Does Huygens’ principle apply to sound waves? To water waves? Explainhpv4j10j tlsyf,zk: qt )qo8 2.

What is the evidence that light is energ;p/yqgv dg+r+y?

Why is light sometimes described as rao:wh n6kp 7-(m:w+c uxkz)u)q1ss k -y tp(enwys and sometimes as waves?

We can hear sounds around corners, but we cannot see around corners; yet both so 06i;)z k94lbtmwmb lgund and lm;g lm6bzl i9 bw0t)4kight are waves. Explain the difference.

If Young’s double-slit experiment were submer1uhvg,abumy2, c3d- mged in water, how would the fringe pa-dya2vg1h u mcb u3m,,ttern be changed?

Monochromatic red light is incident on ak8*a5l/ytb 2h:msoj s double slit, and the interference pattern is viewed on a screen some distance away. Explain how the fringe pattern would change if:/5s sblaoy*h8j2mk t the red light source is replaced by a blue light source.

Two rays of light from the same source destructively interfere if their path6y**s vpg, kto lengths di6*,*ogypktsv ffer by how much?

Why was the observation of the double-sl r-*7pwenvgk 7it interference pattern more convincing evidence for the wave theory of light than the observkgnre*pw77v - ation of diffraction?

Compare a double-slit experims kaeg*c8( wu3ent for sound waves to that for light waves. Discuss the simae8kw sg*u c(3ilarities and differences.

Why doesn’t the light from3a0y( fi 6hkvf the two headlights of a distant car produce an interference patf(6i kf0hy3a vtern?

Suppose white light falls on the two slits of Fig. 24–7, but one slit is +a.,ajiaie*bu jgn8*covered by a rjj ,n.uib* aa8ige*a+ed 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 piece of window glass, it is not brokef9 b -*8 dc5z;l m23fgvixzgaln do*gifz xl3-gdbl9 mf za25cv ;8wn into colors as it is by a prism. Explain.

For both converging and diverging lenstmp2z2.4v3bo 4 knr*-j1 2luo rhcaases, discuss how the focal length for red light differs from that for violet light*1rc. n2oaza -tv2hsb 3mu o4 rj2kl4p.

A ray of light is refracted through three differeng7d.;1oyvtdg:l oxt/t materials (Fig. 24–55). Rank the materials according to th7vyd:;1tt og xl.odg/eir index of refraction, least to greatest.

Hold one hand close to your eye and focus on a distant light source through a na/z8;y. irk5 td4epiurrrow slit between two ./iekp;u54zrry8t di fingers. (Adjust your fingers to obtain the best pattern.) Describe the pattern that you see.

What happens to the diffraction pattern off uexqk( ar4w(0l: m5c a single slit if the whole apparatus is immersed in (a) 4ef q5 (m(kux0cw ar:lwater, (b) a vacuum, instead of in air.

For diffraction by a single slit, what is the effect of increasing 4k k/p0;, onwtr agzr:(a) the slit width, an0koz ,pa4 tr;w:r/ kgnd (b) the wavelength?

What is the differencet/)a2 yq vxi)m**)gybtz5zpf in the interference patterns formed (a) by two slits $^{-4}\;cm^2$ apart, (b) by a diffraction grating containing $10^4lines/cm$?

For a diffraction gratinzwa:a x(qh-0m g, what is the advantage of (a) many slits, (b) closely spac:azx- (qwh0 amed slits?

White light strikes (a) a diffraction grating, and (b) a prism. A raigrq39vnk 9.ownbow appears on a wall just below the direction of t gv 3q9kwo9rn.he 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 400 nm and 700 fvsp,/ /; hdumnm, incident normally on a diffraction grating, fohdumvfs/ / ;p,r 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 li q9v7yvj):gb m-lqlh* ke a soap bubble a bqv h7yj-*ql:)g9lmvnd not for a thick piece of glass, say?

When a compact disk (CD) is held at an angle in white light, the reflzz 2wr/q .3cwnected light is a full spectrum (Fig. 24–5 cnw32 .rqz/wz6). Explain. What would you expect to see if monochromatic light was used?

Why are Newton’s rings (Fig. 24–31) closer together farther from 8 8w:q .+zw4-owauwr lna byr9the center?

Some coated lenses appear greenish yellow when seen by reflected light. Wvx 5j f,81tmiphat wavelengths do you suppose the coating is designed to transmitpi1jmvf5 xt ,8 completely?

A drop of oil on a pond appears brig8/ap5; .icc31 ovzhfp7nb x lyht at its edges, where its thickness is much less than the wavelengths of visible light. What can you say about the index of r 7hp3.cx1;yp vifnbcz /a58loefraction of the oil?

What does polarizatio8r3-6r/bnw b3vck/mx x c q8wvn tell us about the nature of light?

Explain the advantage of polarized 8teto0)bh5 7p tu.p mpt,s8blpag 37ysunglasses over normal tinted sunglasses.

How can you tell if a pair of st()u ny,d3dms knky0+unglasses is polarizing or not?

Two polarized sheets rotated at an a9ekzgq :i5m6 vn ;l; ezr/zlg.ngle 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 Ek ecm a.;23pvnwz8z n6arth had no atmosphere?

If the Earth’s atmosphere were 50 times dens:9f-mh tf, hm-b4exxe er than it is, would sunlight still h-ef9h tmfxe b4:mx, -be white, or would it be some other color?

  Monochromatic light falling on two slits 0.016 mm a,ee:m)-kih5:btgfjks 1vm; ppart produces the fifth-order fringe at an 8; p-mgk):1j e is:,mft5bhkve.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 aejuaj /n w0g ,o)b-yujh5.n-b ngle 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 apartsp5z3ykm, d,tow a6xl (/fs.o . Successive fringes on a screen 5a5d3./t lo( wypx,omskz6s ,f.00 m away are 6.5 cm apart near the center of the pattern. Determine the wavelength and frequency of the light.
$\lambda\;=\;$    $m$
$f$ =    Hz

  A parallel beam of light from3 9lyw j3nw8nc a He-Ne laser, with a wavelength 656 nm, falls on two very narrow slits 0.y3nnwcjw9l8 3 060 mm apart. How far apart are the fringes in the center of the pattern on a screen 3.6 m away?    cm

  Light of wavelength 680 nm falljew5r h3 k3g (*j+qd6sei j5hzs on two 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 aqz6r5 +3 hs(ee3jkhdw5gij j*way. What is the separation of the two slits?    mm

  If 720-nm and 660-nm light passes through two slits 0.58 mm apart, howf in(8sb * z ,7qt,,gc4ba4mz ,wmhihj far apart are the second-orde7 4c,mitz n ,,h*bbqmjsw h(fziga8 4,r fringes for these two wavelengths on a screen 1.0 m away?    mm

  In a double-slit experiment, it is found that blue lightf.m3iv*ao ) ab of wavelength 460 nm gives a second-order maximum at a certain location on the screen. What wavelength of visible lig*io .vba 3mf)aht would have a minimum at the same location?    nm

Water waves having parallel crests 2.5 cm apart pass through two opening;w9ryh799- fv 3/afz)l dgg v/ccs+xsx.hq xm s 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 there be li-dgz.9wx/msq/;9cfrxy 9c)h a7gfvl vsxh+ 3ttle or no wave action?

Suppose a thin piece of glass is placed i8ay ,yf qwb5 f(sy j/xx3v4hd2n front of the lower slit in Fig. 24–7 so tay4f8fd 2 v/xs(,byh5qywx 3 jhat 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 ligha1 w,ocn9ka d1edv r+,t 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 bee o 1va ddwrakn1,+c,9 located?    mm

  Two narrow slits separated by 1.0 mm are illuminated by 544 nm light. u0zi (ccd( a h,yzv.b-Find the distance between adjacent bright fringes on((ui,hvbz zc.0y-d ca a screen 5.0 m from the slits.    mm

  Light of wavelength 480 nm. yl.djrc )5 f+wq9ayz 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 one sp 5 f p,v(z1xsdi*osv0jz/8bz lit of a double-slit apparatus illuminated by 640-nm5 sj/d8,0xzpop ( vs zi*vzb1f light. The center point on the screen, instead of being a maximum, is dark. What is the (minimum) thickness of the plastic?    nm

  By what percent, approxi dc /hu,3irmj.mately, does the speed of red light (700 nm) exceed that of viocrh .j/um 3,dilet light (400 nm) in silicate flint glass? (See Fig. 24–14.)    %

  A light beam strikes a piece of glass at a 60.5uf :vw* c7dbb shdv(8oo*ss100$^{\circ}\,$ 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 containing twobdwqsb,1/ jl9 cagyi16 uk 33y 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.cnippd8zhn307a fi- 80440 mm wide, what is the full angular width of the central diffraction pe p8zdp-ni0cfa73 8hniak?    $^{\circ}\,$

  Monochromatic light f)o)t7ec:yjj salls 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+ohu;dlu *;(qfgc h 5p 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 wide is illuminated by 450-nm light. What is the width v9/+sylxqw -c of the central maximum (in cm) in the diffraction patter/vs-l 9q+wycxn on a screen 5.0 m away?    cm

  Monochromatic light of wavelength 653 nm(zxd n f p.cpyqj j8 l-sx5-jd26)g(se falls on a slit. If the angle between the first bright fringes on either side olgjf .djxjsdqze 8psy2 n)-cpx-56(( f the central maximum is 32$^{\circ}\,$, estimate the slit width.    $\mu m$

  How wide is the central di+3ke3wsqh .;sk m(gc 6vpix8d ffraction peak on a screen 2.30 m behind a 0.0348-mm-wide slis s;6i pewcgv+3h3k8 .qmkxd(t illuminated by 589-nm light?    cm

  When blue light of wavelength 440 nm falls on a single slit, the first dark ba6xbaxil e9qgl7+; * ucnds on either side of ceil6aeg c9x;buq 7x* +lnter are separated by 55.0$^{\circ}\,$. Determine the width of the slit.    $ \times10^{-7 }\;m$

  When violet light of wavelength 415 nm falls on a single slit, ic8. cfe cnou+2t creates a central diffraction peaou.c8 e+c 2fcnk 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 lifd:b9v+7h)og7c c 9li -vbzaygy3;q0y oxy8oght so that the diffraction maximum is 4.0 cm wide on a screen 1.50 m away, what will be the width of t;8 o+7bhdycblv9avof097yg) yqz y3- cx:oighe diffraction maximum for light of wavelength 420 nm?    cm

For a given wavelengtm0epj 3d,jt- bh $\lambda$, 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 maximur3 waio8y:z v /pvia72m when falling on a gratinw:8/i y2a vopaiz v7r3g whose 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 gra qdc lsn(w2t, 85hen y)dsg6r;ting have if the third-order occurs at an 18.ch( dn5d8lgn6s eqr 2sty)w,;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 obser qd* 4q.m)s9tw qbv3ujved atw93 .jdm q) *t4ubsqvq 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 haaq,j j4qx jka6g5akwi48k 4wbk-xu1) k dn+: bs $ 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 a a0rm,ni 4 0dxn$9700-line/cm$ 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 grating with 6000 n b-04uty9fif ;eaaqd-w8t-t lines per cm is i--9d;y8ainttu0 ff4ab tqw - elluminated with 633-nm laser light? Assume normal incidence.   

  Two (and only two) full spec;9ifxsn ;n; o3mzin)3 bmdl-qtral orders can be seen on either side of the central maximum when white light is sent through a diffr- minqd;b;9)in3fn; xz smo3 laction grating. What is the maximum number of lines per cm for the grating?    $ \times10^{ 3}\;lines/cm$

  White light containing wavelengths from 410 nm to 750 nm fal(box i3oh yxjqv.4v t-cp5w)0ls on a grating with- v 0chbyv4p)t5xwioqo.(xj3 $8500\;lines/cm$ How wide is the first-order spectrum on a screen 2.30 m away?    m

  A He-Ne gas laser which produces monochromatic djt :zdrf 6)f9light 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 measumw otlt:2z3e qy mnqj)4w 3d9 vb2r3l7red 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 reflected am h5*/qv x+itft the center of the outer smtiv f*q x5h/+urface 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 24–8 if the glass plates arj:t+rsf4jyegd s)t:g(7 omg6e each ej4yr gsg f)sgd:t6(7:om+j t26.5 cm long?    cm

  What is the smallest thickn6 qn w/e9ou:/ lqfuwy:ess 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 greenis.vx(u bdc;zm+ h 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 (not counting the dark spot at+gt8+s -kgiwk pg5f m, 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 t 8,wit5gf-+g+pkk smg he center than the edges?    $\mu m$

  A fine metal foil separates one em2-a t/ qy9zpcv yy2 wc.7eof:nd of two pieces of optically flat glass, as in Fig. 24–33. When light of wavelength 6727 p:9emy2zc-f.ac y ow/vyt q0 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 two flat glass surfacefr rp uot(t ,(.vxgx ,+.v6g(qog tw1bs if the glass is to appear bright whev.wg6 ,.x(qg bf(tvt, pruox1+gr( ton 450-nm light is incident normally?    nm
What if the glass is to appear dark?    nm

  vA piece of material, suspected of being e m.j/w*wevz) sh z /e1qcnl3qw78:zuz 6pte8a 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 alcoh o i-r,ai.vmg.ej3u8sol $(n=1.36)$ 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 apxu8g9m ayh +n,al*az4paratus (Fig. 24–31) is immersed in a liquid, the diameter of the eighth dark ring decreases from 2.92 cm to 2.48 8m za4 + *xun,9yagalhcm. What is the refractive index of the liquid?   

  What is the wavelength of the light entering an interferometepfz: ombba9o286vw (rr if 644 bright fringes are counted when the movable mirror moves 0.225 mm?9bab8(zr6 2mfw:pov o    nm

  A micrometer is connected to the movable mirror of ar; u (fr1f9wj9e81s w :qlazdsn 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? Th1reuqljfa 18d9f r; (w:zs 9swe wavelength of light used is 589 nm.    $\mu m$

  How far must the mirvlnd3 k fcdca1k/-.y,h .z* v:/oor wvror $M_1$ 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 t jae;tce,i6+ jhrough a small glass container containing a cavity 1.30 cm deep. When a gas is allowed to slowly fill t6 jaj; ,eeic+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 atjupp9r/fo,/p* jdmzapw 1 (c8 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 ainp61d7 / vdm s-ng+nyur–glass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s angle for a diamond submerged in water if the ligh16nn 7-j x f(;f2smv uxyoy;kjt is hitting the diamond1 oxf j6jn 2fyv(y7u sm;;x-nk $(n=2.42)$ while traveling in the water? $\theta_{p}$    $^{\circ}\,$

  Two Polaroids are aligned so that the light passing thrz rs-3)l6 f5iqxh pb,pough them is a maximum. At what angle should one of them be placed )z3f b,l5p h-xp6iqrsso that the intensity is subsequently reduced by half?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be placed ,k qxbn)onb9ng4 me0*so as to reduce the intensity of the incident unpolarized lighom)9q4n,bknx * b neg0t to
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are orvqx2:5/3zt*o s( h5w6 vthg)cssk gymiented 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 38jsjz ce 1qyb.td+nlhw6-8l *3 .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 thuq xx7rse9r/ 8e surface of water for light coming from beneath the surface?u x 9rr8xqe7/s Compare to the angle for total internal reflection, and to Brewster’s angle from above the surface.
If the light is coming from water to air, $\theta_{p}$    $^{\circ}\,$For the refraction at the critical angle from water to air $\theta_c$   $^{\circ}$ If the light is coming from air to water $\theta_p'$   $^{\circ}$

  Unpolarized light passes through five successive Pol-o w e8b0viw-uaroid sheets, each of whose axis mak0--w 8evibu owes a 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength by .gk 0wjcb.:$ 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 aiyl(/y5z ;l ycsrplanes can interfere wi lsyl/; y(czy5th the direct signal 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 separate sources passes through a diffraction grating wrj kh42 w:vt-fith f4 k2t:rh-v wj$ 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 apart. The swdep8 4e ncbof)x8v4:creen is 1.70 m away. A second source of unknown wavelength produces its second-order fringe 1.33 mm closer to the central maximum than the 590-nm light. What is the wavelength of the unknowef8w4: nex pb)8ocd4 vn light? $\lambda_2$    nm

A radio station operating at 102.16q fc76yjc1b .pwqu;k 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 exteq.7ycf;1kqwucb j6 p6nding horizontally in both directions. If the midline is taken as 0$^{\circ}\,$, at what other angle(s) $\theta$ is a maximum signal detected? A minimum signal? Assume all measurements are made much farther than 8.0 m from the antenna towers.

  A teacher stands well back from an outuqd ccttwjj9y4;j6 2( side 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 playgr29u6w;(cd jtqycj4 jtound outside the doorway.    $^{\circ}\,$ either side of the normal.

If parallel light falls on a pa(w *xpy)lj i 2bdt6:ukr:8i single slit of width D at a 30$^{\circ}\,$ angle to the normal, describe the diffraction pattern.

  The wings of a certain beetle have a series of parallel lines across them 8y q,)ystf;xv. When normally incident 460-nm light is reflect,8xsfqy)y;v ted 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 mustuw..h37 )pu5u3z aj( ndgdaru a grating have if there is to be no second-order spectrum for any . uazun 533.j(u7)dwd apuh grvisible wavelength?   $ lines/cm$

Show that the second- and third-order spectra of white light proc cgpd(jw3)k 8duced by a diffraction grating always overlap. What waveleck(gdw)3 jp8cngths overlap exactly?

  When yellow sodium light, awuf91o j 6fq* )t0hir js2/uj$\lambda\;=\;$ 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+/)f9lsi lffi with and the pattern is viewed on a screen 2.5 m from the grating. The incident light beam sfl +)if f9/ilconsists 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 material24 p) ot0s tdhz3hmcq) if a minimum of 150 nm thickness of it, when laid on glass, is needed to reduce reflection to nearly zero when light of 600 nm is insm phz2co hd)0q 4)tt3cident normally upon it? Do you have a choice for an answer?

  Monochromatic light of variable wavelength is inxmbb. zn+ox.1ruzw+r206 zuj *t* xqgcident normally on a thin sheet of plastic film in air. The reflected light is a minimum og6 w zz.1ubbx2rxqrn+u*zx +* m.tj0only 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 negna o077 cw(qbeded 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 layel 8+pb3mgdgnwphtv61i l4 4 -dr between two flat glass surfaces if the glass is to appear dark when 640-nm lm4l d dpwh n 8-3plt1+i6b4vggight is incident normally?    nm
What if the glass is to appear bright?    nm

Suppose you viewed the light transmitted -e ky c -)kxqbsxy,dwn2 7-1c-.lg vcvthrough a thin film layered on a flat piece of glass. Draw a diagram, similar to Fig. 24–30 or 24–36, and describkn1-)xv,b2-wv. sqlc- y 7 xegc yk-cde 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 of gvrs1a 4x 0e0ls;z2nzf a smooth lake is polarized zr;4ln0sz1gve 0 asx2 most strongly?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be placed so as to reduce the e ;qqz-oi9 hq;)xhpa cfz5i5n54ug v9intensity of the incident unpolarizeavq-hc59o) 4inhfq ;ize9q5 gp;zxu 5d light by an additional factor (after the first Polaroid cuts it in half) of
(a) 4,    $^{\circ}\,$
(b) 10,    $^{\circ}\,$
(c) 100?    $^{\circ}\,$

  Unpolarized light falls on two polarizer sheets whva8-*6si us;s5aze 1j nc 0r/b7 pbbnzose transmission axes are at right angles. A third polarizer is placed between the first two so that its axis makes a 62v*6jp;bz8ssc zue 7n 5 asba01r/ nib-$^{\circ}\,$ 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 0rmew cv c7hjq-d f,8+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 throu5u/- dm4dubvkgmz13ul o(fv 4w3qj 4n gh a slit of width 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). Esujq zv4543 m -no4lukudd/bf(vgw3m1 timate the width of the beam when it reaches the Moon.    km

  A series of polarizermu m6i7 mhwt)3y:yyz9s 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 e c3)o4dm 57pawly5cl$(n=1.34)$ 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 wi5t2y ilrbe 2rui) k3s)th each other. They are located arsb23 )uet5 l2)ikyirt 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, enthxaenx.,(j2 cers a silicate flint glass equilateran(h 2.a ,excxjl 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 onegz)nfb 9fb.ilzpr: 6f nm2:n: 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