Does Huygens’ principle apply to sound waves? To water waves? Explain y3si xlpd: 1gko;y+2d.

What is the evidence that light i,7 m -fb9xjyg/eor 7yuayl5 3is energy?

Why is light sometimes described as rays and sometimes as 08pll 4 )dfe mqbyejqu;f9:t5waves?

We can hear sounds around corners, but we cannot see aroundfmmi 5 m :yps*h)t5r+kmd;ni( corners; yet both souns(pkmi yi 5;:+m tmn* md5)fhrd and light are waves. Explain the difference.

If Young’s double-slit experiment were submerged in water,gs8 bk89/k*ytzg 2tj d how would the fringe pattern be changbt 92jtk* sy/z88gd gked?

Monochromatic red light is incident on a double slit, and the interferencew186qd w sfen2 pattern is viewed on a screen some distance away. Explain ho2fqn8dse1w6w w 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 q):-cfss22;4qaru8rd ksnypr1 ;fly destructively interfere if their path lengths -f ss;)qur ;qrn2k18 lrd yfs4p: ayc2differ by how much?

Why was the observation of the double-slit interference*omow vgruzim03 w2euf20jl8)jv.p / pattern more convincing evidence for the wave theory of light than the observa0/if oe0p.or2 mg8l *vmjj 2z)uuv ww3tion of diffraction?

Compare a double-slit experiment for sound i qi.i 2zlzid (d*q1r z opm1.thk710bwaves to that for light waves. Discus(t1p.7ii kqzdz1i .ir 1om0* qd2hzlbs the similarities and differences.

Why doesn’t the light from the two headlights of a distant car producer*g8(,zktcu9vad.oq an interfe,9aotg( uqdv*rkz8. c rence pattern?

Suppose white light falls on the two slits of Fig. 24–7, but onejs ;hbbc8; zu33ygpk1.op+lj slit is covered by a red filter (700 nm) and the other by a blue filter ; 3y h8jg3kp.js lb+z1ucopb; (450 nm). Describe the pattern on the screen.

When white light passes through a flat piece of window glass, it is 6w5 j0;n5ogrrzqxls1 not broken down intsqjn r;0x6ro1 5lwgz5 o colors as it is by a prism. Explain.

For both converging and diverging lenses, discuss(ckeo0u58 tkcpz ,e(o3maf3 rg c2,vm how the focal length for red light differs 3uo ecpcrk508comg2 vmt ,(a(fz k,e3 from that for violet light.

A ray of light is refracted through thud1lmll+6silip p 91+ w:ev7dree different materials (Fig. 24–55). Rank the materials according to their index of refraction, least to9lp1pw1m++l:dls d i7i l6u ev greatest.

Hold one hand close to your eye and focus on w;88ceu lyz 3fa distant light source through a narrow slit between two fingers. (Adjust your fingers to ob;uw8cfe8l y z3tain the best pattern.) Describe the pattern that you see.

What happens to the diffraction pattern of a single slit if t izre6e a3ej 8iqw)4h4w*x0 cbhe whole apparatus is immersed iacej3ii0 * q e bhw4z8rw4e)x6n (a) water, (b) a vacuum, instead of in air.

For diffraction by a single slit, whrjz5w s2d y-amz4o70dat is the effect of increasing (a) the slit width, and (b) the wavelengthd0sda ym-owzz7 45jr 2?

What is the difference in the interference patterns formed (a) by two slits wp/ jt2be/xi;5e5jb e$^{-4}\;cm^2$ apart, (b) by a diffraction grating containing $10^4lines/cm$?

For a diffraction grating, what is the advant,gg6d xsc q9u3age of (a) many slits, (b) closely spaced xqdg9 3, ug6scslits?

White light strikes (a) a diffraction gradbb/p4u18 gu z d9wu;dting, and (b) a prism. A rainbow appears on a wall just below the direction of the horizontal incident beam in each case. What is the color of the top of the rainbow in each case? Expla;89d ud1guz p b/wudb4in.

For light consisting of wavelengths between 400 nm and ;seps: z+iu7 l:b2 ezv700 nm, incident normally on a diffraction grating, for what orders (if any) would there be overlap in the observed spectrum? Does your answeru lzesv;epi+sb : 27:z depend on the slit spacing?

Why are interference fringes noticeable only for a huz; t l2+p2lethin film like a soap bubble and no+uzle 2pht2l;t for a thick piece of glass, say?

When a compact disk (CD) is held at an angle in white z ano8 i)mo54j3u2kltlight, the reflected light is a full spectrum (Fig. 24–56). Explain. What would you expect to see if monochromatic light was 82t i ma )uo3ko5nj4lzused?

Why are Newton’s rings (Fig. 24–31) closer together farther from tdlr.cpp4 96n zhe center?

Some coated lenses appeare(lb 4mj-ww0y greenish yellow when seen by reflected light. What wavelengths wbyem 0j4(l -wdo you suppose the coating is designed to transmit completely?

A drop of oil on a pond appears bright at its edo wxu si.-t)-mi3tgw2zo 1 b-ages, where its thickness is much less than the wavelengths of visible lig i.)x3 i-mbt-t-2oo 1uwasw gzht. What can you say about the index of refraction of the oil?

What does polarization tell us about the nature of lpf n79n r8r*rnoaxd17ight?

Explain the advantage of polarized sunglasses over normal tinted sun5 y(93k3 qhda d3( qss.dotvwyglasses.

How can you tell if a pair of sunglasses isepbc- r r;a+u0zes )x, polarizing or not?

Two polarized sheets rotated at auv h; nr1+jkl97 0vlban 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 had zex:0ib pmi2xi:n0 ;h 6kuy/pno atmosphere?

If the Earth’s atmosf+7u6or.k nfz.yx 6eaphere were 50 times denser than it is, would sunlight still be white, orn+x.y.rz6u6ok7f fae would it be some other color?

  Monochromatic light falling on two slifv2m ,dr*n f1tts 0.016 mm apart produces the fifth-order frinvdm1 r* fn,f2tge at an 8.8$^{\circ}\,$ angle. What is the wavelength of the light used?    $ \times10^{-7 }\;m$

  The third-order fringe of 610 nm lis az;; lds.gs7: ,hkwcght 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 narrow slits 0.048,d6c 2-ypnqcm mm apart. Successive fringes on a screen 5.00 m away are 6.5 cm apart near the center of the pattern. Determine the wa- qc6dcmn p2,yvelength and frequency of the light.
$\lambda\;=\;$    $m$
$f$ =    Hz

  A parallel beam of light from a He-Ne laser, with a wavelength 656 nm, fall,(yc, toiy31 bg; cbtceas(6o: /aitvs on two very narrow slits 0.060 mm atsiaygt ,3:1; o6vb a/t,((e ccciboy part. 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 :q;h ;d8gjc spiyrp+4falls 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 away. What dqsg4: ji ;h;r8+cpyp is the separation of the two slits?    mm

  If 720-nm and 660-nm light passes through two slits 0.58vv7y)umuk*np62j zx( mm apart, how far apart are the seconyk7)*u6pmvx nz(2 v ujd-order fringes for these two wavelengths on a screen 1.0 m away?    mm

  In a double-slit experiment, it is found that bl u qgvh:0f)gdbfu,+9hue light of wavelength 460 nm gives a secon+h0 fqd gg,vhuf:)b9ud-order maximum 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 two openings cbqo r0 1.5nql5.0 cm apart in a board. At a point 2.0 m beyond the board, at what angle relative to the “straight-through” direction would the lr n5qb0o.1cqre be little or no wave action?

Suppose a thin piece of glass is placed in front of the lower slit in rt-afbon31: xFig. 24–7 so that the two waves enter th:rbt1x 3onf a-e 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 me-lo:t -nnz9x 1*c he500 nm is loe t 1e-n on-z*mx:l9hccated 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 544 nm )z r(+ jnhe yn1sor :tth2z8c5light. Find the distance between adjacent b5cjs1 torz):(nr8h2 e yhntz+right fringes on a screen 5.0 m from the slits.    mm

  Light of wavelength 480 n1z9y9ylzoswhr 7.4cy m5i3klm 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 ut+q*ukce4a* ) covers one slit of a double-slit apparatus illuminated by 640-nm light. The ce4 *kcu+qeau*t nter 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) exceed t7 i1cyc b2jgox:wa24phat of violet light (400 nm) in silicate flint glass? (22ci:gpjya 4b cx7o1wSee Fig. 24–14.)    %

  A light beam strikes a pic0 okvo 2ak5+ a n9(od67aqdiwece 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 light containin2nzabnig 52;lsy9xa g.t z3 kf l69h-xg 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 anguli ozg/ *y,*jlx*hhw -har width of the centra/ih**,y zh h*lj-xgowl diffraction peak?    $^{\circ}\,$

  Monochromatic light falls on a sllv-2ys+r ki n(w94vnxit 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 sy++kfz:o74wt/vxg wwm7y:d- ,aggew3c fx) vlit 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 illumiry hns/33tjci *l:ld pp rba60 0:*bhwnated by 450-nm light. What is the width of the central maximum (in cm) in the diffraction pattern on a screen 5.0 m awi3wh/t :h0jr0sncab3 l*p :dryblp6*ay?    cm

  Monochromatic light of wavelength 65 v)8sol k obt+:.hixz(3 nm falls on a slit. If the angle between tozo:b+il.( h vs)t8kxhe first bright fringes on either side of the central maximum is 32$^{\circ}\,$, estimate the slit width.    $\mu m$

  How wide is the central diffraction peak on a screen 2.30 m behind a 0.0348- ng 9lq,wq/3izu4 ziv:mm-widei n u :,zvi9g/z3ql4qw slit illuminated by 589-nm light?    cm

  When blue light of wave5qd 4 fp85yhb;jz 7vqap0 u(nulength 440 nm falls on a single slit, the first dark bands on eith58p(b7p 45q ;unvzda0yhu qjf er side of center are separated by 55.0$^{\circ}\,$. Determine the width of the slit.    $ \times10^{-7 }\;m$

  When violet light of wav3 v7hus4dlsnxfg(9, v elength 415 nm falls on a single slit, it creates a central diffraction peak that is 9.20 cm wide on a screen that is 2.55 m away. How wid 73lg nsh,dv(9x s4vufe is the slit?    mm

  If a slit diffracts 650-nm6 u*vyqkvj/wwvnq ,+ 7 light so that the diffraction maximum is 4.0 cm wide on *vk wy+v/jvqw,7qu 6 na screen 1.50 m away, what will be the width of the diffraction maximum for light of wavelength 420 nm?    cm

For a given wavelength ry5 nn9z+tbc;,j s0if $\lambda$, what is the maximum slit width for which there will be no diffraction minima?

  At what angle will 560jun)e i)h9:p r-nm light produce a second-order maximum when falling on a grating whose hej p 9:)urni)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 whts wz 5aeh7628p7gkk;,+ jacn; qvoa grating have if the third-order occurs at an 187pzahkgw65+a ;2vn8; s o7qhcwkte ,j.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 diffr mwo5x8qj96lc*cjpvp0z8 u m-action grating is observed at a 1cp8l 9 c6wqj8ojmm0pv u x-5z*5.5$^{\circ}\,$ angle. How far apart are the slits?    $\mu m$
At what angle will the third order be observed?

  A diffraction grating 0o /kjb4egw1yz(u 2d2t( ir hl 69irap*1mfno 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 vxa02*1 ssa vn/ql9 alon 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 spectrolj)2z 6)5szwe pv 5qgal order that can be seen if a grating with 6000 lines s6v )5pj2zlzwo5)e gqper cm is illuminated with 633-nm laser light? Assume normal incidence.   

  Two (and only two) full spectral or7g v--xll ftw;ders can be seen on either 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 gratinfvxw- glt7l ;-g?    $ \times10^{ 3}\;lines/cm$

  White light containi4 l xka2,m l4bo/(qwclng wavelengths from 410 nm to 750 nm falls on a grating with (o4mxbkwl4ca2lq /, l$8500\;lines/cm$ How wide is the first-order spectrum on a screen 2.30 m away?    m

  A He-Ne gas laser which produces monochr x9udv f4z9ik2omatic 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 spectrutx(xd :44ngn s l8;wyum 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 wavelength is most strongly ryo o wg4)* wr6ne76+xt7eh whjeflected at the center of the outew7 *ynge74tw+wo h6r)6xh j oer surface when illuminated normally by white light? Assume that $n\;=\;1.34$. $\lambda$ =    nm ,which is an    -  

  How far apart are the dark friy i4grj-6i(r onges in Example 24–8 if the glass plates are each 26.5 cm long?g- 6oij( r4ryi    cm

  What is the smallest thickness of a soap fi0y 1 e:g(lcb b8q1debqdz(x+glm $(n\;=\;1.42)$ 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 yellowpdz6 g -q(u9fi ($\lambda\;=\;570\;mm$ 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 (no6*+l5h6m9 x ndcno9qeezxrh770ff/ k8jiarzt 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 mrf* zidjm870 cxh e6ra/5 9xz9no7e nh+qf6 lkuch thicker is the center than the edges?    $\mu m$

  A fine metal foil sepw8.ptg -hv0 tsarates 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 t.h-tp vw80 sgthick is the foil?    $\mu m$

  How thick (minimum) lqrqf ks9hvc) 59:i 7lfs /u/dshould the air layer be between two flat glass surfaces if the glass is to appear bright when 450-nm light is inciden isrf9:l/ d fscl9 hqk/vu75q)t normally?    nm
What if the glass is to appear dark?    nm

  vA piece of material, suspected of being a stolen0:m x+k6c qi+ads: ie2ka r.wgnfaa 07 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 alcohole ifmbi4 ( jgwc3tt 9 ycx;:3i;1j3qdr $(n=1.36)$ 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 immers f7y j pltd(*wbj xgc,4/k*7sped in a liquid, the diameter of the eighth dark ring decreases from 2.92 cm to 2lt(*7*k jf 7gdpxyjp /4cwb s,.48 cm. What is the refractive index of the liquid?   

  What is the wavelength of the light entering an inpro;x;mb-u v yq nnf6:+yn:k/terferometer if 644 bright fringes are counted w:nxpy+ kq-rfm: nv;; ybn/6o uhen the movable mirror moves 0.225 mm?    nm

  A micrometer is connected to the movai gshz 8 3gfq)jkp...q oaan+*ble 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.gqzpahkfo i8*.gq a ).+3s.jn What is the thickness of the foil? The wavelength of light used is 589 nm.    $\mu m$

  How far must the mirrb*: s7yhwbrq ek4 2hnw9t-2 aeor $M_1$ in a Michelson interferometer be moved if 850 fringes of 589-nm light are to pass by a reference line?    mm

  One of the beams of an interferometer (Fig. 24–59) passes through a 3s5urrgx2gp)g i-5v+ be (wilsmall glass container containing a cavity 1.30 cm deep. When a gas is allowed to slowly +lr5gwre2 -b3)xv pigigs5(u fill the container, a total of 236 dark fringes are counted to move past a reference line. The light used has a wavelength of 610 nm. Calculate the index of refraction of the gas, assuming that the interferometer is in vacuum. $n_{gas}$

  

  Two polarizers are oriented at wl 0dfjhv i041/5dj(az :vrfk65$^{\circ}\,$ to one another. Unpolarized light falls on them. What fraction of the light intensity is transmitted?   

  What is Brewster’s angle for an 3.xf(yphha vk8fw f40 air–glass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s angle for a diamond submerged in water nu/ 4sqykyw+t3+7 opiif the light is hitting the di 7 o/ypq+ ykt+su43nwiamond $(n=2.42)$ while traveling in the water? $\theta_{p}$    $^{\circ}\,$

  Two Polaroids are aligned so xh:2vfv p2wo) that the light passing through them is a maximum. At what angle should one of them be placed so that the intensity is subsequently)22v vx:fhw op reduced by half?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be placed so as to reduce the gve;p :j-qh yytz4sp8a5iesvvb 2(2. intensity of the incident ujzvs aeh .yvbt; ep2:ygiqvs25 (p 8-4npolarized light to
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are orientua9 zye/hyeph+c3 8+x me6g+wed 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 a47f k4wstda6a 8o3xw ut 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 surface of wateryj9, r)t5xljz for light coming from beneath the surface? Compare to the angle for total internal reflection, and to Brewster’s angle from abjj z, 9xyl)5trove 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, e tg-n bz(j 2)whe9juv-ach of whose axis mt)en j2- wh uz9-vbgj(akes a 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength hk74e+wnye .j$ 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 moun 1)p86chqdd iefh4dsg v; .ow;tains or airplanes can interfere wi d4d 1 .;fvwp8)d;ge hi6csoqhth 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 wiuq2tll(v68 wj vql8,kth t,l2wqv88(ul l6jqv k$ 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 v g9 7ddjo( wja(k(/vfpz. nn.narrow slits 0.60 mm apart. The screen is 1.70 m away. A second source of unknown wavelength produces its second-order fringe 1.33 mm closer to the central maximum thandn(f9vd /go.wv(aj. j(z kp7n the 590-nm light. What is the wavelength of the unknown light? $\lambda_2$    nm

A radio station operating at 102.1 MHz broadcasts tdo46 + h-qod hp 2nk31qxh)mwfrom 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 horizontally in both directions.dmhdp21- +whqx k3 4)6tqnoho 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 botbbn;6(i7 3ihe0,x 8sklpowack from an outside doorway 0.88 m wide, and blows a whistle of frequency 750 Hz. Ignoring reflections, estimate at what angle(s) it is n eb 7(86iblo ;h,ixskt3onw p0ot possible to hear the whistle clearly on the playground outside the doorway.    $^{\circ}\,$ either side of the normal.

If parallel light falls on a single sllgb(ykbr ssd: 7;u0 o4it 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 paralltaj h +2,dc8yybf9li+h k1l8fel lines across them. When normally incidentliff, 1a+h9ldj8y +y82btc hk 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 hy u ax,ei:e+do9yc2/r cjw9-eave if there is to be no second-order spectrum for any visible wavew ,c :/u eo+ecder9yyi-2j x9alength?   $ lines/cm$

Show that the second- and third-order sper89c l;a5of qci 7bkf;ctra of white light produced by a diffraction grating always overlap. What wavelengths overlap exactl5;c 8fkbqor9 ;li7fca y?

  When yellow sodium ligh*jvraj2o1x . ;z btj5dt, $\lambda\;=\;$ 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 onnjjw xuux/l*6;o j+j0 a screen 2.5 m from the grating. The incident light beam consists of uxwj;nj/+0 uoljj *6xtwo 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 materi,tweyl ./dx7 aal if a minimum of 150 nm thickness of it, when laid on glass, is ,aye7t/ wlx. dneeded 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 nq.aai 8 yc s14klzv0l/e 4mu,tormally on a thin sheet of plastic film in air. The reflected light is a minimum only f 84t lksyzc4eual0i,q1 /vma.or $\lambda\;=\;512nm$ 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(rwj pp- qstvc4:3g )s 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 yqpg h/0t;*pqz-uc.mglass surfaces if the glass is to ap0pc qghpuz;* y-./qt mpear dark when 640-nm light is incident normally?    nm
What if the glass is to appear bright?    nm

Suppose you viewed the c8sgpr 7zau 1;light transmitted through 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 mc;g zpr a1u8s7inima. 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 t+y 3zbb) uv6tmhe Sun when light reflecting off a smooth lake is polarized most str3b)vzt my+b6uongly?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be placed so ljbj2*yyb 05b as to reduce the intensity of the inciden by2y*0lj5bjbt unpolarized 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 fase bsg32* z.n /b/z0+tgr ,x wgln+wuylls on two polarizer sheets whose transmission axes are at right angles.wnb/ yz sg3gu*gext+/s 2rb, +0.lnzw A third polarizer is placed between 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 plqt6jlg .gx0dfgrfb8 fg3: 2 1daced in 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 slen8g) rfzri08 it of width 1.0 cm and is pointed at the Moon, which is approximately 380,000 km from the Earth. Assume the laser en f)0rr8z8igemits 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 polarizers uqum/k f98ct* 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 irt8/ m;g8pj v$(n=1.34)$ 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 cyz-v1 /,d-c hswvvk(phase with each other. They are locatedd/ 1w zkh-,cyv -vv(cs 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 cof)k qy)e4 9g jy*acyv c+b,l4untaining two wavelengths, 420 nm and 650 nm, enters a silicate flint glass equilateral prism (Fig. 24–abg4yj,ukfvy+y* q ) elcc94) 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 fl*mu7 6utrw7,r 4 jymjnat 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