Does Huygens’ principle apply to sound waves? To water waves? Explainn m.e8vp;y4 hcea8+sh.

What is the evidence/b*(me 02pr il;nzli2y hww(c yuj -3e that light is energy?

Why is light sometimes described as rays and sometimes as waveswvd:, fx m/:d/kfmys5vmnm 8l2+(jec?

We can hear sounds around corners, but we cannojeh8a nzj;4 4hyby12kt see around corners; yet both sound and light are waves. Explain the jye z8a;n14y4 hjh2b kdifference.

If Young’s double-slit experime9qqx fyc 4*nrf610 ltknt were submerged in water, how would the fringe pa 1xkqtqnc*r9f0lyf 4 6ttern be changed?

Monochromatic red light is incident on a dr +4uinvr.x k5ouble slit, and the interference pattern is viewed on a screen some distance away. Explain how the fringe pattern would chan54kvrnui+x r. ge if the red light source is replaced by a blue light source.

Two rays of light from the same source destructively interfere if their path53tiu4t a/wygt d 6wb3 lengt36btiat5wdyg/ w 3u 4ths differ by how much?

Why was the observation of the double-slit interference qqjy:t*+hnj . pattern more convincing evidence for the wave theory of light than the observation of difyqj.*hqj: n +tfraction?

Compare a double-slit experiment for sound waves to that for light h8+nd( jnzpt -spol1+waves. Discuss the8-j++pz (n1osndl thp similarities and differences.

Why doesn’t the light from the yzeuj2r *)t8db95 gs dtwo headlights of a distant car produce an interference pgb ety*s) d2 dzrj5u98attern?

Suppose white light falls on the two slits of Figm e,5(win om,03ldtj r. 24–7, but one slit is covered by a red filter (700 nmdotn lm 5m(rw,3ij 0,e) and the other by a blue filter (450 nm). Describe the pattern on the screen.

When white light passes through a flat piece of window glass, it is x(csv oa)1a7y-7e uhdnot broken down into co1vxyd-o)c(aa e7 s7hulors as it is by a prism. Explain.

For both converging and diverging lenses, di-i81e0 n09jx ytxipdt scuss how the focal length for red light di90e8pxyij0 d -t1ixnt ffers from that for violet light.

A ray of light is refracted through three different materm8rcoo5w,*lh iw/ q9z k.q.jimfjhz 0s 3 06xbials (Fig. 24–55). Rank f53,h/9r 0jcj *z ihm wl.xoq.0wbzo siqmk68 the materials according to their index of refraction, least to greatest.

Hold one hand close to your eye and focus on a distant lig5 md m)pu g0s4w:lal3hht source through a narrow slit between two luwp 3 s4)0d5:hlgmamfingers. (Adjust your fingers to obtain the best pattern.) Describe the pattern that you see.

What happens to the diffracti.;k wzwiux5p+on pattern of a single slit if the whole apparatus is immersed in5kx z +ip;.wuw (a) water, (b) a vacuum, instead of in air.

For diffraction by a single slit, what is the effect of increasing (a) the slyjfv ec 7huvy2i6oyxo3 e,a+.r2 av6+it width, and (b) thei26av+vy yy. oxeou+6a hf3 e,cvj7r2 wavelength?

What is the difference in the interference p3tlfadirz) /:*sub f/xpk*u;atterns 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 advantage tv on/;hd xx99of (a) many slits, (b) closely spn;/dxt ovx99h aced slits?

White light strikes (a) a diffraction grating, and kgj9z ss0; r6isr.4k ) ob.aqg(b) a prism. A rainbow appears on a wall just below the direction of the horizontal incident beam in eachss4bk6 az g)gq..r0i9k;ro sj case. What is the color of the top of the rainbow in each case? Explain.

For light consisting of wavelengths between jnhl qc98mk )e5 p5+dv400 nm and 700 nm, incident normally on a diffraction grating, for what orders (if any) would there be overlap in the observed spectrum? Dohk589 5+jn) vmpel dqces your answer depend on the slit spacing?

Why are interference fringes noticeable only for a thin film like a ssw6qiw0yk hib564 2u noap bubble and not for a th6wws kq5b0n4ui2hy6i ick piece of glass, say?

When a compact disk (CD) is held at c su/n*s;j;qqfog-2r*l p 1yuan angle in white light, the reflected light is a full spesslj/1u ro;c*yng qf;2 p-uq*ctrum (Fig. 24–56). Explain. What would you expect to see if monochromatic light was used?

Why are Newton’s rings (Fig. 24–31) clo lv fyr; kc hwl89,vhfz7r,n:gwix(,6ser together farther from the center?

Some coated lenses appear greenish yellow when seen by reflected li),s/eyw7rtu u jp6yz48 9ptno ght. What wavelengths do you suppose the coating is designed to transmitpopr)w6n74 jys e tz/,8t9yuu completely?

A drop of oil on a pondxcdt(7*.lctv n *j (gk appears bright at its edges, where its thickness is much less than the wavelengths of visible light. What can you s(d*gj7 c*t k (xltvnc.ay about the index of refraction of the oil?

What does polarization tell us about the nature of lix*v cv5g4rw)l ght?

Explain the advantage of polarized sunglasses over x,k6qhx58tx9fcr8wt normal tinted sunglasses.

How can you tell if a pairqtw.fap (v-4i8c* z/mmtu u o4 of sunglasses is polarizing or not?

Two polarized sheets rotated at an anglbc-f7 yq-ynif zka+;6 e 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 f 7gnju 60ci.+oylj; avgbx46 no atmosphere?

If the Earth’s atmosphere were 50 times denser ,0 gam2w6o moe/xv0n:, pjdosthan it is, would sunlight still be white, or wom v so0o 06m2 ,,/wgd:xnejpaould it be some other color?

  Monochromatic light falling on two slits 0.01p21 yf8woj: va6 mm apart produces the fifth-order 2a8vjof 1 pw:yfringe at an 8.8$^{\circ}\,$ angle. What is the wavelength of the light used?    $ \times10^{-7 }\;m$

  The third-order fringe of 610 nm lxooa,y8o zace ;66ef,ight 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 mm apart. Successive 0( ihsylr)no+8jh f9ffringes 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. (0f oh)l rfih+ j98syn
$\lambda\;=\;$    $m$
$f$ =    Hz

  A parallel beam of light from a He-Ne laser, with a waj/hw l8j xwz.71+peopvelength 656 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 3p ex/o+ w187j hjpzw.l.6 m away?    cm

  Light of wavelength 680 nm falls ono6e;krk8 x :q4;dednv 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. What is the separation of the two ox 6e:dnvqd4;e rk;k8slits?    mm

  If 720-nm and 660-nm light pa:dj84 tw egk+b0jxdtez:mz 68 sses through two slits 0.58 mm apart, how far apart are t xt68k0ze:b:8ew+4z j jdmd tghe second-order fringes for these two wavelengths on a screen 1.0 m away?    mm

  In a double-slit experiment, it is found that bzurk6 ztct+i9 di1v kkl 6y8o ja4c-45lue light of wavelength 460 nm gives a second-order maximum at a certain location on tho4ja ti zy1 k +c4utd8l69kzkri-c6v5e screen. What wavelength of visible light would have a minimum at the same location?    nm

Water waves having parallel crests 2.5 cm apart pass through twoa3cpn(( 0elhteqe7 hfl-cl 5 3 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” direction would there be little or no wavp heac(75cll3fe0lh -3 n eq(te action?

Suppose a thin piece ohoo m qazlj 8ce5to1)z2u1q1p 20 g.kpf glass is placed in front of the lower slit in Fig. 24–7 so that the two wtcko.80a) z 11mplu12qj g o2pqhez5oaves 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 light of wavelength 50 p5v(n kuw7uy0qjjjw .l9u( -e0 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.p57quj9lkju yw j(w(0u-vn e. How far from the central bright spot will the second-order maximum of this light be located?    mm

  Two narrow slits separata5el,i6 g5 aumed by 1.0 mm are illuminated by 544 nm light. Find the distance between g,laam56 ei 5uadjacent bright fringes on a screen 5.0 m from the slits.    mm

  Light of wavelength 480 nm in air falls on twp6p nym +1e;vmo 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=1.60) covers one sd 9*w6c)sks7d swu 8w3( vtfhilit of a double-slit apparatus illuminated by 640-nm light. The center point on the screen, instead of being a maximum, is dark. What is the (minimum) thickness of the plastic (3)d8wd6fvcwuskwss9 7*i ht?    nm

  By what percent, approximately, doa,h 41n/ycirxh -o-h oes the speed of red light (700 nm) exceed that of violet lig-ihay4r/ oxnoh,c- 1hht (400 nm) in silicate flint glass? (See Fig. 24–14.)    %

  A light beam strikes a pg7pk hxty5;wvjg cl me*)30. riece 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 olpz;i xygsdu 68o9g9,m 6e6gcontaining 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 anguc 7h vvyj1apd6g 3zm75lar width of the cen6 h7va5zv73dmj 1 ycgptral diffraction peak?    $^{\circ}\,$

  Monochromatic light falls on a slit+,. d /xpqynxn 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 slitp )xl ;jrhr/6 yfu8 pxm9gi;w)5vxu4o 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 illuminated by 450-nm light. What is the width ofd lykv7n6 5hyt** 5lhs3+ umeg the central maximum (in cm) i h+ ls7yuny* k emtd*3v5hl6g5n the diffraction pattern on a screen 5.0 m away?    cm

  Monochromatic light of wavelength 653 nm falls on a slit. Iffi k il;-(wtgb,z,zbs0 n(x- s the angle between the first bright fringes on either side of the central ma;isg zb-,xwl 0,bzftsn(-k i(ximum is 32$^{\circ}\,$, estimate the slit width.    $\mu m$

  How wide is the central dif25vnn-x v(27 opb bm am)e)*0 nomeurffraction peak on a screen 2.30 m behind a 0.0348-mm-wid)25o v r(mvum -b7xnnpem0en2*abof )e slit illuminated by 589-nm light?    cm

  When blue light of wavelength 440 nm falls on a singq(b o*t stxn39wqk*v 7le slit, the first dark bands on either side of centwto qbx* knt97s*q(v3 er are separated by 55.0$^{\circ}\,$. Determine the width of the slit.    $ \times10^{-7 }\;m$

  When violet light of wavelength 415 nmsin a rm,.xozii25* +t 5r;cwvu+ve+s falls on a single slit, it creates a centr +tw 5m;cvers2.a+ois5nzxv i,+u i* ral 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 th4e2xfx+ p ,cqte diffraction maximum is 4.0 cm wide on a screen 1.50 m away, what will be the width of the diffraction maqfe+c2 xx p4t,ximum for light of wavelength 420 nm?    cm

For a given wavelengta-zsht; rcq4-g(-i, fstisd 9h $\lambda$, what is the maximum slit width for which there will be no diffraction minima?

  At what angle will 560-nm light produce a secon-zl.* eo45p*w2 ey :njoorpla u,z+z pd-order maximum when falling on a gratinup *pzozl-lepwa5.,eory+ n : z2o4j*g whose 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 a gr+p (0: zblem- ksyvlt(ating have if the third-order occurs at an 18. vly( e -0tz(ml+:kspb0$^{\circ}\,$ 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 xp0- us avzh))589-nm light falling on a diffraction grating is observed at a 15p s))0 haz-vux.5$^{\circ}\,$ angle. How far apart are the slits?    $\mu m$
At what angle will the third order be observed?

  A diffraction grating haj m4w-aiy3ru5xpf08svg h 75xs $ 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 p7v(os4)13hf g mbgtl 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 lfn 3.gy6haxpyge.-)if a grating with 6000 lines per cm is illuminated with 633-nm laser light? Assume normal incil6)y.a3.fg eh-xp gnydence.   

  Two (and only two) full spectral orders can bn)vmd3um964 qd4lof ve seen on either side of the central maximmdfv4n 4vl936dqou) mum when white light is sent 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-uyap9 *oqt,n so52y e to 750 nm falls on a grating with ay unys*9 e-5,oopt2q$8500\;lines/cm$ How wide is the first-order spectrum on a screen 2.30 m away?    m

  A He-Ne gas laser which produces monocwgq y.omdh 9rxm5.4w8hromatic light 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 6i;k4rjzc,y4k mf w0t 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 kq8amyewlqg ; :35*rc 120 nm thick, what wavelength is most strongly reflected at the center of the outer surface when illec 3ar wgm;k:y5*8 qlquminated normally by white light? Assume that $n\;=\;1.34$. $\lambda$ =    nm ,which is an    -  

  How far apart are the dark fringes in Example bg-1tmo 1g r99o wdxk(sof rwz- gbc2*8;a, dm24–8 if the glass plates are each 26.5 osf2o*ab( ko d8twz9m1g- ,c-9rmx1r; bg wgdcm long?    cm

  What is the smallest thickness ofk6s n2bbx0gu4*c 7grn 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 greenishpz81:5s2f.p bs fz5-idx psr q 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 the dark sp-q*r+kbb2 6twm 7gxp z(d(dgaot at the center) are observed when 550-dx(gz b+ *62(-twqmpg7 bkdarnm light 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 end of two pieces of optically flat g+- m aysv2n m 4:26.arpqub(wjrwzua 1lass, as in Fig. 24–33. When light of wavelength 670 nm is incident normally, 28 dark lines are observed (with one at each end). 1 2ru aw.z4-y:6rw2pmn sv+m(bqujaa How thick is the foil?    $\mu m$

  How thick (minimum) should the air l +f: s)pvxhd3payer be between two flat glass surfaces if the glass is hp dv 3f)s:xp+to appear bright 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 diamondbogk1t4s9u if(z-g8o $(n=2.42)$ 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 alcoho3 c nlnaz.0.5p *vg+qap;(zxkyrxq/il $(n=1.36)$ 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 gju up 1 o28va;l+8rxuin a liquid, the diameter of the1pux ol 288gv;aru ju+ eighth dark ring decreases from 2.92 cm to 2.48 cm. What is the refractive index of the liquid?   

  What is the wavelength of the light entering an interferometer if 6+)w8 hgt xdy0osm-q)oa6h :(hhxueq (44 bright fringes arxeodqo( wq+8-a :hhs) h hu6(0y)txmge counted when the movable mirror moves 0.225 mm?    nm

  A micrometer is connected t xcq .613a:j d-n(al*sfxo mgoo 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 foil? The wave f :61os(o.*lc3xng am-j xaqdlength of light used is 589 nm.    $\mu m$

  How far must the mirror ed.m/*cgnc2b $M_1$ 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 glass .i7buaj -w kg4ialy *: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 *ib.7- aaj lgk4ywui: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 oriented atj lp - ,7 d-vy+4jijon;2ww,dt4xtsz*agz 6 au 65$^{\circ}\,$ to one another. Unpolarized light falls on them. What fraction of the light intensity is transmitted?   

  What is Brewster’s angle forcc ed+6.b8db q an air–glass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s angle for a diamond submergedk,p )vqv9, +bwg xx8yk in water if the light is hitting th )b,8,q9p xwgxvk +kvye diamond $(n=2.42)$ while traveling in the water? $\theta_{p}$    $^{\circ}\,$

  Two Polaroids are aligned so that the light passing through them3y- ;xpvlbyo. is a maximum. At what angle should one of t;3.-y ypxlb ovhem be placed so that the intensity is subsequently reduced by half?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be l zr7(dzs.c0 eplaced so as to reduce the intensity of the incident unpolarized light to 0. erl7(d zczs
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are oriented a zhvr(0zrcd*+g*, j9sgjp5 d ot 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 orient qelznulx6) 4 ic 45;85,ca ihdjfwp5ied 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 water f eu2y/w1yj)dtoam+ q3or light coming from beneath the surface? Compare to the angle for total internal reflection, anduym t/jyw)13od+ a eq2 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 Polaroid sheets, eajz t5 *wgyy.z wv58v3ech of whose axis*wy 5gv8 5w.vtyjze z3 makes a 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength -s 6z;sdol le q*2n/m-y )sofy$ 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 kr yqwep1/8/v:*wec skq*4gw5u we(tfrom mountains or airplanes can interfere with the direct signaywce*1/k/ 5stvewkp:wq8q 4 ( u*gwrel 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 passes througz.*dbglf 6;m gh a diffraction grating with dz6 .*bfgg;ml$ 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 througr ydwncsmx-t)64 nyo3x6; 7zzh two narrow slits 0.60 mm apart. The screen is 1.70 m away. A second source of unknown wavelength produces its second-oznon cxws )dyrt3mx-y 664z7 ;rder 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 MHu9ihpgny* 7f p ,r6vo.z broadcasts from two identical antennae at the same elevation but separatey6hopi79 u * ng,.pfvrd 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 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.ylbi q;xbaq2u; + cw,788 m wide, and blows a whistle of frequency 750 Hz. Ignoring reflections, estimate at what angle(s) it is not ,b+blwuc i ;;qxy 2a7qpossible to hear the whistle clearly on the playground outside the doorway.    $^{\circ}\,$ either side of the normal.

If parallel light fallsko/xxglt *a30 on a single 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 paralby, ,kfm 6voi;lel lines across them. When normally incident fyim;6ok vb,,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 centimetb5ei 8 a4fpqmi yi8)1uer must a grating have if there is to be no second-order spectrum for any vis)mfa1i i4 5q8u8yeipb ible wavelength?   $ lines/cm$

Show that the second- and 2)rlc+usws i0third-order spectra of white light produced by a diffraction grating always overlap. What wavelengths oves2u)rs lwc+i 0rlap exactly?

  When yellow sodium lx8fkjp/iyiwx19 01n xight, $\lambda\;=\;$ 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 viewed on 6p kf3dm 9amw-5hf-u xa screen 2.5 m from the grating. The incident light beam consists of- wa6dx5fhm39- pkm uf 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 r9o yyw r- /.ywsu); bnw x3i-)obexp4if a minimum of 150 nm thickness of itw rb.yp 3xwb)ori-yuy e; )-/ 9wx4ons, 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 answer?

  Monochromatic light of variable wavelength is iq0k:p.tnn1 * )jewbnl n1y5jfncident normally on a thin sheet of plast*lj1n.:tkf50)npw jnqbne y1ic 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 need (i/*utulpf9 f;s4r28:p ca8myjtzr eed 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 air layer between two flat gla0ljc5. 0y.ey0pc hyh - jf;pdasjlp-0ec;y pfc.yj 0adhy 05 h.s 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 transmitted through a thin fil: (50vay8ha;px e4zmewuv:zv m 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 ye:m4v0 hue8wv(5 azvzx p:;a 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 off a smooth la4g) g9tp tig*tke is polarized mt gt pg4*tgi)9ost strongly?    $^{\circ}\,$

  At what angle should the zt9 j4a-f/ sbl crg;zz.5/tu/sqzo ,cpt0e +u axes of two Polaroids be placed so as to reduce the intensity of the incident unpolarized light by an additional factor (after the first Polzgqulpufta /z0o// s4b5 z+t.cz-jc r 9es;, taroid cuts it in half) of
(a) 4,    $^{\circ}\,$
(b) 10,    $^{\circ}\,$
(c) 100?    $^{\circ}\,$

  Unpolarized light falls on two polarizer sheets whose transmission axes aregrg;e1* -y04 ywkuzmn at rigenu*yk1;0rg m zg yw-4ht angles. A third polarizer is placed between 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 ve3i)sn,)vl +azkv gf3jrtical, 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 th1tpg kh b7:kua cq)oq, r-9*w l0zjz0jrough a slit of width 1.0 cm and is pointed at the Moon, which is approximately 380,000 km from the Earth. Assume thu:k,9-z0w)7b aczpk rg h0j*q lt 1joqe 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 polarizer8 z9 z*(tkizoes 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 3y/ fo s2it)er$(n=1.34)$ 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 6j+ v ah2op v/5p-v.uzga/ dqrradiating 6.0-MHz radio waves in phase with each other. They are located at points d/hg6q/5v.vuz av+-aorp 2 jp $S_1$ 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 twoormq 9 c;u*zb2 wavelengths, 420 nm and 650 nm, enters ab*oc m 2z;rq9u silicate flint 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 planoconvex lens has one flat surface andixag 3z : ozxc/03drn(o) 7nup 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