Does Huygens’ principle apply to sound waves? To wat8h 5xn7bcuy.s3zw x g;5vnmfm 05na .lc9uo2eer waves? Explain.

What is the evidence that lig y:dew t/;yds q3ld70bht is energy?

Why is light sometimes described as rays and sometiwsx ox7 (;6er/dz 0t7no,wlw lmes as waves?

We can hear sounds around corners, but we cannot see aroundwwa q kkz+30r* corners; yet both sound and lightq0kz*rwk +3 wa are waves. Explain the difference.

If Young’s double-slit exrwpzpfk ak0nseal5s( :( adf2w 7-6c.periment were submerged in water, how would the fringe p n2a -csapfsl7a.wz6wdk5e( 0 kr( pf:attern be changed?

Monochromatic red light is incident on a double 09xq m)s0kzei slit, and the interference pattern is viewed on a screen some distance away. Explain how the fringe pattern would change mesqxz0k90 i) if the red light source is replaced by a blue light source.

Two rays of light from the same 1fwao ,+ cx-ujq9k+a fsource destructively interfere if their path lengths differ 1cxafk+ q+-9u aofwj,by how much?

Why was the observation of the double-slit 6+ h .r3qy/zxjf mzb-rinterference pattern more convincing evidence f3 +xzhm r/zbyq fjr.6-or the wave theory of light than the observation of diffraction?

Compare a double-slit experiment for sound waves to that for li6 kda04pp/o4cd rknr*ght waves. Discuss the similarities and differencesoap4 c*0 dr6 krdn4/pk.

Why doesn’t the light from the two headlights of a distant car proaji6ho 82tnwbd * k9m)duce an interference patb6adhkt 8 2*jn9iw)motern?

Suppose white light falls on the two slits yzk,+5oty2 ayg z0yjw ,))muwof Fig. 24–7, but one slit is covered by a red filter (700 nm) and the other by a blue filter (450 nm). Describe the pattern on the scre u,jwy+zmao) z0t5g wyyky2,)en.

When white light passk;3 hlw goh;x s7+i4wbes through a flat piece of window glass, it is not broken down into colorso ishg3l7xb +khw;;w4 as it is by a prism. Explain.

For both converging and diverging lenses, discuss how the focal length p5y2c559 6z gz3x:csbiviyc xfor red light di9552zc ic6xi3 :5vyp ygbxsczffers from that for violet light.

A ray of light is refracted through three differentdg2-r: 2.62km q bvwdodsih-a materials (Fig. 24–55). Rank the materials according to their index of refraction, least to great6.gi2aq:-dwm2ob d-d2s rhk vest.

Hold one hand close to your eye and focus on a distant light source 23ja4jai*lnas fw*u9n0 5 nwfthrough a narrow slu0395jw4 2jafnl n*si fn* waait between two fingers. (Adjust your fingers to obtain the best pattern.) Describe the pattern that you see.

What happens to the diffraction pattern of a single slit+ 8rsq yjrz/:* e0heg 3;x.fqow yxu,f if the whole apparatus is immersed in (a) w fyey3rq*0 +uq :rwefzhj,.xg x/s8;oater, (b) a vacuum, instead of in air.

For diffraction by a single slit, ip7g*qugb mc 56. we* jxm)5ddwhat is the effect of increasing (a) the slit width, and (b) the wam .e*x pwuc 567)bgdgi jq5dm*velength?

What is the difference in the interference patterns formed (a) by two sln4hkm:vpu/-0ye( c d sits $^{-4}\;cm^2$ apart, (b) by a diffraction grating containing $10^4lines/cm$?

For a diffraction grating, what is the advanjf.d.8d6k9uk i3km b, 4jtbyph)pni.tage of (a) many slits, (b) closely spaced sli)4dknyjib hdjikp.m.3u9kf6t pb, 8.ts?

White light strikes (a) a diffraction grating, and (b) a prism. mit3c7at4j7 wf0 : aehA rainbow appears on a wall just below the direction of the horizontal incident beam in each case. What is the color of the top 037aih:awf e47cmtt jof the rainbow in each case? Explain.

For light consisting of wavelengths between 400 nm and 70uo54d ihh,* io wkm/c,0 nm, incident normally on a diffraction grating, for what orders (if any) would there be overlap in theck ihmd, 5*o,h4 iu/ow observed spectrum? Does your answer depend on the slit spacing?

Why are interference fringes noticeable only for a thin film like a soap nvwc ,up0tzmkp 498e)bubble and not for a thick piece of glass, w9cznm 8 vtp4e)k p,u0say?

When a compact disk (CD) is held at an angli;tmz*.* hsarow +h+k e in white light, the reflected light is a full spectru+r.hm+ t* za *owskh;im (Fig. 24–56). Explain. What would you expect to see if monochromatic light was used?

Why are Newton’s rings (Fig. 24–31) dukhs9bb )oygo9)wpe //oa8:closer together farther from the center?

Some coated lenses appear greenish yelj1c8ffk v)rf;db51sbt t.x c4/xl0qr low when seen by reflected light. What wavelengths do you suppose the coating is designed to tran8ft .csxj vcrbd xfkblfr11t;0) 5q/4smit completely?

A drop of oil on a pond appears bright at its edges, where its thickness is muchg9 n).xuqi xd8 less than the wavelengths of visible light. What can you say about the index of refraction of the u .8)idgx nx9qoil?

What does polarization tell us aboutozhw9 w8 l4 )zieq.u-y the nature of light?

Explain the advantage of polarized o .l7spa17yr6v s3 imysunglasses over normal tinted sunglasses.

How can you tell if anp(z ou2ypukr 4:k3gr :xp6(r pair of sunglasses is polarizing or not?

Two polarized sheets rotated at an ang),e73has k 5z5 6vsfhudugk1cle 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 n ba:bsy8(wb,:jdqlq0s- j 9b sky if the Earth had no atmosphere?

If the Earth’s atmosphere were 50 times denser than it it -c u(,gfqq31aj w(fgs, would sunlight still be white, or would it be some oth j(c3, fuqgt-w (fa1qger color?

  Monochromatic light falling on two slits 0.016 mm apart produces s,d 64y 76xqlsixo9z )kr6kfv the fifth-order friv,ozkyqk 46sx7) fsir966 ldxnge at an 8.8$^{\circ}\,$ angle. What is the wavelength of the light used?    $ \times10^{-7 }\;m$

  The third-order fringe of 61gvka j qam4yf: na03:+0 nm light 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 0.0;0 uxu7 5skdtf48 mm apart. Successive fringes on a screen 5.00 m away are 6.u; uf0kt xds755 cm apart near the center of the pattern. Determine the wavelength and frequency of the light.
$\lambda\;=\;$    $m$
$f$ =    Hz

  A parallel beam of light from a He-Ne laser, with a wavelenggu)s.0urpi., ptyg vm .u y-t8th 656 nm, falls on two very narrow slits 0.060 mm apart. How far app-).y,g0utruyi.s g8u m v. tpart are the fringes in the center of the pattern on a screen 3.6 m away?    cm

  Light of wavelength 680 nm falls on two slits and prxqv)f7m8iv b 03sud8toduces an interference pattern in which the fourth-ordvi3f vu0s87t mbqx8)der fringe is 38 mm from the central fringe on a screen 2.0 m away. What is the separation of the two slits?    mm

  If 720-nm and 660-nm light pass6 qtlf4y : 46n4id(bhm4 iqfuoes through two slits 0.58 mm apart, how far apart are the second-order fri qmtui:6( ld 44of4qf6bni 4hynges for these two wavelengths on a screen 1.0 m away?    mm

  In a double-slit experiment, it is found that bluek+ q- biszjd4j-(v um) light of wavelength 460 nm gives a second-order maximum at a certain location on the screen. What wavelength of v)szj 4u(+d-j bmkiqv -isible light would have a minimum at the same location?    nm

Water waves having parallel crests 2.5 cm apart pass :fnynvm:0 8+uw cdz;othrough two openings 5.0 cm apart in a board. At a point 2.0 m beyond the board, at what angle relative to the “straight-through” dire;8yomf :u:d+nnvw0czction would there be little or no wave action?

Suppose a thin piece of glass is placen a q/-5qvuf/ed in front of the lower slit in Fig. 24–7 so that the two waves - /v5aqqun ef/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 maxrzw4lxgjiwy 9 s . hq)3e9j43oimum for 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 txo sz 9gh e4yq 9ijwwr3)3j4l.he same slits. How far from the central bright spot will the second-order maximum of this light be located?    mm

  Two narrow slits separated by 1.0 mm are i0wx8zw s3 yuw:c: .baglluminated by 544 nm light. Find the distance between adjacent bright f 3:wwcgy 8ba0z:.xwsuringes on a screen 5.0 m from the slits.    mm

  Light of wavelength 480 nm in air falls on two slitecd,qwemp5t*6y n3, fs0 1rr bs6o)mxs $6.00 \times10^{-2 }\;mm$ 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=1.60) covers one slilhr +,u/pzo au9)z j.d0dgn d;t of a double-slit apparatus illuminated by 640-njnu dg/+ 0).pa;l 9hd, zdzruom light. The 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 sperl80lmokr k59p e49mm ed of red light (700 nm) exceed that of violet light (400 nm) in sr m5e 04mlkk89lp r9moilicate flint glass? (See Fig. 24–14.)    %

  A light beam strikes a piece ofu)e 8r99ec;.cfmsvos m5f -yn 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 lightl7ej9)0+d : p q0iqc8frnfgt.w2t iud containing 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 the full r.gk2nl h h4gxsqa -p f(08v(gangular width of the central diffractinvf(lhr( g8 x - 2pq.gk4gsa0hon peak?    $^{\circ}\,$

  Monochromatic light falls v:rq z7 1uhlk3on 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 a slit that. 3o06 -jkqdgxc9c nk7zcxsd5 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 4, z;i,potvl7po 2pab650-nm light. What is the width of the central maximum (in cm) in the diffraction pat z7l6v2o a ,bpppto;i,tern on a screen 5.0 m away?    cm

  Monochromatic light of wavelength 653 nm falls on a slit. If,0ghgcocj y3q9) bt5u the angle between the first bright fringes on eithergc ,ujq 9g hb50yo)t3c side of the central maximum is 32$^{\circ}\,$, estimate the slit width.    $\mu m$

  How wide is the central diffraction peak on a screen54bme0 u3c1 cs5a cqmy 2.30 m behind a 0.0348-mm-wide slit illuminated by 589-nm lib1qecmm435c5 ya0u cs ght?    cm

  When blue light of wavelength 440 nm falls on a 4 ls w md;qc(0;lljw.nsingle slit, the first dark bands on either side of center are separatn qd wllw cl4s.0m;(;jed by 55.0$^{\circ}\,$. Determine the width of the slit.    $ \times10^{-7 }\;m$

  When violet light of wavelength 415 nm falls on a s s8-s39jhndq qingle slit, it creates a central diffractionj q -ds8q3sn9h 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 maxy-g7 zmqoy73;s/38gao +o3jpwgvek gimum is 4.0 cm wide on a screen 1.50 m away, what will be3e+o yvgqakwg/;3s73 7jy- zg gm8opo the width of the diffraction maximum for light of wavelength 420 nm?    cm

For a given wavelength)ccxn;al/2gy z0 )w sz $\lambda$, 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 falling on a).q xl 2zzwvd;o6sfht8 53)gt* kk tpc grating whoso;st*td)x5z zkt6l c 8.kq2wvp g3fh)e slits 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 az. (*2u njo8rpmpt2yt grating have if the third-order occurs at an 18.0*tp pmz2.joyrn2(tu8 $^{\circ}\,$ 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 ms5m67.yu4npms cj dk1l )e d4grating is observed at a 15.sd74mpy njsm16 k.5ml)e cud45$^{\circ}\,$ angle. How far apart are the slits?    $\mu m$
At what angle will the third order be observed?

  A diffraction grating hasfm 6-9zw9pdny $ 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 normallyca-2nx )mkgm ( l/d -u6mhd+el 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 g8( j1eb6cawzqe j4zc: rating with 6000 lines per cm is illuminated with 633-nm laser light? Asbaze4 61e c:jcq 8j(zwsume normal incidence.   

  Two (and only two) full specu+0-)t i3 vdb8x d 1sboxz/vw8 tvl)qctral orders can be seen on either side of the central maximum when white light is sent 88/cs )zo 3bqtvudlx+)i0v tbw- 1xdv through a diffraction grating. 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 falls06l k 7vur(,ia:he xhwb;-h :l mzrbc6 on a grating with c;le r6hxv(hukl6bzhma b,i:0 -w:r7 $8500\;lines/cm$ 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 known wavelengthtjdyz5 e )xhjk8sn+0 h5- e5fb $\lambda\;=\;6.328\times10^{-7 }\;m$ 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 lineroz5dn6wz , 0vp2 zti+s 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 a+pu6kng*sxnj.mb1;,vv9oe b7:2j aurozx m 1t the center of the outer surface when illuminated normallyrno +2vx,1vg z n ej:9bm1.ku p*o7mjusxb ;6a 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 09vozgei1cu8 ,8: pljl abru1each 26.5 i 9u ,gcl8p zlb18orvj0u: a1ecm long?    cm

  What is the smallest thickness of a s 4fwh+,,bzkl0 4bvh luoap 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 green,c1s-2exr wt yish 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 d: x/ljugqn6)zark 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). How much thicker is the center than the edn:q/gxuj l)6z ges?    $\mu m$

  A fine metal foil separates one end of two pieces of optically flat glass, tec/c1x+ /hl;(lpxp4 bvcq 1zas in Fig. 24–33. When light of wzeq ;p(clh+ltc/ vbx/4x1cp1 avelength 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 n b4 *,i 5osgqka14pezair layer be between two flat glass surfaces if the glass is to appear bro1en 4s,b* zgak54ip qight when 450-nm light is incident normally?    nm
What if the glass is to appear dark?    nm

  vA piece of material, suspected of being a stolen diamog nir2m -;kgn/nd $(n=2.42)$ 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 alcohod:k bh+v)vnv4:w4z, yk(t;7kbv t i kxl $(n=1.36)$ 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 immersed in au1 davu1k)n,0 ggv+kpc;kfv 2 liquid, the diameter of the eighth dark ring decreas,)up+;21kng01v vvk akufd cg es from 2.92 cm to 2.48 cm. What is the refractive index of the liquid?   

  What is the wavelength of the lil 24bzhbq4 8yyght entering an interferometer if 644 bright fring bzh484yqyl2 bes are counted when the movable mirror moves 0.225 mm?    nm

  A micrometer is connectnqq a*;dp(j q/ed to the movable mirror of an interferometer. When the micrometer is tightened down on a thin metal foil, the net number of bright fringes that move, compared to the empty micrometer, is 272. What is the thickness of the f (qqdj qn/p*;aoil? The wavelength of light used is 589 nm.    $\mu m$

  How far must the mirrormeh-f:so2h4 x $M_1$ 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 xo+ agah3f/ tsu40d4ie. 0f xgthrough a small glass 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 reference l0sa4e u4+fo dx.gh/g i3x0 aftine. 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 orienbw8w2ihd cl 7)ted 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;xq/lhzw a0m:–glass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s angle for a dghu1kn j n5y7r2bd2o +iamond submerged in water if the light is hittingugrh 22kjnnd 5+71oyb 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 mahl8l5n8u sf v;ximum. At what angle should one of them be placed so that the intensity is subsequently reduceh v8nfl;l85 sud by half?    $^{\circ}\,$

  At what angle should the axes of two Polaroideawb55t8z3em y8ufq9s be placed so as to reduce the intensity of the incident unp 9emqy8t8faeu5z3wb 5olarized light to
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are oriented at 40cg7::atf -b7fsx(w-f +g joua$^{\circ}\,$ 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 orientedgc/w- )-. pbvnuv :xa.kwf,92urk pbf at 38.0$^{\circ}\,$ 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 surfacei1 db4:agr2 h2, e10aj*s2e xxxwza uz of water for light coming from beneath the surface? Compare tod0g2i22azjsex e1 a,uxr zhab:x*w 41 the 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 five successive Polaroi3n fr3ntzm ;s:d sheets, each of whose axis makes a 45n3nz:rmts; f3$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength 5n dc ;cq-vp: rw:w+we$ 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:gj(i cvhxt7rxr3:f9 from mountains or airplanes can interfere with the direct signal from thet: x97hv 3xg:f rijr(c 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 pasis84z -ftohh )cob32pg: 8/:n htbzssses through a diffraction grating with 48tnso-b82b ithzhs3) /z:g:csophf$ 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 j:aw *bst4.cgtwo narrow slits 0.60 mm apart. The screen is 1.70 m away. A second source of unknown wavelength produt.gwabj4 s:c*ces 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 broaddfsz5 k.+.p bwcasts from two identical 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 its midpoint and extending horizontawf5 bs d.p+zk.lly 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, /29ld3-jfhhbfj gn tx2 5ai 6sand blows a whistle of frequency 750 Hz. Ignoring reflections, estimate at what angle(s) it is not p5hgi/2faxnsj fbjd9-lt2h36 ossible to hear the whistle clearly on the playground outside the doorway.    $^{\circ}\,$ either side of the normal.

If parallel light falls on a * *0ii/ieccskpi: m b j0x:a.asingle 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 parallel+u*iduys ;fo0 lines across them. When normally incident 460-nm light is reflected from the wing, the wing appears;*u oyi+uds f0 bright when viewed at an angle of 51$^{\circ}\,$. How far apart are the lines?    nm

  How many lines per centimeter must a grating hav4 d7f+8mtqsl (zmk- oie if there is to be no second-order spectrum for any visible wavelengthmqzt4s( f+8kdom i 7-l?   $ lines/cm$

Show that the second- andd8akf nry 04)fg dnyqhk5-89 j third-order spectra of white light produced by a diffraction grating always overlap. What wavelengths overlap e8nny5d4jf hdrq k- g)akfy98 0xactly?

  When yellow sodium lig1z5 m8 rz 2x 3n*vcdfub8ukb*vht, $\lambda\;=\;$ 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 pattern is viewedvtz b6 c5(j+pp on a screen 2.5 m from the grating. The incident light beam conspctz pj(+b5v6 ists 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 a clear material 1ftt.u;v cp) jif a minimum of 150 nm thickness of it, when laid on glass, is needed to reduce reflection to nearc1; p t)vf.utjly zero when light of 600 nm is incident normally upon it? Do you have a choice for an answer?

  Monochromatic light of variable wavelength is incident normally on a thin sheoi 2g4- g72ss 8vluoipet i4ug-i ol2s 7pos v82gof plastic film in air. The reflected light 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 ak)z:l04c by iv+01vlt ybjdu3c *i b1an 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 fgqjb8au i zz7)6ljz0*or the air layer between two flat glassj8lzqg*a0z 6ibzu)7 j surfaces if the glass is to appear dark when 640-nm light is incident normally?    nm
What if the glass is to appear bright?    nm

Suppose you viewed the light t82k6hpjtv )vtransmitted 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 size of tt6ph k2vv)j8 the minima compared to the maxima and to zero.
24-30
24-36

  At what angle above the horizon is the Sun when *xk5dp6 0th-lnwpu z- light reflecting off a smooth lake is polarized mo hl6ppdxw5-*n u-t0kzst strongly?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be placed so as to reda,c3/wv8wehj txx) rnc )v; 9huce the intensity of the incident unpolarized light by an additional factor (af;xcjre /ct9)x8hw hn )a,3vw vter the first Polaroid cuts it in half) of
(a) 4,    $^{\circ}\,$
(b) 10,    $^{\circ}\,$
(c) 100?    $^{\circ}\,$

  Unpolarized light falls on two polarizer sheet17 2tgzs(o5xos9: n iw 9y r)da0tjrdqs whose transmission axes are at right angles. A third polarizer is placed betwe9s (z7d1s0r92nxi qtogjdy: o5ar )wten the first two so 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 placed in succession with their axes verth 68eh9qbc;j aical, 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 pointe wo8e 96vm mmg .tqjst4gbv/*y)l tr/6d at the Moon, which is approx6tmw/q. )vmmjo89b gtrstv6*l ge4/y imately 380,000 km from the Earth. Assume the laser emits 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 polarizers are each placev7h6yjserk-: d 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 ,c .gvl)mdofrn. 14 2mo3 gplo$(n=1.34)$ 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 phag5p umqt/.e5ise with each other. They are located at mt .i/ g55epqupoints $S_1$ 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 ligl gsfxu378 /ixht containing two wavelengths, 420 nm and 650 nm, enters a silicate flint glass equixxs3luf/ g8i 7lateral 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 flat suu+o1wuwe)cuj9e 7;w h rface 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