Does Huygens’ princi vd1-3m 6ylyneya ,(aah*0olm ple apply to sound waves? To water waves? Explain.

What is the evidence that light is energy-rxm7q.4tf m o?

Why is light sometimes described as rays and sometimes as waves?dn: em l1tbxaa0ki4a p.:ka(3

We can hear sounds around corners, but we cannot see around corners; yet bogaf9at)c 90 etth sound and light are waves. Explain the differttc )0aea9f 9gence.

If Young’s double-slit n4nipw znw)r r8761q rexperiment were submerged in water, how would the fringe patternnr6wz r7)1 prnq ni48w be changed?

Monochromatic red litd *m rmlnc+02ght is incident on a double slit, and the interference pattern is viewed on a screen some distanc*lmm2n c0 +trde 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 destructively interfere gd-hc(k+xt d 8if their path lengths hdxg(kc8d+ t-differ by how much?

Why was the observation of the double-slit interference pattern8d3n sw0 wd9;sye tgk*zfr05r more convincing evidence for the wave theory t0 5dns9gr;sewywd* 0r8k3fz of light than the observation of diffraction?

Compare a double-slit experiment for sou3fj,moyt2nvny3ozt r 0+a.d)nd waves to that for light waves. Discuss the similarities and diffe djmy3fnton.vzt+rao0 )y3, 2rences.

Why doesn’t the light from the two headlights of a distant car produce an in63 m/z8q6n;zzxww/ cayv 1kznterferm;z/wyn3z kqz6 z1n/6v8acxwence pattern?

Suppose white light falls on the two slits of Fig. 24–7,p./hjwk 1bzwh bz0a3 1 but one slit is covered by a red filter (700 nm) and the other by a blue filter (450 nm). Describe the pattern on twh w/z1k 03bpa1 hjz.bhe screen.

When white light passes through a flat piecer0 xo wx+cc,a: of window glass, it is not broken down into colors as it is by a prism.r+cwx0x: ,aoc Explain.

For both converging and diverging lenses, discuss how the fopic3lh 03l7k1dmps +zcal length for red light differs from that f lz3lk shdc310 p+mpi7or violet light.

A ray of light is refracted through three different materrmf86o. 1 qk e2)-wm1 :oycqueq mdpu3ials (Fig. 24–55). Rank the materials aqe13cqmuy-fqdo.1) mkru2 m w:8p6e occording to their index of refraction, least to greatest.

Hold one hand close to your eye and focus o/2qqi.:j1xli( hu e 6oarz-uon a distant light source through a narr: ulx qzh.16qriouio-/a j (e2ow slit between two fingers. (Adjust your fingers to obtain the best pattern.) Describe the pattern that you see.

What happens to the diffraction pattern of a single slit if )2v26 cslcupm i i,pv8n a(;cmthe whole apparatus is immersed in (a) water, (b) a vacuum, instead of in air. pvs vcmp8l2inm(i);cu2c ,6a

For diffraction by a single slit, what is aqtiax . 84jajr5i8+uthe effect of increasing (a) the slit width, and (b)8a+ji.iu jata85q4 xr the wavelength?

What is the difference in the interferen ex./ w/(*lfiu qwou,oce patterns formed (a) by two slits $^{-4}\;cm^2$ apart, (b) by a diffraction grating containing $10^4lines/cm$?

For a diffraction grj1r5l7j +pk snating, what is the advantage of (a) many slits, (b) closely splnpj1k jr57 +saced slits?

White light strikes (a) a 7t ,mk 3lymm7 ,lerej7 yk40r0xe5kardiffraction grating, and (b) a prism. A rainbow appears on a wall just below the direction of the horizontal incident beam in each case. Whj7 yml50y re,7m0lrkk34e7mxr e a,ktat is the color of the top of the rainbow in each case? Explain.

For light consisting of wavelengths between 400 nm and 700 nm, incident n g 8i3f l+*o4xi*igeawormally on a diffra ail43 io8e+* wgx*fgiction 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 snus-nx0 )kq pn 3,qx,fringes noticeable only for a thin film like a soap bubble and not for a thick pikns - 3,uxx,spq0) nnqece of glass, say?

When a compact disk (CD) is held at an angle in white light, the reflected lig35ch/mt4 fj(42kz7 fddqzbdv q.ql) oht is a full spectrum (Fig. 24–56). Explain. What would you expect to see if monochr)zz q(of 75 qcv4t dkbqj.dd23hm4lf/omatic light was used?

Why are Newton’s rin v bi.elag , 53wk90qbnzm1-ofgs (Fig. 24–31) closer together farther from the center?

Some coated lenses appear greenish yellow when seen by +va3ih sacs :; yk;,8 hrbvkn;reflected light. What wavelengths 8;3 ;bha;crnk v,iky: hsav+ sdo you suppose the coating is designed to transmit completely?

A drop of oil on a pond appearkk,h 5iq dz9;rs bright at its edges, where its thickness is much less than the wavelengths of visible light. What can you say about idkr q59;zkh ,the index of refraction of the oil?

What does polarization tell us about th. u2yvo0qw/ mqe nature of light?

Explain the advantage of polarizedfoxcl567dm pf /.vw h68xqf/b sunglasses over normal tinted sunglasses.

How can you tell if a pair of sunglasses is polarizing or svq(+u mpi-/ knot?

Two polarized sheets rotated at an angi- d nn*t 6ec1 pliq(8d7wgx+fle 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 ifavzrnt ,vi n2 y +r*45-ad xj:o7cza-i+y ec5n the Earth had no atmosphere?

If the Earth’s atmosphere were 50 times deush2h)u83 pvdnser than it is, would sunlight still be dh82vu)3 suphwhite, or would it be some other color?

  Monochromatic light falling on two slits 0.016 mm apart producese ib ryi);.vs g 261-6h/tjvhfsh aw8l the fifth-order fringe abih- r 1.v/)6gss;l2hytai we 6vhjf8t an 8.8$^{\circ}\,$ angle. What is the wavelength of the light used?    $ \times10^{-7 }\;m$

  The third-order fringe of 61m7e/5+hkpr t1f dpk4ofi) l :h0 nm light is observed at an angle of 18$^{\circ}\,$ when the light falls on two narrow slits. How far apart are the slits?    $\mu m$

  Monochromatic light falls on two very narroy(cbk6 b p2 nn4gru59dw slits 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 the wavelenpbd 9rcg 25nyb k4(6ungth and frequency of the light.
$\lambda\;=\;$    $m$
$f$ =    Hz

  A parallel beam of light from a mpum:nj0x0vcbc-e ( ( 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 (:jmcn ce v0 bmu-p(0xcenter of the pattern on a screen 3.6 m away?    cm

  Light of wavelength 680 nm falls on two ap0kui ))9d kvslits 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.0pdu kv)aki9) What is the separation of the two slits?    mm

  If 720-nm and 660-nm light passes throuu75kmn j mexd5l;7 5 n2jkyr5ngh two slits 0.58 mm apart, how far apart are the second-order fringes for these two wavelengthsjrn2k5mkj;nedxy 5 7nu m557l on a screen 1.0 m away?    mm

  In a double-slit experiment, it is found that blue light of wavelength 460 nm ; mi9p9(g g: 7a )4yyztghsot 3z) me/rlmdw/vgives a second-order maximum at a certain location on the screen. What wavelength of visible light would have a minimum at the same log) m/w; pzmystmh)/4y3trleg 7g az:od(9v9i cation?    nm

Water waves having parallel crests 2.5 cm apart pass through two oppp7 yt6gycp jo3ow,o61pq7 w*;dfxs 2enings 5.0 cm apart in a board. At a point 2.0 m beyond the board, at what angle relative to the “straight-through” dir yo6wd;o7ppx1g2t7poc6*ys3 wj , fpqection would there be little or no wave action?

Suppose a thin piece of glass is placed in front of the lower slit io:-bov1 6e jak 4o*kucn Fig. 24–7 so th6*14 o eujk:bak co-ovat the 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 ,6r eat or lr+leti/;7/+ xwjm500 nm ist;i+7 6j/rrwt+ ,aroll / meex 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 located?    mm

  Two narrow slits separated by 1.0 mm are illuminated by 5:psji/n b53+b b0uijq44 nm light. Find the distance between adjacent bright fringes ouns5b ij0p+i: /bjb3 qn a screen 5.0 m from the slits.    mm

  Light of wavelength 480 2*s(irk v7 tlinm 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) covers o sbb(01 duiexq0by+9jne slit of a double-slit apparatus illuminated by 640-nm light. The center point on the screen, instead of being a maximum, is dark. What is the (minimum) thicknes 1 jqbbxi0( dbe+0yu9ss of the plastic?    nm

  By what percent, approximately, does the speed of red light (700 n3m3lsos1rw-3 e zmne1y(c/un m) exceed that of violet light (400 nm) in s13(m/ sl erozcn3we-1su n3 ymilicate flint glass? (See Fig. 24–14.)    %

  A light beam strikes a piece of glass at cos w07pen (6)6tbs-gvq7cxw 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 containpsf)gz:bj8kj 4d7. x( fgo8hying 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 anrsz+wi4 ifp-+(1j ,hcgdj6c bgular width of the ceghi,z iw (jc jfc+14pds6r+-bntral diffraction peak?    $^{\circ}\,$

  Monochromatic light falls on a slits r68n.msh3.+cu 3q bos)h yeq 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 slit2 0kw+awf4 hhc that is $ 3.20\times10^{ -3}\;mm$ wide. Estimate how far the first brightish diffraction fringe is from the strong central maximum if the screen is 10.0 m away.    m

  A single slit 1.0 mm wide is illuminated by 450-nm light. What is the widthkbo p c syl()ir9.r4k+ of the central makr)9pro(4+ . cibl kysximum (in cm) in the diffraction pattern on a screen 5.0 m away?    cm

  Monochromatic light of wavelength 653 nm falls on a slit. If the ag n e73y:ty8;ia 7qkitzdt;w4 ngle between the first bright fringes on either sidi4k:7yady iwn;te;z 783tqgt e 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 beh5i oiqbda y-39ind a 0.0348-mm-wide slit illuminated by 589-a3y9obi -qi d5nm light?    cm

  When blue light of wavelength 440 nm falls on a single slit, 6q- 5v 5lgxyulthe first dark bands on either sid v6 55-lyuxgqle of center are separated by 55.0$^{\circ}\,$. Determine the width of the slit.    $ \times10^{-7 }\;m$

  When violet light of wavelength 415 nm falls2;ilyb,/9 5,-.zkahg z)zm ainxfan;g1i cvy on a single slit, it creates a central diffracting; zvi/ka), hi9c1za;ln.x ygfm za2yb5i,-on peak that is 9.20 cm wide on a screen that is 2.55 m away. How wide is the slit?    mm

  If a slit diffracts 650-nm light so that the diffraction ma v9;2knsemeqky c*+e0ximum is 4.0 cm wide on a screen *v9m ek2s;cey0eq kn+1.50 m away, what will be the width of the diffraction maximum for light of wavelength 420 nm?    cm

For a given waveleng4e/ )u y b.exb)tqu.bfth $\lambda$, what is the maximum slit width for which there will be no diffraction minima?

  At what angle will 560-nm light produce a second-ordee1 tywx(:x; dzr maximum when falling on a grating whose slits are 1yw :dx (xtez;$1.45 \times10^{-3 }\;cm$ 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 vml ozv8 q:nu50,y jk*have if the third-order occurs at an 188,qyl:5k*oz m 0v vnuj.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 diffraction grating is obserd/ ueax0 1f :anhg2:akved at aa:une2h x 0:ak1fd/ag 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 r6crfu5ol( ew )m8+ea$ 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()w dg,n; cwzh 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 if a grfs**6bn(o0;e(e hj o5 focy fyating with 6000 lines per cm is illuminated with 633-nm laser light? Assume normal incidenco n*5fojh ebfy(fes *;c yo6(0e.   

  Two (and only two) full spectral orders can be seen on either s ilh hizx+9xl00h qz)-ide of the central maximum when white light is sent through a diffraction grating. What is the maximum number of lines per cm fori 0 xzlhh-z+)9xh il0q the grating?    $ \times10^{ 3}\;lines/cm$

  White light containing wavelengths from 410 nm to 750 nm fall;n+ u7ci9q vsyfz yo-3s on a grating with s+v;qo9 i7n-z3 yyfuc $8500\;lines/cm$ How wide is the first-order spectrum on a screen 2.30 m away?    m

  A He-Ne gas laser which produces miq8j+ 7qv12hdjfage5 onochromatic 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 spec mt4f/2/yfcig* do g8za82hec trum 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, what wavelc 7 c-kc/uc-jgength is most strongly reflected at t kcu7c/cc-jg -he 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 5; cuk fzic /mmnun-3vmus63* dark fringes in Example 24–8 if the glass plates are each 26.5 cm fk-nn3c;suum 6z53*/uci m vmlong?    cm

  What is the smallest thickness of a soapuk3r2q3g6i jl 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 yellow kic+rmvx2)pzw95:8 c: szyjq ($\lambda\;=\;570\;mm$ 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 z6 z1-f0kowp wrings (not counting the dark spot at the center) are observed when 550-nm light falls normally fpok z6ww1-0zon a planoconvex lens resting on a flat glass surface (Fig. 24–31). How much thicker is the center than the edges?    $\mu m$

  A fine metal foil separates one edp1 kzn8z;gzg ;5kgy8qy(l)y,rku c *nd of two pieces of optically flat glass, as in Fig. 24–33. When light of wavelength 68, gnkzd k; zczp1ylu58*(q;r)ygy kg70 nm is 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 twe; 1fumu n3r-2u1cb ;cbyj-h ndq1at0o flat glass surfaces if the glass d-b-r y ;2ct 1a;qf 3neh0u1uujm1ncbis to appear bright when 450-nm light is incident normally?    nm
What if the glass is to appear dark?    nm

  vA piece of material, suspected of being ah4b-a: gw t)ne 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 alcohr- f6mrmx73l1v0mw stol $(n=1.36)$ 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 immer tav.l(2zhc47: vhaqox:,epxbvh6 2r sed in a liquid, the diameter of the eighth z hqa22c h:xlx7 ,.v h4(6pro v:avebtdark ring decreases from 2.92 cm to 2.48 cm. What is the refractive index of the liquid?   

  What is the wavelength of the light entyb -),e gka/msering an interferometer if 644 bright fringes are counted when the movable mirror moves 0.225 mm? kegy),- abms/   nm

  A micrometer is connected to the movabl:bvgtx x x58x,7(mo +0jwxdefe mirror of an interferometer. When the micrometer is tightened down on a thin metal foil, the net number of bright fringes that move, compared to the empty micrometer, is 272. What is the thickness of the foil? The wavelength of xxvw,ft+ x(xbe058g x mo7: jdlight used is 589 nm.    $\mu m$

  How far must the mirro7lmrj5 2ken 13hnd(-qrma4d or $M_1$ 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 iyn )t b,vnwf;1nterferometer (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 are counted to move past a reference li v1t)n ,wfybn;ne. 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 oriet.;q:h hj5wpepj2;fr/5 . a/mmlrpl rnted 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 ae ,7 fcakm2x0gir–glass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s angle for a diamond submerged in;x u-x-o)runi;d w 7au water if the light is hitting t;7)au xw r-n;od-uxiuhe diamond $(n=2.42)$ while traveling in the water? $\theta_{p}$    $^{\circ}\,$

  Two Polaroids are aligned so that the light passing through them/3dw;1qvbm(eb hvnrk 8*cp gq9r 4zt) is a maximum. At what angle should one of them be placed so that ( hb13kt z8w* qg;crnmdv)/p49eb r qvthe intensity is subsequently reduced by half?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be placed so as to 1 g-mpvd8gx,jaec.u4 reduce the intensity of th 4ugdx8jv p.1-ge amc,e incident unpolarized light to
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are oriente .p/ewz ai mqau61)6ped 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 oriented at 5emb :.f bd7ts38.0$^{\circ}\,$ 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 th lwd3-fq)m.qt9 gli* ie surface of water for light coming from beneath the surface? Compare to the angle for total internal reflection, and to Brewste lfw -i3qgt9 d)ql.im*r’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 pa da:.uokfm dbn) r:i)(i*le*gsses through five successive Polaroid sheets, each of whose axi fi.bd)*rikl ngm(o) d :*ea:us makes a 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength c7o1ie 9 kn7i2,aym3vkbf+k s$ 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 m pdwyo: f0aeu t35 o.zv)u*d-aountains or airplanes can interfere with the direct signal f-dvf uwyzp* 3uda.5)te:ao0 o 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 shf/1e u*mw6zn7 u nv1w)b wot3eparate sources passes through a diffraction grating with v/u*o ebf7w t3)6zmunw1h n1w$ 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 nv hbo,mj(6ofseifh z63..x+tm passes through two narrow slits 0.60 mm apart. The screen is 1.70 m away. A second source of unknown wavelength produces its secon(f o.jm,3sho6v+fz e xh6 b.tid-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 operating at 102.1 MHz broadcasts fq3g3yl x w xdf/lki+1n6f:++gqek7 sqrom 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+dexq qgf/3kni s x+g w1fqy:l6l7 3k+ 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 )c +ihgfawz;; 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 the doorway.i z)f;caw+;h g    $^{\circ}\,$ either side of the normal.

If parallel light falls on a single slit of width7(s73 9kw bm9g:avsw(d k sjrv 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. Wheu *1,yxizgg lu56*zjon normally incident*,uy6 g1zgouxz*ijl 5 460-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 grat 8 ak5mbtvsj-8 tr520ay+vspiing have if there is to be no second-order spectru5k v50pa t si2rjsyt- m8vb8a+m for any visible wavelength?   $ lines/cm$

Show that the second- and third-order spectra of white light produced by mf8h+ps ,fx+:iz(o/ppr +x b8)pnza za diffraction grating always overlap. What wif :)( 8+ p+ rz popxz8mbxap+fzs,h/navelengths overlap exactly?

  When yellow sodium lq2/ nzmzff3p )jbv01zrl -o0/gwn0 9paip bu ,ight, $\lambda\;=\;$ 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 andcxgm:aa 1tlyjm t.466 the pattern is viewed on ataat:6 4jymc6.m l g1x screen 2.5 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 minimum of,p y++t0knwknjx3 ) qa 150 nm thickness of it, whnk+qnytw pk, 3+ja) x0en laid on glass, is needed to reduce reflection to nearly zero when light of 600 nm is incident normally upon it? Do you have a choice for an answer?

  Monochromatic light of variable wavelength is incident normally on a thin shee8o9 bkwlx3s y8t of plastic film in air. The re8boyx 9l s8kw3flected 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 neededkhr u. pvmlu; ;fhs1)1 for an anti-reflective coating $(n=1.38)$ applied to a glass lens in order to eliminate
(a) blue (450 nm),    nm
(b) red (700 nm) reflections for light at normal incidence.    nm

  What is the minimum (non-zero) thickness for the air layer between two flat gl6i71(p;h1/ jg1lpqw txvt frsassgp7wq/1;rtsvh t li6pfx(1j1 surfaces if the glass is to appear dark when 640-nm light is incident normally?    nm
What if the glass is to appear bright?    nm

Suppose you viewed the light transmitted through a thin film layerepp+ kc,,zvf ;3 g-u17dreykbud on a flat piece of glass. Draw a diagram, similar to g,uefdp+r;7vp-c3 zyb kku ,1Fig. 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 horinmbdtu40j d )ol;z ys ds89y93zon is the Sun when light reflecting off a smooth lake is polarized most strongly? ds un9 yst 9)o;l4y0dzdm8jb3   $^{\circ}\,$

  At what angle should the avah:mcteb1. 1xes of two Polaroids be placed so as to reduce the intensity of the incident unpolarized light by anacb:e11.tvmh additional factor (after the first Polaroid cuts it in half) of
(a) 4,    $^{\circ}\,$
(b) 10,    $^{\circ}\,$
(c) 100?    $^{\circ}\,$

  Unpolarized light fa, zzle 2-grj/udqum-5lls on two polarizer sheets whose transmission axes are at right angles. A third polarizer is placed between the first twzz2 e-j lmd,rq u-g5/uo 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 gup80qtv8 6ae- ,vga ztheir 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 width 1.0 cm and is pointed at1ez- xn x4ufelhx81 a4 the Moon, which is approximately 380,000 km from the Earth. Assume the laser emits waves of wavelength 630 nm (the red nea1-xxz feh4xl 148ulight of a He-Ne laser). Estimate the width of the beam when it reaches the Moon.    km

  A series of polarizers are each pl* ,cq.bqfy-cqm sqn 8/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 xhm+y m g+-pu-$(n=1.34)$ 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-M t :vt qdncfdlbvt:+:-1 e0r(rHz radio waves in phase with each other. They dnt: t 0rt: c:f1q-vd(+brelvare 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 k a479w .d. mu 6rbqbpssk lf0y55l:oon5e*cv nm, enters a silicate flint glass equilaterb5f0s l v yn7w ps.dk5olcmuk 4q.5:9o6re a*bal 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 ke ygm:0j8*:y,kz zrqone 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