Does Huygens’ principle app-q7l 0h p3; wtz+t woidekrar-0g )-erly to sound waves? To water waves? Explain.

What is the evidence that light is enerml/jy2:y.w du gy?

Why is light sometimeslk1gp54z3) uz y j,vv)fyezw5 described as rays and sometimes as waves?

We can hear sounds around corners, but we cannot see around czj4l ds4.im(sorners; yet both sound and light are waves. Explain the diz s(4m.jl4 sdifference.

If Young’s double-slit experiment were submerged in water, how would the frinl1 p2 -z 6mqa1fh4njwyge pattern be chan4wf2l1 zyjhq a1 6mp-nged?

Monochromatic red light is incident on5,. zwk8n aj 3zhhetse2,*ts/b r+ip e a double slit, and the interference pattern is viewed on a screen some distance away. Explain how the fringe pattern would change if the red light soup,tje/zea,hes2nrk3i 8* w.tz5bhs+ rce is replaced by a blue light source.

Two rays of light from the same source dr ;f2 miirbi kr1-ee6,estructively interfere if their path lengths dif ri2;i,e6brm -f1rekifer by how much?

Why was the observation of the double-slit interference pbc+ siy(ovm 3+attern more convincing evidence for the wave theory of light than the observat cmob++v3sy(iion of diffraction?

Compare a double-slit experiment for sound waves to that for lightjzz+gn.je /s 6 waves. Discuss the similaritie/+nj6gzz.s e js and differences.

Why doesn’t the light from the kz+ dl:ly8 l4a med59stwo headlights of a distant car produce an interferenc4:le+m5d adl89z ksl ye pattern?

Suppose white light falls on the two slits of Fig. 24–7, bcu .f3ck ym82sb) njn)s*)pizut one slit is covered by a red filter (700 nm) and the other by a blue filter (450 nm). Describe the pcicjn2fnm)ps yb .)zk8)*us3 attern on the screen.

When white light passes through a flat piece of window glass, it is not broks.gi h-5rncg0en down into colors as it is by a 5 -gi0c.rgnhsprism. Explain.

For both converging and diverging lenses, discucscs0;d.jv .kxc3k5u ss how the focal length for red lc3 v5s0 xk.s;ukdj c.cight differs from that for violet light.

A ray of light is refracted through three different materials (Fig. 24–55*4d0 v vqmjq1y-lpww a 9+ijs,). Rank the materials according to their index of refraction, least +iaq-y, jmqjw91lv0*4wsp vdto greatest.

Hold one hand close to your e87s0(** .a:um vwx dhanwmktlye and focus on a distant light source through a narrow slit lw:0aun *.w msxdk7 m*v8a(h tbetween two fingers. (Adjust your fingers to obtain the best pattern.) Describe the pattern that you see.

What happens to the diffraction pattes41 2v z,3moukl.aea arn of a single slit if the whole apparatus is immersed in (a) water, o3al1.avu ems ak24,z (b) a vacuum, instead of in air.

For diffraction by a single slit, what is the effect of increasing (a) the n-pt;0d uk3tv: ,wjwb slit width, and (b) the wavelengtvj tnk; pd ,bw-03w:tuh?

What is the difference in the iz/5c2m;phuhe :d w+annterference patterns 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 adv/wz1nltvm+ x zi2*w8 hantage of (a) many slits, (b) closely spacel/m+1z witxv*h 28z nwd slits?

White light strikes (a) a diffraction grating, and (b) a prism. A rainbowg1x pmj9i w/x7. l.vhj9zn3pf appears wvn /9p.jx zl9 m1j p73hi.gxfon 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 each case? Explain.

For light consisting of wavelengths b(-a8 py jxkcmktj4y: 6etween 400 nm and 700 nm, incident normally on a diffraction grating, for what orders (if any) would there be overlap in the observed spectrk(akjx4t :cmypyj-6 8 um? Does your answer depend on the slit spacing?

Why are interference )-/hs4fjmnvrt1c.ke fringes noticeable only for a thin film like a soap bubble and not for a thick piece of glassfje/rn-v) .h 1ck4tm s, say?

When a compact disk (CD) is held at an angle in w:wnlslf l/9*f hite light, the reflected light is a full spectrum (Fig. 24–56). Explain. What would you expect to see if monochro9sl*lw f f:/nlmatic light was used?

Why are Newton’s rings (Fig. 24–31) closer together farther from i e6e2lm+k i6othe center?

Some coated lenses appear greenish yellow when seen by reflected24cnmysf6pje/ bk:p,-z -b ti light. What wavelengths do you suppose the coating -i:2ep/bzf spyb-j6,t n mck4is designed to transmit completely?

A drop of oil on a pond appears bright at its edges )vuz.e4 2vkd av4*hky, where its thickness is much less than the wavelengths of visible light. What can you sa* )dvz4y e 4.vvuhkak2y about the index of refraction of the oil?

What does polarization tell us abouhd, tij,*t ,i57gfc7 ers 9pkyt the nature of light?

Explain the advantage of polarized sunglasses ovewb o0-qd4ze 4/h)o trsr normal tinted sunglasses.

How can you tell if a pair of sunglass,0rq(hj6 tctx2n.i1cj6hg sxes is polarizing or not?

Two polarized sheets rotated .evh0s; n l enwkuff)v7h)a 7yr8,y4t at an 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 Earth hadmr qb,(8w er 3(xim:ybn7:5,.lihcmu cd(eah no atmosphere?

If the Earth’s atmosphere were 50 times denser than it is, w) p9ju,x tuit(ould sunlight still be white, or would it be ui ttu(p9),xj some other color?

  Monochromatic light falling on two slits 0.016 mm apart produces the * ( m9pjbnoua8fifth-order frinou* 8nmb(aj p9ge 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 observed at an angv+lno 1k 6m3jgle 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 (94g,hic2 ccdqk r w;rl-p 4p: g7vtfuslits 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 k4p -497vgd2;qrw ,ctirpcfh( c :ulg the wavelength and frequency of the light.
$\lambda\;=\;$    $m$
$f$ =    Hz

  A parallel beam of light from a He-Ne laser, with a wavelength 656 nm, falls ts w9ajy3wj)7) t0jbp on two very narrow slits 0.060 mm apart. How far apart are the fringes in the center 0p jj wjt)y73b 9tas)wof the pattern on a screen 3.6 m away?    cm

  Light of wavelength 680 nm falls on s /ksi),*o yfztwo 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 z /)ofsi*ks,yis the separation of the two slits?    mm

  If 720-nm and 660-nm light passes through two slits 0.58 mm apart, how/l60s5yka8k inwe7ini:a :w k far apart are the second-order fr5nwe s:l6 n0ikai/87iak:w ykinges for these two wavelengths on a screen 1.0 m away?    mm

  In a double-slit experig fa: w*x4l/lv+;b(ek u4fges ment, it is found that blue light of wavelength 460 nm gives a second-order maximum at a certain loca a*+xgfel(;wl4keus4/ b v f:gtion on the screen. What wavelength of visible light would have a minimum at the same location?    nm

Water waves having parallel4w te7 mjj61t* clybj7 1cs 4p6ay1wbc crests 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 “straight-through” direction would the67ma 1w jc61bw471yytjejtc l4cs p*bre be little or no wave action?

Suppose a thin piece of glass is placed in front of the lower slit a 56i3sj.c 4gkz , lccmvn)h:nin Fig. 24–7 so that the two waves enter the slits zvc5jinkc n3a).6s 4hglm,:c 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 lipnr3*wz .,qu6jw :n8,iiuja oght 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 bright spot will the second-order maximum of this light be io,uq iaju :jw6r 3,nwn*p.8z located?    mm

  Two narrow slits separated by 1.0 mm are ihx1or+onwy;g avr/0yeb 4 +d-t+gu 4clluminated by 544 nm light. Find the distance between adjacent bright fringes on a screen 5.0 m frcr+vegowg 0h+yt/;oyx a4rd -+b4u1n om the slits.    mm

  Light of wavelength 480 nyp( t y d.5:y+gygfjy,m in air 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 (n=1.60) cojdgt*fix8n 0 .vers one slit of a double-slit apparatus illuminated by 640-nm light. The center point on the screen, instead of being a maximumfn8*d.tixgj 0, is dark. What is the (minimum) thickness of the plastic?    nm

  By what percent, approx1aqa )a9mr kheuw8h .mt5 wi44(wvan8imately, does the speed of red light (700 nm) exceed that of violet light (400 nm) in silicate flint glash4)au48r.aq wa im(5nwv1t8k9mea w hs? (See Fig. 24–14.)    %

  A light beam strikes a piece of gv(mkv4niz+( u,ykb e4lass 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 jha7)xfil)*ke m /o6pcontaining 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 ongz- 2l9 wxno 8dk2ga+i8wont9 a slit 0.0440 mm wide, what is the full angular width of the central diffractii-8 +2nd w9zkatwgo2lg8 x on9on peak?    $^{\circ}\,$

  Monochromatic light falls :al( cn6waw6c 0denk8 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 520 nm falls on a slit that iboozrf.t7d 2e9xzltyi-68 f6 s $ 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 lr:fx jxv:dq*-c6- suy ight. What is the width of the central maximum (in cm) ivx jc: d-yr6qf:*xu-sn the diffraction pattern on a screen 5.0 m away?    cm

  Monochromatic light of wavelength 653 nm falls on a slit. Ifby(vps27txs+3 iyu8o the angle between the first bright fringes on either side of the cio7 (2bytvs uysp+3x8entral maximum is 32$^{\circ}\,$, estimate the slit width.    $\mu m$

  How wide is the central diffractbgcw4gytsi 2 :u m 3n9xy0af3*ion peak on a screen 2.30 m behind a 0.0348-mm-wide slit09i:ngfuct4 mbygays3*w32 x illuminated by 589-nm light?    cm

  When blue light of wavelength 440 nm falls on a single slit, the first dark banj/08(c l rnq/e6txfy sds on either side of center a tq0jx ye(nrl8 /6/fscre 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 slit, it creates a ce+-hrc hpliy+ k *(i.kyntral diffraction peak that is 9.20 cm wide on a scr( c*hhk+priy i. ly+-keen that is 2.55 m away. How wide is the slit?    mm

  If a slit diffracts 650-nm light so that the diffraction maximum is 4.0 cm wide cma;ki)*nf 53x;jh pj5 lg05of ba+khon a screen 1.50 m away, what wihh 5a;jlk+cg55xj faf; npi3b*0 mok)ll be the width of the diffraction maximum for light of wavelength 420 nm?    cm

For a given wavelengt1blmd/emfob*r0 6 y3k h $\lambda$, 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 fallin:2s-0zdxb)jsq zs-s4(yu .w9 m fm6 7jsncabjg on a grating who9q( uzb4 y2z:dsssmf)j0c wx-s6nj j .b-sa7m se 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 grating have if the third-ok/bb.*qii w u l3pzy9pi9)yh,rder occurs at an 1bl.9)ih /*z buwy piyki3,p q98.0$^{\circ}\,$ 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 wjp, v/5yia,tdiffraction grating is observed at a w j,pyat /5iv,15.5$^{\circ}\,$ angle. How far apart are the slits?    $\mu m$
At what angle will the third order be observed?

  A diffraction grating hasn-2ptko ffrg6i/o19 nr tzfbs1jv+ 29 $ 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- m4xcr: t.uwt 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 6r9 idn3uvw kp9p91now:h*tw if a grating with 6000 lines per cm is illuminated with 633-nm laser light? Assume w h6nwp:pud3tni999orw* vk1 normal incidence.   

  Two (and only two) full spectral orders can be seeph0je :ry6g*xn on either side of the central maximum when white light is sent through a diffraction grating. What ijh*60rg yx:pe s the maximum number of lines per cm for the grating?    $ \times10^{ 3}\;lines/cm$

  White light containing wavelengths from 410 nm to 750 nm falls on h;e.bm68sq yga grating with ;8b6 .qmgse yh$8500\;lines/cm$ How wide is the first-order spectrum on a screen 2.30 m away?    m

  A He-Ne gas laser which gvm (dsj3d.vun/ t4w+produces monochromatic 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 spectru+uui+ tgywa5u43c5f *2 lotl vm lines 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, wt,4:xt e3v euyhat wavelength is most strongly reflected at the u:4 t,v3yxeet center of the outer surface when illuminated normally by white light? Assume that $n\;=\;1.34$. $\lambda$ =    nm ,which is an    -  

  How far apart are the dark fringes in Example 24–8pzw x nyd +nk2wf(yoy) *+(4xu if the glass plates are each 26.5+ fox(yyu2z n( dwp*+)yk n4xw cm long?    cm

  What is the smallest thicknesjl5,ebc mnn73s 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 greenishqki9/.+ 5gh +jf euxqt 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 (no:ph(vscrn/j )(wd: zx f)k,u tt counting the dark spot at the center) are observed when 550-nm light falls normally on a planoconvex lens resting on a flat glass surface (Fig. 24– r)cw,k:/p t(uxd snjzv)f:(h31). How much thicker is the center than the edges?    $\mu m$

  A fine metal foil separates one e*,ft+z wug d:.oi /gljnd of two pieces of optically flat glass, as in Fig. 24–33. When light of wavelength 670 nm is incident normally, zw+ g.l ogu*dj ti:f/,28 dark lines are observed (with one at each end). How thick is the foil?    $\mu m$

  How thick (minimum) should the aihza9 zrjngn.j*y/ wq8 f)s2g1r layer be between two flat glass surfaces if the glass is to appear bright when 450-ng1wqg8.zh fj/yr* snj)2 nz9am light is incident normally?    nm
What if the glass is to appear dark?    nm

  vA piece of material, suspected of being a stolen diamon6/ ja:lur0p msd $(n=2.42)$ 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 alcoh8ip3w m/g +-h 8,yflwpcz kj1eol $(n=1.36)$ 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, hs)) ; ihjv;eyo:xk8k the diameter of the eighth dark ring decreases from 2.92 cm to 2.48 cm. What is the refractive ind)y );hkj:; i8oskhe vxex of the liquid?   

  What is the wavelength of the light entering an intn ysx (s lfz10-wmd1.4c/xkx xerferometer if 644 bright fringes are .l1zx1 kfcx/n -4 0x s(smyxdwcounted when the movable mirror moves 0.225 mm?    nm

  A micrometer is connected tyjf1)bwq r8x -o 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 )wb8y 1xj -qrfto 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 mirror 90w) y uk ;(1xnphnvhh$M_1$ 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 interferometbic(9u6yw1 w evc 8b1der (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 arc9wv1wcei8d y6 (bu1b e 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 orien6/z*6 t- s / aim2ykhdtw7pezc td.vd:ted at 65$^{\circ}\,$ to one another. Unpolarized light falls on them. What fraction of the light intensity is transmitted?   

  What is Brewster’s angle for an aikh )v8t0-7lne j*9nebhlr gm3r–glass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s angle for a diamond submerged in water if the light is hittinvsa6dxd k 7v6/a85-xzcjen r 3g the div jx6zrkvcae d/a 8d3s5n -x76amond $(n=2.42)$ while traveling in the water? $\theta_{p}$    $^{\circ}\,$

  Two Polaroids are aligned so that the light passing through them is a mass 8jva3vvu g4*u08d jximum. At what angle should one of them be placed sos3j8vvvj8u 0 asgu d*4 that the intensity is subsequently reduced by half?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be place(5.dcv xbw2 pbwozg2 051yko ud so as to reduce the intensity of the incident unpolarized ligh o x z0(525vbw2pykbg.oc1d uwt to
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are orienteiye2 i z.iy/+omzc 9e+d 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 orie)o:(hbfx)rpa k 4xt3e nted 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 ofh+un7j7/r my)s 3 gjuh;aw9 qnf the surface of water for light coming from beneath the surface? Compare to the angle for total internal reflectiona qj/ + 77;3hwrhgynus m9jnu), 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 -)x gjf):lwg +:jbdw6flpbe 8 Polaroid sheets, each of whose axis makes a :fbj6-gl8wg)jb p:d+ xfwl)e 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength f)gy;:qrx o)j,n 14en qht-lr$ 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 whbom8 d;er ,8+ d40 fy+ pjbm5ck9bwfhaves reflecting from mountains or airplanes can interfere with the direct signal f o + 8hwhr+k0fy58fbmdm9bb,jdpc4e ;rom 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 through a diffraction gra; anjr 7k+u )mc(ns+jfting with 7j(kr cunan +jm)sf;+$ 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 aoodv sk:ga 4hk94u /y8part. The screen is 1.70 m away. A second source of unknown wavelength produces its second-order fringe 1/8oy4sd: 9khvgu4o a k.33 mm closer to the central maximum than the 590-nm light. What is the wavelength of the unknown light? $\lambda_2$    nm

A radio station operating at 102.1 MHz broadcasts from two identical antyzs:6o2;/ucbh0 ui, d gu(s4pf m8nvj ennae at the same elevation but separated by an 8.0-m horizontal distance d, Fig. 24–60. A maximum signal is found along d6,uvsiu :/sp (;f 8nb2j mz4 u0yoghcthe 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 j h 1u(okfvgn8b0pi5ew1pp4.-hj( n;yk e6j vfrom an outside doorway 0.88 m wide, and blows a whistle of frequency 750 Hz. Ignoring reflections, estimate at what angle(s) it is not possible to hear the whistle clearly on the playground outside thwpi 8;fjvvn1(- gkeopu1 0jjh45nhe. kbpy6(e doorway.    $^{\circ}\,$ either side of the normal.

If parallel light falls on ax luid( qi6*7rq0 g7cz 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 ath1 seu4a*ef 4cross them. When normally inciden1u44faseeh* t t 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 no secon +0gu: hdnrqx70ub iv8zr 4ll+d-order spectrum for any visible waveh4znx8br 0dlgl u7qr:v ++iu0 length?   $ lines/cm$

Show that the second- and third-order spectra of white lig- u9:dyi9hawag;cz l.m.zf(k y2s88d c j7leeht produced by a diffraction grating always overlap. What wavelengs9jwh(ddc 87ykli-ay me z9:f.; 8lce.uz2agths overlap exactly?

  When yellow sodium light,7bhghh qakwt -1b1,cz1 v,tk)tdz:m ( $\lambda\;=\;$ 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 b *fj;6gasnd e j9/an2on a screen 2.5 m from the grating. The incident light edb26/a*j;j nf 9sg nabeam 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 orf:cme5v 8l gw7)o 2apf 150 nm thickness of it, when laid on glass, is needed to reduce reflection to872fwcrpeml oa )gv5: nearly zero when light of 600 nm is incident normally upon it? Do you have a choice for an answer?

  Monochromatic light of variae13awfr el28/trldl -ble wavelength is incident normally on a thin sheet of plastic film in airr l a-d3ler /lewt812f. The reflected light is a minimum only for $\lambda\;=\;512nm$ and $\lambda\;=\;640nm$ in the visible spectrum. What is the thickness of the film $(n=1.58)$? [Hint: Assume successive values of m.]    nm

  Compare the minimum thickness needed form 9o4:ml8iud w 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 betweei/r+n*/v taax(guzz,k 2* fo un two flat glass surfaces if the glass kx*a( uvn,rifu zto 2z/ga* /+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 tva3c: q3*,a nlgbdf0ru9zc; vn )teu-hrough a thin film layered on a flat piece of glass. Draw a diagram, similar to Fig. 24–30 or 24–36, and describe the conditions required for maxima and minima. Consider all possible values of indecn9 uur* avle:,3 ;tqbaz3d -cfgv)n0x 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 horiz/h wwfmxmu30: on is the Sun when light reflecting off a smooth lake is polxw0hmm3f : u/warized most strongly?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be placed so as to reduc(. 5 ;is)a wsylgkp:rbjh/u qwd.65r)zzuga8 e the intensity of the incident unpolarized light by an additional factor (after the first Polaroid cuts it in 5r5yq .( 8bs) r6h.dzl pw:auij;wu /k)agzg shalf) of
(a) 4,    $^{\circ}\,$
(b) 10,    $^{\circ}\,$
(c) 100?    $^{\circ}\,$

  Unpolarized light falls on two pol -zeouv45o7daufk 94m arizer sheets whose transmission axes are at right angles. A third polarizer is placed between the first two so tha4f9z547u umdaveo -okt 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 verticalrczfbs 4-l 8/qsn1(v;de /bdj, 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 qlkh 2q67+7rqp2d tvp1.0 cm and is pointed at the Moon, which is approximatelyt 6q7l72dqprhk+p2qv 380,000 km from the Earth. Assume the laser emits waves of wavelength 630 nm (the red light of a He-Ne laser). Estimate the width of the beam when it reaches the Moon.    km

  A series of polarizerghmej ;(1eeyuo20pd 8s 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 d.uh3 8y.:pihz3vvlq8z*efg * a0rwa$(n=1.34)$ 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 antennasihxy4 ah 2dxnk)rj)-6 radiating 6.0-MHz radio waves in phase with each other. They a-)h) i426yxndr hkjx are 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 wav97pyebqp 1xh: elengths, 420 nm and 650 nm, enters a silicate flint glass equilateral qp9x7h1 bp:ey 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 and one zo ru lh.2u:doi/za9-z/d-hs 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