Does Huygens’ principle apply to sound waves? To water waves? Explau8:az+cfta8 rb cp; en r17;gein.

What is the evidence that light is enerl kzav1,f42 t8v(jruehi v0c 6gy?

Why is light sometimes described as rays ank jb0ctz- db5rnyq/(:i4t *tsd sometimes as waves?

We can hear sounds around corners, but we cannotr gaegh pq wv-r5yc,902m3d0t see around corners; yet both sound and light 3- av5c ry2mtd9q,h p0gew0gr are waves. Explain the difference.

If Young’s double-slit experiment whvfjf ltgqg o4 1q*(bo4 g5-2xere submerged in water, how would the fringe pato*5xg1f 4j oqfq4gglh-2( btvtern be changed?

Monochromatic red light is incident on;mfc1 i4c .9rilrkjh4 a double slit, and the interference pattern is viewmr44c1 jlc;.ii9 frhked on a screen some distance away. Explain how the fringe pattern would change if the red light source is replaced by a blue light source.

Two rays of light from the same source de ;u+ ho lla)48bmtwl-estructively interfere if their path lengths diff +4oewlmlt8ab ul;)-her by how much?

Why was the observatiodml ;4yz 5sif3z+1eio n of the double-slit interference pattern more convincing evidence for the wave theory of light than the observation of o3e 15fml iz +yi4d;szdiffraction?

Compare a double-slit experiment for ::m cgwclr1(qj*x x3h sound waves to that for light waves. Discuss the similarities and diffcxgh1(:xw jmq*3cl: r erences.

Why doesn’t the light from the two headlights of a distant cfz ff 48mxb, g/th :8+3tjqocy m4u6gyar produce an interference 4 +og mmyjff8fbut8 ,6 xcg:zq34/hytpattern?

Suppose white light falls on the two slits of Fig.ee:n0p 4wr;d w 24–7, but one slit is covered by a red filter (700 nm) and the other by a blue filter (450rpnww 4de; :0e nm). Describe the pattern on the screen.

When white light passes through a flat piece of wind.zcg-*jf qzq 7q 3r-bxow glass, it is not broken down into colors as it is by a prism. Explai*x q7q-rzb-cq3 jz .fgn.

For both converging and diverging lenses, discu-1a on*ah b ha)fm)+pzss how the focal length for red light differs from f)hha ) + *1znpom-aabthat for violet light.

A ray of light is refracted through lc8z; 5pqpbav1)gmd:idl:* n three different materials (Fig. 24–55). Rank the materials according to their nmzdqladlbp c8*:gv1p:) 5 i;index of refraction, least to greatest.

Hold one hand close tou nx5el0lp0 w2 your eye and focus on a distant light source through a narrow s5x2wl0en0u l plit between two fingers. (Adjust your fingers to obtain the best pattern.) Describe the pattern that you see.

What happens to the diffraction patz(n:*( wlcf xktern of a single slit if the whole apparatus is immersed in (a) water, (b) a vacfcw: xl(kz* (nuum, instead of in air.

For diffraction by a single slit, what is the effect of increasin i3uoi:(y8nd; bplk.ig (a) the slit width, and (b) the wavelength?y :iid ;k 83(plnoibu.

What is the difference in the interference patterns formed (a0 /7 rsagmc3ye) by two slits $^{-4}\;cm^2$ apart, (b) by a diffraction grating containing $10^4lines/cm$?

For a diffraction grating, wh/,xo 7s +jwfzhat is the advantage of (a) many slits, (b) closely spaced slf/z , +johwx7sits?

White light strikes (a) a diffraction gratingtfq17 f; kmj0wjptj74, 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 the7kt1tqw4fm jj;jp7 f0 rainbow in each case? Explain.

For light consisting of wavelengths between 400 nm and 700 nm, incin d8y, bakb*4hcp)ah 7dent normally on a diffraction grating, for what okcb,aa 8y*bhh7d)n4p rders (if any) would there be overlap in the observed spectrum? Does your answer depend on the slit spacing?

Why are interference fring 4 xbukka;-i-nes noticeable only for a thin film like a soap bubble and nxba- i;kuk4-n ot for a thick piece of glass, say?

When a compact disk (CD) is held at an angle in white light, the r6q6i lwt+p m buih59a:fu;4nseflected light is a full spectrum (Fig. 24–56). Explain. What wouldt sm;lh uw 66pf94ab:qi5iu n+ you expect to see if monochromatic light was used?

Why are Newton’s rings (Fig. 24–31) closer together farther from the6:n5d-vqf 4nr mas(k u center?

Some coated lenses appear greenish yellow when seen by reflect:xkw8vjg ++q -j -bupned light. What wavelengths u 8jp:-wnvkx+g-+ bjqdo you suppose the coating is designed to transmit completely?

A drop of oil on a pond appears bright at its edges, where itsvu1d5sjd6 bb * thickness is much less than the wavelengths of visible1d6j vud5bb*s light. What can you say about the index of refraction of the oil?

What does polarization tell us about the nature of n cqck sv z y+nep(c6h5x7zn:8 -*or:glight?

Explain the advantage of polarized sunglasses over normal tinted suna5kg lg-ef,i-.pf s4g glasses.

How can you tell if a pair of sunglasses is polarizing orf7utaylq ,; 8f not?

Two polarized sheets rotated at an angle of*hb **n1javl,fh yh a5 90$^{\circ}\,$ with respect to each other will not let any light through. Three polarized sheets, each rotated at an angle of 45$^{\circ}\,$ with respect to each other, will let some light through. What will happen to unpolarized light if you align four polarized sheets, each rotated at an angle of 30$^{\circ}\,$ with respect to the one in front of it?

What would be the color of the sky if the Earth had no atmosphen nf/ pcxuw;fl3y*/i4re?

If the Earth’s atmosphere were 50 times denser than it is, would w7-k*x atabqna/y9 g*sunlight still be white, or w w*bqxtga -9k7naay*/ould it be some other color?

  Monochromatic light falling on two slits 0.016 mm apart pr. pp 41eqk pkf+n8i*oioduces the fifth-order frinek8i.fk o4*n+1 qi pppge at an 8.8$^{\circ}\,$ angle. What is the wavelength of the light used?    $ \times10^{-7 }\;m$

  The third-order fringe of 610 nm light is observy mofk;w/w q,8dqt56led 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 m dvb-m3 12t3rh (gfazdm apart. Successive fringes on a screen 5.00 m away are 6.5 cm apart near the center of the -dva2h 1rbdzf(gt33 mpattern. Determine the wavelength and frequency of the light.
$\lambda\;=\;$    $m$
$f$ =    Hz

  A parallel beam of light from a He-Ne laser, with a waveleng k:9e sa-z 8dan+2juklln kx08ut;q 6oo-,sk kth 656 nm, falls on two very narrow slits 0.060 mm apart. How far apart are the fringes in the center of thsskk a-ek8k6 9a: uo2k x,t0dll q +nuoz;-jn8e pattern on a screen 3.6 m away?    cm

  Light of wavelength 680 nm falls on two slits and produces an interference 1; nc(yiqn g290tzt mspattern in which the fourth-order fringe is 38 mm from the central fringe on a screen 2gnmtc0iny91 2q; st(z.0 m away. What is the separation of the two slits?    mm

  If 720-nm and 660-nm light passes through two slits 0.5x n( eoj;; mun4fg9rkhrig3 ,+8 mm apart, how far apart are the second-order fringes f4nhr3;9in (ukgxg;j+ore, fmor these two wavelengths on a screen 1.0 m away?    mm

  In a double-slit experiment, it 969m tl mwp0qm vctjyni04 9u/is found that blue light of wavelength 460 nm gives a second-order maximum at a certain location on the screen. What wavelength of visible light woumi9m/ytl 9w6j0u 0c94mq ntvp ld have a minimum at the same location?    nm

Water waves having parallel crestn d-hq v)5 erx-o:2ddxs 2.5 cm apart pass through two openings 5.0 cm apart in a board. At a point 2.0 m beyond the board, at what angle relative to the “strd dhn-q-25vex:x od)raight-through” direction would there be little or no wave action?

Suppose a thin piece of glass is plj( v6kzun )btcmlu4:m7v7i /ndn +d.baced in front of the lower slit in Fig. 24–7 so that the two waves enter . )mbzkdnnv+n 7j7mu 4:cdi6v /(tbul 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,x+/p-vpwih 0 9le2oh w the third-order maximum 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 the same slitsphh+o vex wli2p-0 /9w. How far from the central bright spot will the second-order maximum of this light be located?    mm

  Two narrow slits separ 4p /h)pqga)ya)eago:ddph*/w j ut .:ated by 1.0 mm are illuminated by 544 nm light. Find the distance between adjacenjga4y h:aqptwpg:oedp)*.u)/a d/) h t bright fringes on a screen 5.0 m from the slits.    mm

  Light of wavelength 480 nm in air falls o,4a:tvi *ossin 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=1.60) covers one slitfsw.o jh 3+t*b of a double-slit apparatus illuminafho jtb *.3+swted 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?    nm

  By what percent, approximately, does the speed of 1ecdspbw .nvp ;zs,/og*(t9lred light (700 nm) exceed that of violet light (400 nm)1 ; .ossc(g,9*dptepnlz wb/v in silicate flint glass? (See Fig. 24–14.)    %

  A light beam strikes a piece of glass at a 60 cwy0*es *jcv+.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 contg *cgpd;;m3hu , x m8bu.cd1mkaining 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 fu; s77z ieigf(vll angular width of the central diffraction peagev (zfi7 i;s7k?    $^{\circ}\,$

  Monochromatic light falls on a slit that076maqx az3aq tu0z-k 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 fl) jjx re rt;9q78as81afv8 l3:iyydmalls 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 i5 zf eil82owu2s illuminated by 450-nm light. What is the width of the central maximum (in cm) in the diffractio5o8e wz2u 2lifn pattern on a screen 5.0 m away?    cm

  Monochromatic light of wavelength 653 nm falls on a slit. If the angle s0oukg* )/khcc5qn 5v between the first bright fringes on either side of th5/ush5 k*gc0v)q ocnke central maximum is 32$^{\circ}\,$, estimate the slit width.    $\mu m$

  How wide is the central diffraction peak on a screen 2.30 bs9yf1g-s0yw y i//cj xj lz39m behind a 0.0348-mm-wide slit illuminateyf si-j 9x91 c3zlyyw/ gj0/bsd by 589-nm light?    cm

  When blue light of wavelength 440 nm f zx lp+z632pi0+lddyb alls on a single slit, the first dark bands on ex+3 2 p+ldyzbdp0liz6ither side of center are separated by 55.0$^{\circ}\,$. Determine the width of the slit.    $ \times10^{-7 }\;m$

  When violet light of wavelength 415 nm falls on a single smkh-g)q /mcs2yha1w4u 1c5 jslit, it creates a central diffraction peak that is 9.20 cm wide on a screen that is 2.55 m away. How wide is theh 15a)s-j 2uhqcw1/mgcy4 kms slit?    mm

  If a slit diffracts 650-nm light so that the diff bm :pi*(,q3:og/e.bkzau avqraction maximum is 4.0 cm wide on aao b ,aekvu:q i(z3.*g :qp/mb screen 1.50 m away, what will be the width of the diffraction maximum for light of wavelength 420 nm?    cm

For a given wavelengthhkqr7ejrye2svqq7 6is )8-(v $\lambda$, 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 va2hj5cj6yo1- .,rol xj vc/z falling on a grating whose slitj cy ,-hv5z 1xao6/vrl2coj.js 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 have9 wo.xpq1bwy3 if the third-order occurs at a .op xwb319wyqn 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 dif1 0g go es8)bf(lyga:tfraction grating is observedg 1y08obl g(gs)etf:a 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 has ruy4 dz)+fn6f $ 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+uv4ma n2 mb(w 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 ,b;x,9r ej 3cvg2zqwmorder that can be seen if a grating with 6000 lines per cm is illuminated with 633-nm laser3 9,2z ,qjvwrce gxm;b light? Assume normal incidence.   

  Two (and only two) full spectral orders can be seen on either sizs/fy 7ik13pq wpg,v6hj x526qimf, wde of the central maximum when white light is sent through a diffraction grating. What is the maximum number of lines per cm for the gratin py52pmjivi,s1 /, 6qqw7ghw xkz36ffg?    $ \times10^{ 3}\;lines/cm$

  White light containing w1l+xx3t cj/u 4dhy2st avelengths from 410 nm to 750 nm falls on a grating with jtsy+ ld4h/ x3cxu2 t1$8500\;lines/cm$ 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 wc2u vhg z ;9bsvi -brz18ynm19avelength $\lambda\;=\;6.328\times10^{-7 }\;m$ 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 p1ldhp51lob ;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, wha xk1 uj2beuv:z6(aho 7t wavelength is most strongly reflected at the center of the outer surface when illu162 : vax(e7uohz bukjminated 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 iu6c +ws:xvg(ree --qsf the glass plates are each 26.5 cm lo s exg -6wvusq(:cre+-ng?    cm

  What is the smallest thickness of a soap f7rc .lc-5 w4xs,xkq(z ;wvdam ilm $(n\;=\;1.42)$ 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 yello(osy yy()kma5 .1m.s4(yp 6t fbourlew ($\lambda\;=\;570\;mm$ 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 rin2blbu6daislr2 63x 7k gs (not counting the dark spot at the center) are observed when 550-nm light falls nokbu bl632s2r dla6 x7irmally 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 4)ivybcs7 b3b one end of two pieces of optically flat glass, as in Fig. 24–33. When light of wavelength 670 nm is incident normally, 28 dark lines are observed (with one at 3 )bsi4v by7bceach end). How thick is the foil?    $\mu m$

  How thick (minimum) should the air layer be between two flat glass b1ic *nut1( ymsurfaces if the glass is to appear bright when 450-nm light is inc*ym1nbc(it u1 ident normally?    nm
What if the glass is to appear dark?    nm

  vA piece of material, suspected of be/ q dbk*b, vb.eb5)oz d*br6gqing 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 alcohzn5(y(snz ctj.p d, +col $(n=1.36)$ 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 appart2m5wx ko*sq1 atus (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?k t* 1q2ms5wxo   

  What is the wavelength ofhni.a j0 esf+0 the light entering an interferometer if 644 bright fringes are. +f00n haiejs counted when the movable mirror moves 0.225 mm?    nm

  A micrometer is connected to the movable mirror of aq 6 9 ixuztvsni)bl4+1n 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. Whl i9 4)t nz+b6ivsuxq1at is the thickness of the foil? The wavelength of light used is 589 nm.    $\mu m$

  How far must the mirn3jvbp x/9plqzh po cz6 u(,(+ror $M_1$ 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 xi ogahqo0919rf .4+o4xmjjd)js)nj 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 refraction of the gas, assuming that the interferom 9onro) 4h.049d jxai fxmj)+qojsj1g eter is in vacuum. $n_{gas}$

  

  Two polarizers are oz4jnr)pjj:wcir-8( lriented 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 wi;z g1(zt zec(3gdo0an air–glass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s angle for a diamond submerged in water if thestwjfcbi2h6 (u d.+: r light is hitting thhj.ftc+sw2r6: i(bud e diamond $(n=2.42)$ while traveling in the water? $\theta_{p}$    $^{\circ}\,$

  Two Polaroids are aligned so that thl19 w+f.xrss ne light passing through them is a maximum. At what angle should one of them be placed so that the intensity is subsequently 1s+x9l f.wsnrreduced by half?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be place,e-f 0jazdv19uhtb-h d so as to reduce the intensity of the incident unpolarizvt1 -eduhaz j 0-,hb9fed light to
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are or(5l ut yo*q;2pzkkla -iented 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 orientedh3t, td;f vip ,ysnblh-);kn9 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 wak8 id4/zv.rj bm: szh.ter for light cdj.hs8m r :z bz./kv4ioming from beneath the surface? Compare to 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 Polaroid sheets, k23)3 hmw eelbhz 4ha-each of whose axis makeb4 )melhez2a khw33h-s a 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength -1 w ,,nm2nrzz/ 1y/wtw hjxvj$ 5.0\times10^{7 }\;m$ passes through two parallel slits and falls on a screen 4.0 m away. Adjacent bright bands of the interference pattern are 2.0 cm apart.
(a) Find the distance between the slits.    mm
(b) The same two slits are next illuminated by light of a different wavelength, and the fifth-order minimum for this light occurs at the same point on the screen as the fourth-order minimum for the previous light. What is the wavelength of the second source of light? $\lambda_2$    $ \times10^{-7 }\;m$

  Television and radio waves reflecting from mountain1a 937vto):ncjnz vhm s or airplanes can interfere with the direct signal from the station. n 9hont31)jczmv v7:a
(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 diffractc+c0 fovk eo596 1napxion grating with p ofcn+5c0okax 9e16 v$ 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 narrc fz7hhnii;+; ow slits 0.60 mm apart. 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 wavelength of the unknon;zh;+cih fi7wn light? $\lambda_2$    nm

A radio station operating at 102.1 MHz broadcasts from two identical antennae- 6f jr6bmd8qb at the same elevation but separ6d8-r mqfbb j6ated 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 0.88 m 3pp s+. :crqfbwide, and blows a whistle of frequency 750 Hz. Ignoring reflections, estimate at what angle(s) it is not possibfp. bc:pq 3s+rle to hear the whistle clearly on the playground outside the doorway.    $^{\circ}\,$ either side of the normal.

If parallel light falls u(9 apg ju: +vocjkt**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 parallel lines across them. f :+tyswac v:.When normally incident 460-nm light is reflected from the wing, the wing appears bright when viewed at an avw :ta:csyf. +ngle 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 7/s 4akvds fu6 drf-e+zc3pq4 second-order spe zqcas46fe7r f4p+dd s3vk/ -uctrum for any visible wavelength?   $ lines/cm$

Show that the second- and third-order spectra of whitepa fwjb lw, s.juz*4phf-7*+ j light produced by a diffraction grating alwayh+juw .-74baz*jfl fpwjs,p*s overlap. What wavelengths overlap exactly?

  When yellow sodium light, j2irzh4 2 flrl 5/7l b7h1ipwc$\lambda\;=\;$ 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 th bpv8 6,)t;z-ld930sev je m,qniz gqoe pattern is viewed on a screen 2.5 m from the grating. Th- m,ovt g6z e,lbend0vq3sipq;jz 8 )9e 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 of 15n q 1f/tc :.)+vkbvxvln:zrh 4 yb7w3z0 nm thickness of it, when laid on glass, is needed to reduce reflection to nearly zeflnw1 xv:h/yz bkc.bn4:v+qv)t r7z 3ro 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 norox5 .m2 ixnimd5.t1ohyz ; qsh5y b68xmally on a thin sheet of plastic film in air. The reflected light is a8x2..qnt m5o 56z y dohs5hmbixx;y1 i minimum only for $\lambda\;=\;512nm$ and $\lambda\;=\;640nm$ in the visible spectrum. What is the thickness of the film $(n=1.58)$? [Hint: Assume successive values of m.]    nm

  Compare the minimum thickness needed for an anti- we fmqhj cz248c5.q+wreflective 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 be i*aqx-bnjy)nqil cl p0,zo+6.wzg, *tween two flat glass surfaces if the glass is to appe6q)oz+q 0y,w.ipjz cn*i-,bgn* al lxar dark when 640-nm light is incident normally?    nm
What if the glass is to appear bright?    nm

Suppose you viewed the light transmitted th .-c;oo gozccuv.n0 ;6apc2ep rough a thin film layered on a flat piece of glass. Draw a di02czpop;a 6oo cc c v.u-.neg;agram, 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 the horizon is the fda0d*29 z ouqSun when light reflecting off a smooth lake is polarizeddo fd9 2*zauq0 most strongly?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be placed so as to revfw 0m4c.aj,kduce the intensity of the incident unpolarized light b4jv .mkf aw0c,y 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/l2i ,fr 9 jt7adbhzfdpk5)9w transmission axes are at right angles. A third polarizeh7 25,kd)rb9a/ dw tipfljz9 fr 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 l:-z b mwt8rjhw3.nv-0/dt iovertical, 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 wn1g kb q/4w1mg3xlk x2idth 1.0 cm and is pointed at the Moon, which is approximately 380,000 km from the E/ wl1x13kqmg2ngb k4xarth. 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( x76cisv.wsvk 5sh4 f 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 uc(7 k x2d-yyo$(n=1.34)$ 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 r 7( -)0:enwamlh.b qop gqxj)6.0-MHz radio waves in phase with each other. They are located at .eq h(bow a-nqmxpj0 g7)l:r)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 contaihrlvbefv. .f2 d3oa8( ning two wavelengths, 420 nm and 650 nm, enters a silicate flint glass equilateral rvfda.(e3o 2l8vf hb.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 mhl7a, dzv1b+t0 z*w ohas 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