Does Huygens’ principle apply to sound waves? To wqfl) /wfgwb ;vkx)k5u;: /9 es rc4v5xqx(qotater waves? Explain.

What is the evidence tha*-x o fvm w4qrv7(/kriy (aks;t light is energy?

Why is light sometimes described as rays and *kcy hl.m zjg h)y8*q;sometimes as waves?

We can hear sounds around corners, but we caq*:q5r dy7rj:hhzk 41zghm( z nnot see around corners; yet both sound and light are waves. Explain ther5hk 4 *h qd :hjmz7yrz:qg(z1 difference.

If Young’s double-slit experimeuv,js zw y/)nk)kz/q0 nt were submerged in water, how would the fringe pattern be changzw),/ vks0 nu yjz)qk/ed?

Monochromatic red light is incident o*g :t zsqus3t)n a double slit, and the interference pattern is viewed on a screen some distance away. Explain how the fringe pattern would change if the ret3zs )q ug*s:td light source is replaced by a blue light source.

Two rays of light from the same source destructi jt 8y9fwtir2,vely interfere if their path lengths differw fiy98,2jtrt by how much?

Why was the observation of the l;q+ bxrn26hwdouble-slit interference pattern more convincing evidence for the wave theory of light than the ob;+bq6xlhnw2r servation of diffraction?

Compare a double-slit edpc )av smi.,;xperiment for sound waves to that for light waves. Discuss the simiavis),m .p ;cdlarities and differences.

Why doesn’t the light xrw,u51+d7wv wo 8j iofpov-.from the two headlights of a distant car produce an interferencfowi-8vpu 75 1w,ov.jodrxw + e pattern?

Suppose white light falls on the two slits of Fig. 24–7, but one slit is r qd-:iqnldfwoqf+07ul9 x4ty /3e, ecovered by a redqr -iw:n+u , 0feq73dtde94lql fx/yo filter (700 nm) and the other by a blue filter (450 nm). Describe the pattern on the screen.

When white light passes through a flat piss*a lqg p+r;9ece of window glass, it is not broken down into colors asgr;* + qlp9sas it is by a prism. Explain.

For both converging and diverging lenses, discuss how the focal length )m4 gnt hyfdk 9946izmfor red lig)9h49i gy dn mkz6tm4fht differs from that for violet light.

A ray of light is refracted through thro iuyqz0+90 inee different materials (Fig. 24–55). Rank the materials according to their index of refraction, least to gre+y90zonui qi0atest.

Hold one hand close to your eye and focus on a distant light source through a b(s 1yhtp3gwo9ec,u p 6t*w0 wnarrow slit between two fingers. (Adjust your fingers to obtain the best pattern.) Describe the pattern that you set6o1ypgct30uw,swhw9 ( *p ebe.

What happens to the diffraction pattern of azrvp+k1ao/e ng-mcj . +7in 4v single slit if the whole apparatus is immersed in (a) water, (b) a v+p4e 7cz/vnmnj rai+1kgo .- vacuum, instead of in air.

For diffraction by a single slit, what is the effect of increasing (awbibq)d;k qf+d to d6o, 3uo()) the slit width, and (b) the waveleng d;k6)tdfoiu),b(oqqw+ 3o dbth?

What is the difference in the interference patterns formed (a) *j92vbgdz-6jua xd ; rby two slits $^{-4}\;cm^2$ apart, (b) by a diffraction grating containing $10^4lines/cm$?

For a diffraction grating, what is the aejc.h4ud8vf t*v 22fddvantage of (a) many slits, (b) closely spaced slitsvuh t2 8f.4j 2cddf*ev?

White light strikes (a) a diffraction grating, and (b) a pris /8hy dpkaw1;r5d ne2jm. A rainbow appears on a wall just below the direction of the horizontal incident beam in each case. What is the color of the top of the rainbow in eak/j ryep 1;5wnah28ddch case? Explain.

For light consisting of wavelengths between 400 nm and 700 nm, incidentsu2*ofq p9w t9 normally w9 *opf qs9u2ton a diffraction grating, for what orders (if any) would there be overlap in the observed spectrum? Does your answer depend on the slit spacing?

Why are interference fringes noticeable only for a thin film like a soap bubt mno g0c0sl(r )6quu n55cp wfy)/v.cble and not for a thick piecu0f o/c ypsglt (5rv6))0nqwc5 .mnu ce of glass, say?

When a compact disk cy 1qmahp1ua54(uv1 h(CD) is held at an angle in white light, the reflected light is a full sp ph 4umqy5 ua1hv1(1caectrum (Fig. 24–56). Explain. What would you expect to see if monochromatic light was used?

Why are Newton’s rings (Fig. 24–31) closer together farther from the ce/0pzzb:(4 fi7 8y4 :fdnxzluj(h*nsqfl :jy k nter?

Some coated lenses appear greenish yellow when seen by reflected light. Whatkp+zsb3 zb u9p:-cz9 t wavp-:z b pz9ub zc+s3tk9elengths do you suppose the coating is designed to transmit completely?

A drop of oil on a pond appears bright at its edges, where its thickness ia a;2i 5 omf5loz2bwn(s much less thaa5 lwi n(5obo;m2 afz2n the wavelengths of visible light. What can you say about the index of refraction of the oil?

What does polarization tell us about the nature of,dy tntwbu 4p9 v-mc; /eu)qm8 light?

Explain the advantage of polarized sungl-g 4h oqq x(klth*9c+vasses over normal tinted sunglasses.

How can you tell if a pair of sunglasses isg3l(0(g xtta s wqg8nf2,n kmzb* 6tb6 polarizing or not?

Two polarized sheets rotated at 5nypw c77cwc/sa5qh lx 4ads0 jtg 2t3w 4y15yan angle 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 Earts ;u:n93asww/ etqcs0:zf d5 kh had no atmosphere?

If the Earth’s atmosphere were 50 times denser than it is, would s jv .do)4zbn)sunlight still be white, or woulov.n4)zbjds ) d it be some other color?

  Monochromatic light falling on two slits 0.016 mm apart produces the fifthdtd*m 34vqdj3 -order fringe at avd*d qt433mjdn 8.8$^{\circ}\,$ angle. What is the wavelength of the light used?    $ \times10^{-7 }\;m$

  The third-order fringe of 610 nm light is observed x3dpwb a ,u 1yj ti8+3 esgtpqp-()+upat 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 apj9y.twqhtb9ka.s f5/i47q p mart. Successive fringes on a screen 5.00 m away are 7t/w .is qa.99ty4bkpmjq5 hf6.5 cm apart near the center of the pattern. Determine the wavelength and frequency of the light.
$\lambda\;=\;$    $m$
$f$ =    Hz

  A parallel beam of lioyuce/p8 - po8rk3,biwv;bul sl 4 s-qr8 so,+ght from a He-Ne laser, with a wavelength 656 nm, falls on two very narrow slits 0.060 mm apart. How far apart are the fringes in the center of isl; p8oy8okvqcp-ru ,,-b /sueow l4r38s b+the pattern on a screen 3.6 m away?    cm

  Light of wavelength 680 nm falls on two slits and produces an interferencehq2 ym*pvn0 u, pattern in which the fourth-order fringe is 38 mm from the central fringe on a screen 2.0 m away. Wv,2hq umnpy0*hat is the separation of the two slits?    mm

  If 720-nm and 660-nm light passes through two slits 0.58 mm apart, how f1lwv rn /,3/zp ve1v+cxn +urbar apart are the/u+ prblv3,11+ e xwrc/ zvvnn second-order fringes for these two wavelengths on a screen 1.0 m away?    mm

  In a double-slit experimwdr7x8)ll:6p w uv/rwent, it is found that blue light of wavelength 460 nm gives a second-order maximum at a certain location on the screen. What wavelength o/dwwwr:vx )p7 rll6 u8f visible light would have a minimum at the same location?    nm

Water waves having parallel crests 2.5 cm apart pass through tw1: r 4q/t+phly/j rse0*xnq+l umz ib8o openings 5.0 cm apart in a board. At a point 2.0 m beyond the board, at what angl+ nqrmp/1+tu h*s :lji 0r4e 8yzbql/xe relative to the “straight-through” direction would there be little or no wave action?

Suppose a thin piece of glass is placed in front:fc hs o y6.muia2iw /qgz si39e3(ph9 of the lower slit in Fig. 24–7 so that thsq:u (e6 gsi3i/2a. yom3czh9 f9wiphe two waves enter the slits 180$^{\circ}\,$ out of phase (Fig. 24–57). Describe in detail the interference pattern on the screen.
24-7
24-57

  In a double-slit experiment, the third-order maximum for light of wavelength 5xku+gg f9cu,200 nm is located 12 mm from the central bright spot onguf, gx2c+k 9u a screen 1.6 m from the slits. Light of wavelength 650 nm is then projected through the same slits. How far from the central bright spot will the second-order maximum of this light be located?    mm

  Two narrow slits separated by 1.0 mm are illuminar6 l;w fes eh:3+ngco.bp(zb- ted by 544 nm light. Find the distance between adjacent bri o; lpzfw:n6beeg3+(.cs b-hrght fringes on a screen 5.0 m from the slits.    mm

  Light of wavelength 480 nm in air +70d 59ekf3cznbe zjc falls on two slits $6.00 \times10^{-2 }\;mm$ apart. The slits are immersed in water, as is a viewing screen 40.0 cm away. How far apart are the fringes on the screen?    mm

  A very thin sheet of plastic (nr04yso x(dbd(=1.60) covers one slit of a double-slit apparatus illuminated by 640-nm light. The center point on the screen, instead of being a maximum, is dark. r(sxy( 0b4odd What is the (minimum) thickness of the plastic?    nm

  By what percent, approximately, doe-qon n**a(hves the speed of red light (700 nm) exceed that of violet light (400 nm) in silicate flint glass? (See Fnven - **q(aohig. 24–14.)    %

  A light beam strikes a piece of glass akiif wd3kw82;t 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 cont9d zate*7i qm m4z+aokih35(pg*xr2waining 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 angular widtp /tu-od8,eii 3 :xff;rq4fdth of the cent qd;f,fe/ o4-ird utf83x:pit ral diffraction peak?    $^{\circ}\,$

  Monochromatic light i 56ty .cxe8 x1,fboqwfalls on 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 5r9m7rp6nn4 (pqxymd;a rd/.m20 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 mmx/x /gpp69rug ; .b/h+trb epv wide is illuminated by 450-nm light. What is the width of the bhe ;ux6p/.r gp/r v+pb/gtx 9central maximum (in cm) in the diffraction pattern on a screen 5.0 m away?    cm

  Monochromatic light of wavelength 653 nm fa3m cx8csz7d22x r,od/as0 hb hlls on a slit. If the angle between tbm/ 2sch o380r7 hsad, xc2zxdhe first bright fringes on either side of the central maximum is 32$^{\circ}\,$, estimate the slit width.    $\mu m$

  How wide is the central diffraction peakcexl6urv) i/v+:f(xh on a screen 2.30 m behind a 0.0348-mm-wide slit illuminated by hvi/x6x(:leu+cv )f r 589-nm light?    cm

  When blue light of wavelength 440 nm falls on a single slvia xlv5w -/r1it, the first dark bands on either side of center are separated by 55.0vl rva5/w1i-x $^{\circ}\,$. Determine the width of the slit.    $ \times10^{-7 }\;m$

  When violet light of wavelength 415 nm falls on 3yxjss nt ( z,sl.:wz*a single slit, it creates a central diffraction peak t,ynlwtz3 s*.xj:( s szhat 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 diffrayz)19r1a/a w xp;hh dwction maximum is 4.0 cm wide on a screen 1.50 m ah a wp /hy)1a9zd1;xwrway, what will be the width of the diffraction maximum for light of wavelength 420 nm?    cm

For a given wavelengjv,gd p6g yalk/n a(48th $\lambda$, 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 whenixvr6uc p yi5:wmw),1 falling on a grating who,iw cy5 :xvr16 upw)mise 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 grat j + ;1yxc;l6i+q kxh duojhxq:go4/8fing have if the third-order occurs at an 18.6;ox1gk+dxjq8/yc 4ojh u; iqlhfx :+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 fallfzg: dg+w1s,m+ nhi2 iing on a diffraction grating is observed :m ws2g d+gnh zi,f1+iat 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 haskf ;nwt/qnkp -a850zjnn4 o .e $ 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 akny1ol1 q**mq $9700-line/cm$ 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 ;ts ogf3yl2mq:ou2n7 rd w +4vif a grating with 6000 lines per cm is illuminn+usr27q y wl2:;mvto o4gdf3ated with 633-nm laser light? Assume normal incidence.   

  Two (and only two) full spectral orders can be seen on either ly p3of*nuj4k aiuzoy ff.9t75ps 69(side of the central maximum when white light is sent through a diffraction grating. What is the maximum number of lin5z f (okouu ps99 46y3f7pal .yn*tjifes per cm for the grating?    $ \times10^{ 3}\;lines/cm$

  White light containing wavelengths from 410 nm to 750 nm falls on a gratl1d9u*(cqw yb ing with 91ubd*q wly (c$8500\;lines/cm$ 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 wavelengt38b. f tiehe 1y,sa:mzh $\lambda\;=\;6.328\times10^{-7 }\;m$ 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 measured6zxvvgi z4)*s 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 mwl/w ,m9h fya/of.mnj(:i :ele + jz;dost strongly reflected at the center of the outer eljz m(9wm/ ;oadljy:/e: f ,n+w.hfisurface when illuminated normally by white light? Assume that $n\;=\;1.34$. $\lambda$ =    nm ,which is an    -  

  How far apart are the dark fringes in ymnrci txnhr14 v 8q97sddfh /e7 ;1l0Example 24–8 if the glass plates are each 26.5 cm long? 1 nrtm0vi9 7/sy74hne1 lqxcr8;hdf d   cm

  What is the smallest thickness of a soap fo*h0bk0 g)wdn)h*ys c as--mtilm $(n\;=\;1.42)$ 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 ,ljpe u9-h :say)(nau($\lambda\;=\;570\;mm$ 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 cou(t4stay);,hjkkk ;u l nting the dark spot at the center) are observed when 550-nm light falls normally on a planoconvex lens resting on a flat glass surfh4 ,kuttaj)( ;k;kylsace (Fig. 24–31). How much thicker is the center than the edges?    $\mu m$

  A fine metal foil separates one end of tcur/:j t 6t 98xd8;.brztzlmtwo pieces of optically flat glass, as in Fig. 24–33. When light of wavelength 670 nm is 9 u zzr t8;l/d8ctrtb:mxjt6.incident normally, 28 dark lines are observed (with one at each end). How thick is the foil?    $\mu m$

  How thick (minimum) should the air layer be between two qx:srr7c 7ty:r2yyh 5flat glass surfaces if the glass is to appear bright when 450-nm ligh:rcy sqxr7h7r5y :2 ytt is incident normally?    nm
What if the glass is to appear dark?    nm

  vA piece of material, suspected of being a u14,q 8g bnftistolen 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 alcohol(aw ;q8owsxhv rco(kj:1w6h2 $(n=1.36)$ 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.d-7ci09dc j th 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 liqui0 9hddctcj7- id?   

  What is the wavelength of the light entering an interferometer if 644 bright frm 7 k 90:qewectecmx46inges ar m4x7e k9 :0eecwc6tqme counted when the movable mirror moves 0.225 mm?    nm

  A micrometer is connected to the movable mirror ob)33yg+).pzd fhw e nbf an interferometer. When the microh+b 3g.p3f)en bwyd)zmeter 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 is 589 nm.    $\mu m$

  How far must the mirus1 mdiohdf y/: q sqqh9v,4:9ror $M_1$ 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 smal01va- 0j.qtg b wa2ln0fng5zul glass container containing a cavity 1.30 cm deep. When a gas is allowed tw 51-2qt f0agug 0j.navl0zbn o slowly fill the container, a total of 236 dark fringes are counted to move past a reference line. The light used has a wavelength of 610 nm. Calculate the index of refraction of the gas, assuming that the interferometer is in vacuum. $n_{gas}$

  

  Two polarizers are oriented at , *m 1 vqc9(mdd;tsoba65$^{\circ}\,$ to one another. Unpolarized light falls on them. What fraction of the light intensity is transmitted?   

  What is Brewster’s angle fo r):vgj4,q zj)ttu,y ur an air–glass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s angle for a diamond submerged in water if the l e)uf y-v1n 01lv6weruight is hittinu-y0w6vr1 v )1nelfe ug 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 maxheipd pwu: c9p.f y77uo(7q-zimum. At what angle should one of :e7i w yqhp(z9op-77 fu.u pcdthem be placed so that the intensity is subsequently reduced by half?    $^{\circ}\,$

  At what angle should the axes of two Polaroizu +.cjsjs9f 4 secw.1ds be placed so as to reduce the intensity of the incident unpolar1wz s9jcj+..ce 4ssf uized light to
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are oriented*q vw* rg5ove, 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 oriensz3 s9 c/tfy.wted 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*md)s(q ite n6 reflections off the surface of water for light coming from beneath the surface? Compare to the angle for total internal reflection, and to Brewster’s angle from a6qsdet*(m) in bove 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 sp( .7 l.eswej8fxi.;vu hrzqu8 s *gc4uccessive Polaroid sheets, each of whose ae..4gc x frqls j7; p*wu8hivs8uz.e(xis makes a 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength r)w. 306eo ,ts jturcp9adj:z $ 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 frkzou 1t9i,ir3 om mountains or airplanes can interfere with the direct signal from the statio, z13 9irutikon.
(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 grating xa r-+qjvvs;/with ;-vr xjv+sq/a $ 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 sle5weg.9h9 ;9oi lj tiddyv20zits 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 thotd99eli2 9;jvg yiedw.5 z 0he central maximum than the 590-nm light. What is the wavelength of the unknown light? $\lambda_2$    nm

A radio station operating at 1m9 kgdh,y8h 7w02.1 MHz broadcasts from two identical antennae at the same elevation but separated by an 8.0-m horizontal distance d, Fig. 24–60. A maximuhw8d97h mg,k ym 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 vtg- s kr7o a;;;kbkt/back from an outside doorway 0.88 m wide, and blows a whistle of frequency 750 Hz. Ignoring reflections, estimate at what angle(s) it is;o/gs v ;;t-kr7tbakk not possible to hear the whistle clearly on the playground outside the doorway.    $^{\circ}\,$ either side of the normal.

If parallel light falcf1u:adhq n m-a 3 dq*)bt+8yuls on a single slit of width D at a 30$^{\circ}\,$ angle to the normal, describe the diffraction pattern.

  The wings of a certaiy7p(gr3d - ssvol,(i xn beetle have a series of parallel lines across them. When normally incident xg(7d rolsvy,3(s ip- 460-nm light is reflected from the wing, the wing appears bright when viewed at an angle of 51$^{\circ}\,$. How far apart are the lines?    nm

  How many lines per centimeter must a grating have if there is to be ;2t41nt.,kzvqq h3 himvdb +p-xj3n qno second-order s31mnv+ tq,dh2itx ;n 43.q pj -vhbzqkpectrum for any visible wavelength?   $ lines/cm$

Show that the second- and third-order spect 7b+e9-iw9qlpo-e it wra of white light produced by a diffraq-eo 99i e7bl+tp-wwi ction grating always overlap. What wavelengths overlap exactly?

  When yellow sodium ligh: sy/0rdpm5zr t, $\lambda\;=\;$ 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 viewepeaub5a* q /*zd on a screen 2.5p*5*ua/zeqab m from the 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 minimuvmrb e0c+ tl9-aa ;b-ym of 150 nm thickness of it, when laid o 0 ;t9y-aarevmb- blc+n 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 inci-4jpi 5nq:n hdoml(4adent normally on a thin sheet of plastic film in air. The reflected light is a m :-d 5j4 ima(p4hnolnqinimum 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-reflective :2 *-ee.vssbr /+stzlw8dsazcoating $(n=1.38)$ 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 glag(+jqyra+ 6ovss surfaces if the glass is to appear dark when 640-nm light is incident no6y+r+ ogj(q varmally?    nm
What if the glass is to appear bright?    nm

Suppose you viewed the light transmi d)nqv7xa *xq9tted through a thin film layered on a flat piece of glass. Draw a diagram, similar to F7qqx 9ax)v dn*ig. 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 Sun when light reflecting off a smoos.pylu1( z v:r2u/oat th lake is pola/uz2 :.ap1vt(suylorrized most strongly?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be skqbfg3.u980sup h4 nc0r j f:placed so as to reduce the intensity of the incident unpolarized light by an additio8h qf.surgsfb4 09k:j3c0np unal 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 0qv+2t 5vsa qmtd1r:n transmission axes are at right angles. A third polarizer is placed between the fi v2:qtrt1msd5+n0a qvrst 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 vertical, atkd 0ul3-tsml 9 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 Moon ew-ouq;5z0j y, which is approximately 380,000 km from the Earth. Assume the laser emits waves of wavelength 630 nm (the red light of a He-Ne laser).o0z-u;w 5jy qe Estimate the width of the beam when it reaches the Moon.    km

  A series of polarizers are each placed a 3 fd +y+,0wq:lde t ;qdmwegd*d/-rfat 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 dzgkrwl*:o78 hko4l +$(n=1.34)$ 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 phase with bvxc3lj3 6np)each other. They are jxlv6n33pb )c located at points $S_1$ and $S_2$, separated by a distance $d\;=\;175m$, Fig. 24–61. What are the first three points on the y axis where there will be destructive interference? (Destructive interference in this case means that a radio receiver placed at that point would pick up no signal).    m    m    m

  A parallel beam of light containing two wavelengths, 420 nm and 650 nm, eymaif8(j5 -o l ljn0y,nters a silicate flint glasslf amn,j8i (0oy -5jly 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 2a3q z26lvy 2* :*yesytbv rwyhas 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