Does Huygens’ principle apply to sound waves? To *b4l..yjllgzw b dvn0q,d)5wukz ,6gwater waves? Explain.

What is the evidence that light is enbwev81y+b, ;toz qi/ fergy?

Why is light sometimes described as rays and sometimes as wave3xtbxawocmrav oc:-/md di7u)a2 :qm/ .+os*s?

We can hear sounds around corners, but we cannot see aroundx 2gxb2yh465i ex0 drp corners; yet both sound and light are waves. Explain the differencx6pe05xgx yb2 irh4d2e.

If Young’s double-slit exeag (n ,yn+o3wperiment were submerged in water, how would the fringe pattern be changa(n3 , e+ywnoged?

Monochromatic red light is in+rr u28gi8l ta2igo ;ncident on a double slit, and the interference pattern is viewed on a screen some distance away. Explain how the 2 oni8rg2ria ;lgu8+tfringe pattern would change if the red light source is replaced by a blue light source.

Two rays of light from the same source destructivh - ekx76n.ujcely interfere if their path lengths differ by hok - 7cj6euxn.hw much?

Why was the observation of the double-slit interference pattern more tav l y1t5bfb3,v j1g+cx*t seh 5k2.econvincing evidence for the wave theory of light than thyl,fx 1+t*15 vs jkb5atb 23tg veehc.e observation of diffraction?

Compare a double-slit experiment for sound waves to that for light waves. Di yr -d,+o36w uwvjwhss5r*) i.pzj8 frscuss the similarities and differencuvj)sz.+syiorh 5p jww3f*r6 -8r ,w des.

Why doesn’t the light from the two headlights of a distant car produce an q/vq yp7c o::cinterf qo7/:: ccypvqerence pattern?

Suppose white light f ec h77dir9eh0icxciu +*jg.: alls on the two slits of Fig. 24–7, but one slit is covered by a red filter (700 nm) and the other by a blue filter (450 nm). Describeuh e.dcjc+ hi7* 7:rei9c0gi x the pattern on the screen.

When white light passes thrl5f 6viwle .y;ough a flat piece of window glass, it is not broken down into colors as it is by a p; flev6.w5y lirism. Explain.

For both converging and diverging lenses, discuss how the focal length for red5i:rflt2du yzq63 a0d light differs from that for violet 5adq6 2t0:3u idrzlyflight.

A ray of light is refra(,g to7cqn , lige.vn4cted through three different materials (Fig. 24–55). Rank the materiae,on ltgv.4n qig c7(,ls according to their index of refraction, least to greatest.

Hold one hand close to your eye and focus on a distant light source through a nabnhl )cmg 0u::rrow slit between two fingers. (Adjust your fingers to obtain the best pl n::uchm0)g battern.) Describe the pattern that you see.

What happens to the diffraction p q h/;mzg6z(gvattern of a single slit if the whole apparatus is immersed in z;h q (g/6vmzg(a) water, (b) a vacuum, instead of in air.

For diffraction by a single slit, whats+kvokgv rr ( 65n5n9n is the effect of increasing (a) the slit width, and (b) the wavelengt5n9(gvosn k56knr v+r h?

What is the difference in the interference patterns formed (a) i t :jwzsk0;l,en.g2jby two slits $^{-4}\;cm^2$ apart, (b) by a diffraction grating containing $10^4lines/cm$?

For a diffraction grating, what is the advantags-4 .qh 0cypmuj45tz(*ja kgm7ky*ei e of (a) many slits, (b) closely spacedci4e7j5u-gpm 0k sm y*q4h*ta.z y( jk slits?

White light strikes (a) a diffraction grating, an +xps5yen 7+bfd (b) a prism. A rainbow appears on a wall just below the direction of the snebf+y 5x7+p horizontal incident beam in each case. What is the color of the top of the rainbow in each case? Explain.

For light consisting of wavelengths between 400 nm and 700, sgmi69(iwc+ kc 4fd(fb l7fz nm, incident normally on a diffraction grating, for what orders (if any) would th+9(w,cb6 7gm( fzcfsi l 4ifdkere be overlap in the observed spectrum? Does your answer depend on the slit spacing?

Why are interference fringes noticeable only fora;rga.tb 3djm0x .)v y0 stnr0 a thin film like a soap bubble and not for a thick piece of nt daj0.g) mr;a3byx00v.trs glass, say?

When a compact disk (CD) is held at an angle in white light, the reflecte1 3begmw ztt56e1r.nud light is a full spectrum (Fig. 24–56). 65 3.1rem 1tnt ubwzegExplain. What would you expect to see if monochromatic light was used?

Why are Newton’s rings (Fig. 24–31) closer together fartheru u9 c(-0 vbysr.o mad;sng8x1 from the center?

Some coated lenses appear greenish yellow when seen by reflected light.7f p 4zhspa qw2z4*r*u What wavelengths do you*2upf4*ras4p7 z zwqh suppose the coating is designed to transmit completely?

A drop of oil on a pond appears0i kh/jl2b7 +l(bnii b bright at its edges, where its thickness is much less than the wavelengths of visible light. What can you say about the index of refraction of the oii/b(bh0 27k nlilijb+ l?

What does polarization jc9keb4tl;-sv 0v yft93 4qnctell us about the nature of light?

Explain the advantage of polarized soeiuv;;x3w ,uzdrbnw/ ht y /(:+5k uxunglasses over normal tinted sunglasses.

How can you tell if a pfmq 1nfv r5/l ;6rh2bndk(ms-,ans1 e air of sunglasses is polarizing or not?

Two polarized sheets rotated at an angle nq1r30uu,lsmgsn t: 6of 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 Earyt9v u* l+ulo-th had no atmosphere?

If the Earth’s atmosphere were 50 times denser than it f7*v1 gr8 edowis, would sunlight still be white, or would it be some other colgdw* fv87er1oor?

  Monochromatic light falling on two slits 0.016 mmizp..ynar:dh; i7gmz ie99( y apart produces the fifth-order fringe at an 8.8zznh(7. a;igmiry: y. dpe9 i9$^{\circ}\,$ angle. What is the wavelength of the light used?    $ \times10^{-7 }\;m$

  The third-order fringe of 610 nm light ir/0ib:j0rzn2iy bq j1uqicq-z x op) *.2crg5 s 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 sl-4pjib;hp 9ta ,byl36zb hsl 7its 0.048 mm 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 frequency of the lighl9 hzs7,36lbp; h 4byt abpj-it.
$\lambda\;=\;$    $m$
$f$ =    Hz

  A parallel beam of light from a He-Ne laser, with a wavelength 656h 5 rer v1.e9tixt uc9*xu1eu(a gv*u6 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 scre h 6ee.uu rtr5 u9gucv*1at(*1xxive 9en 3.6 m away?    cm

  Light of wavelength 680 nm falls on two slitp cw)/mjp9 g8zs and produces an interference pattern in which the fourth-order fringe is 38 mm from the central fringe on a scpwm9 )pj8c/ zgreen 2.0 m away. What is the separation of the two slits?    mm

  If 720-nm and 660-nm light passes through two slits 0.58 mm apart, how far vmi)vut;3(zx8yt zbpop 5:s; apart are the second-order fringes for these two 8ptu)b(sm 5zx3 p :;i;ztyvvo wavelengths on a screen 1.0 m away?    mm

  In a double-slit experiment, it is found that s6-/4sescg o ney g1jc0j3c3yblue light of wavelength 460 nm gives a second-order maximum at a certain location on the screen. What wavelengso3sgnc06sj31 /cg- 4yje ecy th of visible light would have a minimum at the same location?    nm

Water waves having parallel crests 2.5 cm apart pass through two openi i xag3.tl34yengs 5.0 cm apart in a board. At a pointxl3ie.4gt3ay 2.0 m beyond the board, at what angle relative to the “straight-through” direction would there be little or no wave action?

Suppose a thin piece of glass is placed in front of the lower slit,euz2ms g4g8p in Fig. 24–7 so that the mu4sp,g2z 8 getwo 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 for liga0z )jrc q1vh)ht 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 brigh cj 1qv)0ahr)zt spot will the second-order maximum of this light be located?    mm

  Two narrow slits separated by 1.0 mm ioff43p4z rvm f7(w s;are illuminated by 544 nm light. Find the distance between adjacent bright fringes on a screen 5.0 misz4fp(vf 7fm w;o4r3 from the slits.    mm

  Light of wavelength 480 nm in air falls on two b* 4up/9jqo o jl7ugi ;jw57kjslits $6.00 \times10^{-2 }\;mm$ 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)*j::;ldsxv5w rm -efv covers one slit of a double-slit apparatus illuminated by 640-nm light. The center point on the screen, instead of being a maximum, i;r* v:vw5x-se f j:dmls dark. What is the (minimum) thickness of the plastic?    nm

  By what percent, approximately, doek( v*,l.zx(m;ooytxrhq7mots7u2 ;0ueo 0 lxs the speed of red light (700 nm) exceed that of violet light (400 nm) in silicak qh;os o,2rtllo0e(; tv *ummu(xox7 yx.z07te flint glass? (See Fig. 24–14.)    %

  A light beam strikes a piece of g)e(kc m5 +dbyelass 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 contaz; h32kjfybv5 ining 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 yl -w75en,n 9 floh4mzangular width of the central d-n y nzm,hel wof4759liffraction peak?    $^{\circ}\,$

  Monochromatic light falls on a slit that isdm4kku7w2j3 f)huf 3z $ 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 d, vir ro 5,)biw72x h9rp*tvh520 nm falls on a 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 ilf(owoay5ixak 1y1)j 29dp h.iluminated by 450-nm light. What is the width of the cenk1ao.y5i pwy2dfhjia1o x )9 (tral 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 ang2nuciauz,m;- ) np c:gle between the first bright fringes on either side of the central maximum is am )ngnuu;2p-ci,zc: 32$^{\circ}\,$, estimate the slit width.    $\mu m$

  How wide is the central diffract1/4 mk 3el knh3mmn+hvion peak on a screen 2.30 m behind a 0.0348-mm-wide slit illume33h1h nl kvm/m+kmn 4inated by 589-nm light?    cm

  When blue light of wavelength 440 nm falls on a single slit, the fiqcvb *wp(nv ,6rst dark bands on either side of center are sepp(v wc*bnq6, varated by 55.0$^{\circ}\,$. Determine the width of the slit.    $ \times10^{-7 }\;m$

  When violet light of wavelength 415 nm falls on a single slit, it creates kdw 7oe7mc(y4 a central difoym e4d(wck77 fraction 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 tlwnlyt v 4:(j+rsi6m+ he diffraction maximum is 4.0 cm wide vni( l6l 4jsy:tmr w++on a screen 1.50 m away, what will be the width of the diffraction maximum for light of wavelength 420 nm?    cm

For a given wavelengthnx )8p*3tmvrc y9 erks ;8ys6h $\lambda$, what is the maximum slit width for which there will be no diffraction minima?

  At what angle will 560-nm light pr.q 9fs5f/x.fxc+oxa 8u v )jclrp ,x9soduce a second-order maximum when falling on a grating whose f9x5.ap)vox qr, f xcju8x/sc9f.s l+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 cent/,teukm ,z/k ei5pex8(am8yiimeter does a grating have if the third-order occurs at ay5,me za itkee, (k8 up/x/8min 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 bu5 / luptm:-l589-nm light falling on a diffraction grating is observed :/u 5mtllpb-u at 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 h34efe4 gk/wv4zt7kw qas $ 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 normally on a ifkv+i+mc e4.ktn/.c$9700-line/cm$ 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 nv,0e ):aozxmwith 6000 lines per cm is illuminated with 633-nm lasean 0m: ov,xz)er light? Assume normal incidence.   

  Two (and only two) full sd(f+ sjd 9wul0ikcm66f5 zm7k pectral orders can be seen on either side of the central maximum when white light is sent through a diffraction grating. What is the maximum number of d+i9zmd cw5m7 sf lf(j66k0uk lines per cm for the grating?    $ \times10^{ 3}\;lines/cm$

  White light containing wavelengths from 410 nqw;jtf9oz7 g-+ekfwmb 4u6 v7m to 750 nm falls on a grating with6v4wg9 f+fz qm7w-otue7j k;b $8500\;lines/cm$ How wide is the first-order spectrum on a screen 2.30 m away?    m

  A He-Ne gas laser which produces monochromatic lighr79z +lkqzy: it 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 mbp/y 0hj/.cr zhjs2f4 easured 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, w0e8ty gb m ayxx -4quk; mpx,8x(s54 +hyk(wmqhat wavelength is most strongly reflected at the center of the outer surface when illuminateyxs(yqhxb m5yum ,xx ma;t-k48e wk g4+0qp(8d 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 tzhpa dn/q( 41rdm))ki+ xshf1 he glass plates are each 26.5 4 anf+s(hdz) hi r)mqd1xp/1k cm long?    cm

  What is the smallest tha:e3kicv6i4 r ickness 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 greenish yellow 2cmpghv 7w4th sli6 sy-d/b70 ($\lambda\;=\;570\;mm$ 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 tsib qsj5 ,,+dmhe dark spot at the center) are observed when 550-nm light falls normallys,b5idq+, ms j 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 end of twov9ka mqx6m hjyf-s.+- pieces of optically flat glass, as in Fig. 24–33. When light of wavelength 670 nm is incident normally, 28 dark lines are 9f- 6axv-k+jmqsm.hyobserved (with one at each end). How thick is the foil?    $\mu m$

  How thick (minimum) should the 4- , h,gmes6jzvf)hvo air layer be between two flat glass surfaces if the glass is to appear bright when 450-nm light is incident nor-ghz , v6 ehvmo4s,f)jmally?    nm
What if the glass is to appear dark?    nm

  vA piece of material, suspected of8 tm6mhoov ot8 (4.u:nikx77z hxa 3mivz ,+xp 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 alcoh ( kfxewa+4gn6ol $(n=1.36)$ 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 a liquid, the d bgvjlp-ra+7z9iwl 92iameter of the eighth dark ring decreases from 2.92 cm to 2.48 cm. What is l+l9wp gz9v7bij 2a- rthe refractive index of the liquid?   

  What is the wavelength of the light entering an inteqf ;a* +8xhs y:x0zzrm7cu 7qwrferometer if 644 bright fringesrsz 8a 0 cqz ;+fuyqmwx7h7*x: are counted when the movable mirror moves 0.225 mm?    nm

  A micrometer is connected to the movable mirror of an interferometer. When a2h +ufn( vv3pthe 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 foil? The wavelength of light used pvv2h3anu( f+ is 589 nm.    $\mu m$

  How far must the mirroc 7 blyav, 8mk.exbb1e;2vx7 qr $M_1$ 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 interf,q 1pqm 3wo(gh4jom k,erometer (Fig. 24–59) passes through 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 line. The light used has a wavelength of 610 nm. Calculate the index of refraoomq mqh1pw , (3k,g4jction of the gas, assuming that the interferometer is in vacuum. $n_{gas}$

  

  Two polarizers are orienteet8i m;.,beyod 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 ai6uzwgqb w2z e8a2:j. tr–glass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s angl7( hpm /.tnf5z a3xylqe for a diamond submerged in water if the light is hitting the diamond75ltf y.hnqap3(xz/m $(n=2.42)$ while traveling in the water? $\theta_{p}$    $^{\circ}\,$

  Two Polaroids are aligned so that the light passing through them is a txp+n c*via /5 ;zwgx9maximum. At what angle should one of them be placed so that the intensity is subseq*vt+w9 x iazgc/ 5npx;uently reduced by half?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be:g +7 ) rtm1bdyjr8bzl placed so as to reduce the intensity of the incident unpoladl8br+j yz tg7r:1)bmrized light to
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are orient-i 2 kuycag2wu 36js5led 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 oriengzk xf7p2f;h7 ted 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 surface of . -uedne.fgmes4n 5/x water for light coming from beneath the surface? Compare to the angle for total internal refe-xee g nu4. 5fmd/.snlection, 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 s ix)b mgcs- 0g2f0lk4euccessive Polaroid sheets, each of whose axis makes 0bx4leg c-)m2skif g 0a 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength pp/xs7mnt s44kov6f+ $ 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 reflecting3twu4zqpk9 xa( alc z 9oo477g from mountains or airplanes can interfere with the direct signal from the stzq9 t4 low9aa74o7(g kzx3 pucation.
(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 passes through a diffraction grat7 k,z/ ,evfg xctwh598m-a wgwing with wt5a e7m8-w,fk9,hvg gxc/wz $ 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 mm aparf(p/gf:dutte 15* hobt. The screen 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 e/1uhod* b p5tff :gt(wavelength of the unknown light? $\lambda_2$    nm

A radio station operating at 102.1 MHz broadcasts from two identical antena,/(azeslno ty1v-k7/zg nr2 nae at the same elevation but separated by an 8.0-m horizontal distance d, Fig. 24–60. s-r/n tnvkl/z27ea y(,o1g zaA 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 back from an outside doorway 0.k/h)pkxa iv3 n13 gf 6mhj;i:l5(kynp88 m wide, and blows a whistle of frehk5x ;(ljygni hk31pnfp6i :k)av 3m /quency 750 Hz. Ignoring reflections, estimate at what angle(s) it is not possible to hear the whistle clearly on the playground outside the doorway.    $^{\circ}\,$ either side of the normal.

If parallel light falls on a single slit of z+srfkv.l/)jmh bw 4ys *jxpm*y/ 7u+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 liw1ug n6r5)o 1oa)wv+3 xrdjalbfo((qv :8riwnes across them. When normally incident 460-nm light is reflected from the wing, the wing appears bright when vie j8ora 6wfw1v3(orr g5qw+ nd: ul)oa(v) i1bxwed 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 bj4g rxya9k zaz f0l )+f;-bu9de no second-order spectak 4ua )+9d9jg-y b ff;x0zlrzrum for any visible wavelength?   $ lines/cm$

Show that the second- and*foak;arqls nf3;7,a third-order spectra of white light produced by a diffraction grating always overlap. What wavelengthfko7aasf a ;r3n lq,;*s overlap exactly?

  When yellow sodium light, 4x /ozcex.q(gcsl9h6f ay;3l $\lambda\;=\;$ 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 pat c58x0im 35/exhzs zzptern is viewed on a screen 2.5 m from th5z0p5c8/mxhsx ie zz3 e grating. The incident 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 a clear material if a minimum ofx u 2amxf3lv6oi r9 8-1uq+bol 150 nm thickness of it, when laid on glass, 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 anau3m ooi-2xlv9q6ux + f8l1b rswer?

  Monochromatic light of variable wavelength is incident normally on a w-b 7 atfozph3c/nv*(smd a0 n0 b;3zzthin sheet of plastic film in air. The reflected light is a 7 sb03-tn/wznza * o;p 3bavhfzm0 d(cminimum 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-reflectiveuvctlp79a 4rcze 44;,;pe exa 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 x7l9 os;5dcduav :cz.2t fj(lfor the air layer between two flat glass surfaces if the glass is to appear dark when a2;c.5 svxo( :dt dclf ujzl97640-nm light is incident normally?    nm
What if the glass is to appear bright?    nm

Suppose you viewed the light transmitted through a thin film layeaadclo .-mo g/ zh:79ugj8c v1red on a flat piece of g/au7 .doz8ajgh-1v:ol cgc9mlass. 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 the minima compared to the maxima and to zero.
24-30
24-36

  At what angle above t ,7ufxeocc 7 fas,av8 n:.2ohshe horizon is the Sun when light reflecting off a smooth lake is polarized most strongly,fo auefo2:c, c vnh.s 8xs7a7?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be placed so as to redbtoq,m6lfjj5 uh74gu ,o( sy 62 ybuw7uce the intensity of the incident unpout476o7oy 2 jq5uhsb6 l ,wju(y,m fbglarized 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 transmission ah;p zxvt6i2348 zkjpc xes are at right angles. A third polarizer is placed between the fir8xi 6ck4thppzz2v; 3jst 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 succedbk n 9 bupdj05e4k6kv .))2vbtfu9aj ssion 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 pointed at the Mo cmb*u 29yi;dfj-uv+ xuq/vv6on, which is approximately 380,000 km from the Earth. Assume the laser emits waves of wavelength 630 nm (tub u mqjvdy ;f+2ix6*-ucv9 v/he red light of a He-Ne laser). Estimate the width of the beam when it reaches the Moon.    km

  A series of polarizersphgi6ax5sarz -n; (x+ 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 ex(rg np 73uh+9g3xgt$(n=1.34)$ 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 radilj g.j x;:hxsh(h z95+6bypjfo waves in phase with each other. They are located at poh g5(: bsx.jh+lyfz69;jj p hxints $S_1$ 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, 420 nm and 650 nm, enters al1 tt8x 39sqqv silicate fll9 t8xqqtsv31 int glass 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 planoconvex0lqhz ck8a4n)wy6 :m2l+zy (2xanrd u lens has one 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