $\lambda\;=\;$ 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 with and the patternx3l c 5ipg4j2woak1+i is viewed on a screen 2.5 m from the grating. The incixai+2gk1i 34o wlpj5cdent 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 refraction of an md j3ijm)3i8mdcd alg q8.1, clear material if a minimum of 150 nm thickness of it, when laid on gqm m )d1nad,jlc mj38i3.i8dglass, is needed to reduce reflection to nearly zero when light of 600 nm is incident normally upon it? Do you have a choice for an answer?

  Monochromatic light of variable wavelengt85hzp.1m didwv4vef h6g53ebh is incident normally on a thin sheet of plastic film in air. The reflected light is a minimm5 618z43 ddw vpehh5vi.efgbum 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 neede0 wdb u.ix5tjjip+ f. v7qasd0)+fm5w d for an anti-reflective coating $(n=1.38)$ 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 aw z-wk h,cao 7 cgla8w2z;+a69wjxm0 uir layer between two flat glass surfaces if the glass is to appear dark when 640-nm l;a m ao9wz-8 u6wkgj,a xwzlwc70c+2hight is incident normally?    nm
What if the glass is to appear bright?    nm

Suppose you viewed the lightrj,h :.oneii8xij* t) transmitted through a thin film layered on a flat piece of glass. Draw a diagram, similar to Fig. 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 sizeh,xn. i8i tie:j )oj*r 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 re ku b cr1u/:xyaq)ssqch6w8+/flecting off a smooth lake is polarized most strokchqr+ a qbx8w)u /u1s cs6/y:ngly?    $^{\circ}\,$

  At what angle should the axes of two Polf hv78wqrbkyfe2km*;kouk,81u i8 1 b)maek: aroids be placed so as to reduce the intensity of the incident unpolarized light by an additional factor (after the first Polaroia1m*uefkyfi 1q br:;k, ) 8ukkw kve78moh8b2 d cuts it in half) of
(a) 4,    $^{\circ}\,$
(b) 10,    $^{\circ}\,$
(c) 100?    $^{\circ}\,$

  Unpolarized light falls on two polarizer shew7t i8c72hq izbgt ;*6j 0ogxlets whose transmission axes are at right angles. A third polarizer is placed between the first two ljb62hz7t0gx gt *oi ;8w7q ciso that 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 pla:1by y8zhkg /tced in succession with their axes vertical, 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 through a slit of width 1.0 cm and is point fdp p7l:cxy.5i,3cuoed at the Moon, which is approximately 380,000 km from the Earth. Assume the laser emip5ypf co:xi. 3lcu7,dts waves of wavelength 630 nm (the red light of a He-Ne laser). Estimate the width of the beam when it reaches the Moon.    km

  A series of polarizerspd8hl v-/ ss zuylu80*rn3)d k are each 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 1.i)j( h/yr we no(go ,lvlj8l$(n=1.34)$ 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 radifg/2dqu)e )z2w c;kkxo waves in phase with each other. Th);22qu xdf /z kkewcg)ey are 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 wavelme)e);l rzx09s;2wi 8a a mkomengths, 420 nm and 650 nm, enters a silicate flint glasa lr9xe2mi; o0 sk));mwzema8s equilateral 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 one ft1ey.q hy,od ,lat 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