Does Huygens’ principle app5h+n uyjb+ow 7ly to sound waves? To water waves? Explain.

What is the evidence +ur;l knd0i -kthat light is energy?

Why is light sometimes described as rays and s u2 1ik f2vk3fou97ily6pmm6rzds3 3dometimes as waves?

We can hear sounds around corners, b/*6rr2y- uixpzbem5 of2e2 yrut we cannot see around corners; yet both sound and light are waves. Explain the differencb/ox-ry*2izrye 5r up2 f2e 6me.

If Young’s double-slit experiment were submerged in water, how would the fringwq* b,y m5ry78m.nv ytskm1l6 e pattern be chan6ks8q1bm 5 yn.rltmy ,vm7 *ywged?

Monochromatic red light is incident on mkq-u2+ s fem)sk v39ka double slit, and the interference pattern is viewed on a screen some distance ausq2m + vmfk 3)k9e-skway. 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 destructively interfere if their path l )6 x0yiotmu4hev u6v2engt06) 6vmvyuho x4 eui2ths differ by how much?

Why was the observation of the double-slit interference pattern more couut1 zgodofz7k g42-8nvincing evidence f728ou1udgot4 zfz- k gor the wave theory of light than the observation of diffraction?

Compare a double-slit experiment for sound waves to that for light waves. Disaj bc /1 /ow3hyft-+ewcuss the similarities and differenceshf3t bew /j1a+wo c/-y.

Why doesn’t the light from the two headlights ofz.8 szxxm5o(:b7 tjhh a distant car produce an interference ps8zbt:zmh j5 (.xo7h xattern?

Suppose white light falls on the two slits of Fig. 245v45arxsjs :( d,az -lzh,kos–7, but one slit is covered by a red filter (700 nm) and the other bjss,dk,sa 4 va:z5hxr z 5l-o(y a blue filter (450 nm). Describe the pattern on the screen.

When white light passes through a flat piece of wymxr1r1 vfe35indow glass, it is not broken down into colors as it is b frx513ev1y rmy a prism. Explain.

For both converging and diverging lenses, discuss how the focal length a,3 g12asoijj5.;px( befqz nfor red light differs from thj 52 bf1s,zegpa;q.3 (oianjx at for violet light.

A ray of light is refracted through three f6 1ewrj 9-rslby2 , )mvno(fhdifferent materials (Fig. 24–55). Rank the materials according to their index of refrac(brljf)1 6fh v-esr92wn,omy tion, least to greatest.

Hold one hand close to your eye and focus on a distant light source +e. gee*c6r ,pyfra4ythrough a narrow slit between two fingers. (Adjust your fingers to obtain the best pattern.) Describepee+ a. cg,*rf yr6ey4 the pattern that you see.

What happens to the diffraction pattern of a singlecwpu ox-t(3o5 slit if the whole apparatus is immersed in (a) water, (b) a vac3c-(5x oput wouum, instead of in air.

For diffraction by a single slit, what is the effect of increasing (a) the syus(m:zmie jdk w:wspn/p); u7a( im/ru24o ( lit width, z::p uokwu2m(msipi7m un )rd /j;w(a(y e4/sand (b) the wavelength?

What is the difference in the interference patterns formed (a) a kjk /cr.g6zl;6b2-ja /vgcaby two slits $^{-4}\;cm^2$ apart, (b) by a diffraction grating containing $10^4lines/cm$?

For a diffraction grating, what is the advan 6xekhfcv 9+,btage of (a) many slits, (b) closely sve9 hk+cf 6,xbpaced slits?

White light strikes (a) a diffraction oeftv5-8di*y grating, and (b) a prism. A rainbow appears on a wall just below te-yi ftov*5d8 he 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 between 400xj 1 u3pwkm1u8a1 pgu* nm and 700 nm, incident normally on a diffrw8u1k *a1gx j13pump uaction 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 onf vvvi411 -ifqly for a thin film like a soap bubble and not for a thick piece o1-1i v4fvif vqf glass, say?

When a compact disk (CD) is held at an angle intuj 9(74t iatj white light, the reflected light is a full spectrum (ta49ujt jt( i7Fig. 24–56). Explain. What would you expect to see if monochromatic light was used?

Why are Newton’s rings (Fig. 24–31) closer togethe*ash nt8ru x;jf ta q/8:*d/tlr farther from the center?

Some coated lenses appear9 -tgxcqb0eb- greenish yellow when seen by reflected light. What wavelengths dot-be b9xq 0gc- you suppose the coating is designed to transmit completely?

A drop of oil on a pond appears bright a 1wg:wal1rm no8 6- bvrsy dzt1tqb1*7t its edges, where its thickness is much less than the wavelengths of vzrnt mq1r:1lwy ag6*s8 11w dtbob7v-isible light. What can you say about the index of refraction of the oil?

What does polarizationds7bkl 7ahit fq0nc883k y03c tell us about the nature of light?

Explain the advantage of polarized sunglasses over normal tinted sunglassesa xv)z qq+ioie( gv088.

How can you tell if a pair of sunglasses is polarizing or0c-7p em l nbjv( (khe2fx9b 3z6utdb:g -1axh not?

Two polarized sheets rotated at anqhut okh::jz*z 1gtjh:(f b** 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 ,ap.. mm,wlcg sky if the Earth had no atmosphere?

If the Earth’s atmosphere were 50 times denser than it is, would sunlighq+r rg/j0op/td z- zu05fmmd4 t still be white, or would itdm q0- 5 f4jo0+ur/tprzgd/zm be some other color?

  Monochromatic light falling on two slits 0.016 mm apart producesjkly vx,sp 0u5 -5wbj7 the fifth-order fringe at w5lujjvb, p0 xk ys57-an 8.8$^{\circ}\,$ angle. What is the wavelength of the light used?    $ \times10^{-7 }\;m$

  The third-order fringe of 610 nm light i1 mzc; d79jht;n2lihfy3gv u2s 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 0.0i+uh,g(7j5mrwnj3gn: zku w( 48 mm apart. Successive fringes on a screen 5.00 m away are 6.5 cm apart near the cgww z(n guu+5:(k, ji 7jmhnr3enter of the pattern. Determine the wavelength and frequency of the light.
$\lambda\;=\;$    $m$
$f$ =    Hz

  A parallel beam of light from a He-Ne laser, with a wew 8wxi d;,1k zq.o8zoavelength 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 3.6 m 8o e.1; xwzqzow8kd,i away?    cm

  Light of wavelength 680 nm falls on two slits and produces an interference ny7q2h pzwrs;+sh -8.ey (tui pattern in which the fourth-order fringe is 38 mm from the central fringe on a screen 2.0 m away. What is the separat-(;h827+hu rtizy pnyqew s s.ion of the two slits?    mm

  If 720-nm and 660-nm light passes thr9jq p +yfgbpn1)2 4mdsough two slits 0.58 mm apart, how far apart are the second-order fringes f2y4 1qpf gmj)dn9psb+ or these two wavelengths on a screen 1.0 m away?    mm

  In a double-slit experiment, it is founv lhv .*0kqw3ad that blue light of wavelength 460 nm gives a second-order maxim3q*0v. k vwahlum at a certain location on the 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 twos)zp0a);q jjc 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” direc0) jpjzqac); stion would there be little or no wave action?

Suppose a thin piece of glass is placed in front of 1 z n1tgd v4 )k5vb,6nvs1ytgmthe lower slit in Fig. 24–7 so that the two waves enter the slits 18 , 4vvd)tmtvnnby 1z61g skg150$^{\circ}\,$ 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 fo b ddk259zyhp5r light of wavelength 500 nm is located 12 mm from the central bright spot on a screen 1.6 m from the slits9 52 d5yzphkdb. 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 illuminated by 544 d b* f)dnx8oc/)esx8unm light. Find the distance between adjacent bright fringes on a screen 5.0 m from the slits /s)8nb8 d*duofcxe )x.    mm

  Light of wavelength 480 nm in air falls on twowy--o2h 7cs uq,zr-kr 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 slit of a double-slir plxs rs57c/xe(32bht apparatus illuminated by 640-nm light. 7xrl(pxe /5s3h bs cr2The 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 red light (700 nm) exh)h/mjco 8 1rh4t ts*fceed that of violet light (400 nm) in silicathr*htfs/1oj 8mhtc4 )e flint glass? (See Fig. 24–14.)    %

  A light beam strikes a l.jn;r2:i 1eirj lrn s r;ma-,lmk+b( piece 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 lig9h qs: (d :b*e(t6pjtxtwanxvcg34s / ht containing 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, w+qyh ;9 dow8jp5og 3bvhat is the full angular width of the central diffract3hovy9p 5 gowb8;+dqj ion peak?    $^{\circ}\,$

  Monochromatic light falls mk;5 5cwuu)4s ( rzsqzon 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 n ,mr:a lc(+no 0php00wweceo,ihe 3i+m falls on a slit that is $ 3.20\times10^{ -3}\;mm$ wide. Estimate how far the first brightish diffraction fringe is from the strong central maximum if the screen is 10.0 m away.    m

  A single slit 1.0 mm wid:h(ey76+now1f aw xsh e is illuminated by 450-nm light. What is the width of the central maximum (in cm) in the diffractn+16(weayx of7 whsh:ion pattern on a screen 5.0 m away?    cm

  Monochromatic light of wave* cdvgz6yket3hu 8.(pip 6j+ zlength 653 nm falls on a slit. If the angle between the first bright fringes on h(c j8 tzdkzgip+vu6y 36*.peeither side of the central maximum is 32$^{\circ}\,$, estimate the slit width.    $\mu m$

  How wide is the central diffraction peak on a screen 2.30 m behinyklb) 2 kju)jost+5k0 d a 0.0348-mm-wide slit illuminated by 589-nm light?l)t25y0j bu) +skojkk    cm

  When blue light of wavelength 440 nm falls on a single slit,kihxb7e+4r p3iax j9 4 the first dark bands on eitherxh7i +kp ija4b9xe r34 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 ak-wb0+uu8r5brh4/iit7r iy r single slit, it creates a central diffraction peak that is r -5rb0u78yr/4ruiw+htkbii 9.20 cm wide on a screen that is 2.55 m away. How wide is the slit?    mm

  If a slit diffracts 650-q mqkh) ;69oe i;pjh0jnm light so that the diffraction maximum is 4.0 cm wide on a screen 1.50 m away, what will be the width of the diffraction maximum for light of wavelength 420 nm? jk;qq960eompjh; h i)    cm

For a given wavelengtnrm; ,:p6j2g; +.bxur pkgn lz*bij2mh $\lambda$, what is the maximum slit width for which there will be no diffraction minima?

  At what angle will 560-nm light produce a second-orderjs tl/*v ucs2(dd8t3m maximum when falling on a grating whose slits t(/j ss3cd8tv2u*ld mare $1.45 \times10^{-3 }\;cm$ 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,07y ne tvin+* yx(geg the third-order occurs at an 18xinevget *+y( n7y,g0 .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-njn x,f gt.h)i. l8)u1l+ iiw1c0qbpwnm light falling on a diffraction grating is observed atctl iwng.pf +qu)8x i) 11wij .l,0hnb a 15.5$^{\circ}\,$ angle. How far apart are the slits?    $\mu m$
At what angle will the third order be observed?

  A diffraction gratingw116 d ytxr3h2gox2sgtz, +im has $ 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 onlxn:7t0t gg4mww1 wq8ofe(z3 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 bessp9b-:own4,yf*3y o su5(iit r vs+j seen if a grating with 6000 lines per cm+t4f(oovn sb5y*iu39 r y,issj-w: sp is illuminated with 633-nm laser light? Assume normal incidence.   

  Two (and only two) full spectral orders can be seen on eis; ccyz0 inysy6h87m smn/9 e0ther side of the central maximum when white light is sent through a diffraction grating. What is the maximum number of lines per cm for the 89c synes;h0 /cm ns7z0ym6yigrating?    $ \times10^{ 3}\;lines/cm$

  White light containing wavelengths from 410 nm to 750 nm falls on a grat4qyk:w1b9z 9 ss3fwk cing withskf9kw :wcz943ysb1 q $8500\;lines/cm$ How wide is the first-order spectrum on a screen 2.30 m away?    m

  A He-Ne gas laser which produces monochrz 3gkd 7q; azin-z2c*xaf6e 9pomatic 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 meabgkvawt55nv7m st-73sured 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 most strongly re0w2w;sk x9t haflected at the center of the outer surface when illuminated normally by white light? Assume atwhk0 2w;s9 xthat $n\;=\;1.34$. $\lambda$ =    nm ,which is an    -  

  How far apart are the darke2ydm ,b4v5tz fringes in Example 24–8 if the glass plates are each 26.5 cm tv4 zebdm 5,y2long?    cm

  What is the smallest th( you xvo*e+1dickness of a soap film $(n\;=\;1.42)$ that would appear black if illuminated with 480-nm light? Assume there is air on both sides of the soap film. $t_min$    nm

  A lens appears greenish 0 pagx77xtzzx8g41da 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 darkfrj;c vz4a - mcns1q l:dj,0i*(5o,9 llgvnbj Newton’s rings (not 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. 24–31). How much thicker is th1-sjav9*5mll 4jj g0q(,l cdr f:;bznin,ocve center than the edges?    $\mu m$

  A fine metal foil separas/kp3zom sb*tmvo/ vm80 + dh-tes 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 each end). How th+bm8 s-mh *koptvo3zd v0s/m/ick is the foil?    $\mu m$

  How thick (minimum) should the ai :lptod+.7 lna4we;m6 b (smrvr layer be between two flat glass surfaces if the glass is to appear bright when ;:mbev snt+7 l(pm6ardw.4 ol 450-nm light is incident normally?    nm
What if the glass is to appear dark?    nm

  vA piece of material, *uig qbz(+psk5*h uobb8 a+a/suspected of being a stolen diamond $(n=2.42)$ is submerged in oil of refractive index 1.43 and illuminated by unpolarized light. It is found that the reflected light is completely polarized at an angle of 59$^{\circ}\,$. Is it diamond? ----待选择----yesno 

  A thin film of alcohoz/f+eej3:el .23x 7uqune gl ul $(n=1.36)$ 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 vkt vldpp,g/pruv9:3 cvfw8;d),u 7q immersed in a liquid, the diameter of the eighth dark ring decreases from 2.92 cm to 2.48 cm. W vp 3 vpgu9dtk)7fu r8w,;,qlv/pcv:dhat is the refractive index of the liquid?   

  What is the wavelength of the light entering an interferometv3;bjrmw :;knal ,(b/-zf ew1nhdk2ger if 644 bright fringes are counted when the movable mknge/ j:k b;z1;dnv2( -hl,3w wbfam rirror moves 0.225 mm?    nm

  A micrometer is connected to the movable mir *y f9 zg)uhfq-0nbgu/ror of an interferometer. When the micrometer is tightened down on a thin metal foil, the net number of brigh y /bf09uunzf*)qg-ght 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 mirror3jxc;ngtrl8h tz q) g48)8bnh $M_1$ 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. 24–5mujcarudwsf8z +n91- .k :,mh9) passes through a small glass container containing a cavity 1.30 cm deep. When a gas is allowed to slowly fill the container, a total of 236 dark fringes are counted to move past a referj81,c.mzf9 k:r nuasd+-uhwmence 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 orieadk0bu*j0iup q;m,q1nted at 65$^{\circ}\,$ to one another. Unpolarized light falls on them. What fraction of the light intensity is transmitted?   

  What is Brewster’s anglnr(xivfa7o2z/:g kc z w3u+t3e for an air–glass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s angle for a diamond submerged in water if the lighq g i2*z1aacya05h r00,5gpeyfmh)ns t is hitting the diamond n y1)*5ac02 yfap qe0z0ahsigrh g5, m$(n=2.42)$ while traveling in the water? $\theta_{p}$    $^{\circ}\,$

  Two Polaroids are aligned so that the light pakg gj 16f ed*rzb(otbh.w)38 wssing through them is a maximum. At what anglew 1kzh6tfgd 3g()rebwj .*o8b should one of them be placed so that the intensity is subsequently reduced by half?    $^{\circ}\,$

  At what angle should ;kqpbvbc v+vr 7.)j8v the axes of two Polaroids be placed so as to reduce the intensity of the incident unpola8.j vkr;v v+v7pbbq c)rized light to
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are oriented a9ki3(7x blw7xof -uir t 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 oriented ckjve,k ,)zf+ 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 su df(zr bqw, v-fmvg:s5-tji+6rface of water for light coming from beneath the surface? Compare to the angle for total internabg:5dm s-fq-+fvjzvi6, w t (rl 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, each of w lp;jzxuwibqc+(2h)for8 e8r0y2 -hxhose a- rz8b + y8jrxchewofh p)20q;2uil(xxis makes a 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength )jo fuhaq.o1be.l,z 2$ 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 mountains or airplanes can interfoh9p*lk e2-x c5ibpat:5 qq- iere with the direct signh a5*ec:top2qk-ipl 5q x b9-ial 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 s/4q.)en de bvxeparate sources passes through a diffraction grating with 4 qdenvx)./be$ 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 njp:b/4 l5 4afil ver6parrow slits 0.60 mm apart. The screen is 1.70 m away. A second source of unknown wav p:bflir5ajp 4v6 4l/eelength produces its second-order 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 operati*qb2j(fam*c ;3mx)y)8vwdgq+ la)gm f ayfw6 ng at 102.1 MHz broadcasts from two identical antennae at the same elevation but separated by an 8.0-m horizontal distance d, Fig. 24–60. A maximum signal is found along the midline, perpendicular to d at its midpoint and extending horizonta3* m lf2x(*yc v)w+qam qg8am yd)wfafbg); 6jlly 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 wide, and blows a wtbi9fn-e h66z ntx1 z1histle of frequency 750 Hz. Ignoring reflections, estimate at what angle(s) it is not possible to hear the whistle clearly on the playground outside the doontx6fhz11 z-e tn9 i6brway.    $^{\circ}\,$ either side of the normal.

If parallel light falls on a single sli4cirk sz : v4 y54bm3c5xeg9qxt of width D at a 30$^{\circ}\,$ angle to the normal, describe the diffraction pattern.

  The wings of a certain beetle have a seriegr7 n9w1k6d0dzr po4k s of parallel lines across them. When normally incident 460-nm light is reflect4r1pdok60ndw7 z k9gr ed 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 gratig6/ hex *l+nalng have if there is to be no second-order spectrum for any visible wanh+e* xg 6a/llvelength?   $ lines/cm$

Show that the second-.u o ;wqxmz;gik 8) ,lpfh e*:suum4j6 and third-order spectra of white light produced by a diffractium;eql i4kos6,xw :)u*fu8 . gpzhjm; on grating always overlap. What wavelengths overlap exactly?

  When yellow sodium light*8;, em 0bjvj krb-axt, $\lambda\;=\;$ 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 q*s 1l fql)fad )js,4fod;a-u a diffraction grating with and the pattern is viewed on a screen 2.5 m from;,df) aq4s-fjqsfdl*al 1o)u 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 minimum of 150up.fg bclx3;0* o4lrr nm thickness of it, when laid on glass, is needed to reduce reflection.4x*r3lpluc;r gf o 0b 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 incident normafwiwrbd4;wx8 8 y z:(olly on a thin sheet ow( wiy84bor; 8zw:xdff plastic 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 needed for an anti-reflective coati ;-fwwzay- :trng $(n=1.38)$ 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) thicknes6g ;5i+sypycq j:gm q7s for the air layer between two flat glass surfaces if the glass is to appea5gqm+gjs6i: cy ;q7 pyr 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 film 8yn k6sigtt65layered on a flat piece of glass. Draw a diagram, similar to Fig. 24–30 or 24–36, and yi6gts5k tn68 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(f.*oejlbn svi0vw ; 4o qj2 idbn42z, is the Sun when light reflecting off a smooth lake is polarized wz ls,jev 4b(jo4;nnf22 di 0i *qvob.most strongly?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be placed ul9ix5qg3*m 7h vm+jec:m cg 7xxd6.kso as to reduce the intensity of the incident unpolarized light by an additional factor (after the first7c.3 eg:mumcxdj7+i69 xlk* h vq5mgx Polaroid cuts it in half) of
(a) 4,    $^{\circ}\,$
(b) 10,    $^{\circ}\,$
(c) 100?    $^{\circ}\,$

  Unpolarized light falls on two polarizer sheets whose transmission /8e5mhzli,3p x mtg6waxes are at right angles. A third polarizer is placed /gipe w3z lt5m8x,hm 6between 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 ia1*g*3ds v. z vthdzmu;*yfp/n succession with their axes vertical, at 30$^{\circ}\,$ to the vertical, at 60$^{\circ}\,$ to the vertical, and at 90° to the vertical.
(a) Calculate what fraction of the incident unpolarized light is transmitted by the four polarizers.
(b) Can the transmitted light be decreased by removing one of the polarizers? If so, which one?
(c) Can the transmitted light intensity be extinguished by removing polarizers? If so, which one(s)?

  A laser beam passes through a slit of wo) 2d;/0happa;vo ndkidth 1.0 cm and is pointed at the Moon, 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). Es)vd;0o pha/ a;k2 dpnotimate the width of the beam when it reaches the Moon.    km

  A series of polarizers are each pliclqq,acd ;q. 3f7 hu,aced 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 :yw 8q zp/z+phma1s:*p8.mfy ni4y bxi zr 6l2$(n=1.34)$ 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 each other. pjgl d-rd8j/w) h49hi They are located at pointh)i /-hpj8 rd4 lgw9djs $S_1$ 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 cor47ztmvp 9uzn- o9.kl (c6p grntaining two wavelengths, 420 nm and 650 nm, enters a silicate flint glass equilaterokz(v7 -9gmrlpu pzn.6 r9 4tcal 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 ;ci;hm08 zws zlens has one flat surface and one with $R\;=\;18.4\,cm$ It is used to view an object, located 66.0 cm away from the lens, which is a mixture of red and yellow. The index of refraction of the Lucite is 1.5106 for red light and 1.5226 for yellow light. What are the locations of the red and yellow images formed by the lens? [Hint: See Section 23–10.]
$d_{i-red}$    cm
$d_{i-yellow}$    cm