Does Huygens’ principle apply t 7u pa6d4g5ysuuwupbn3+:uq/y 7i sw)o sound waves? To water waves? Explain.

What is the evidence that ev;ph.c gvc.3udk; s:-r aqh0light is energy?

Why is light sometimes described as rays and sometimes as waveh97b 8hlro uf)s+it 0xs?

We can hear sounds around corners, but we cannot see around nyjw6ttw b/6.corners; yet both sound and light are waves. Explain the diffew6bttn/ y j.w6rence.

If Young’s double-slit experiment were submerged in water, how would the frinr)-rn8i8 xx8e r ;s-2dkkrd jjge jx)rnjrr8-s ; kr828 - kxddeipattern be changed?

Monochromatic red light is incident on a double slit, and the uo+kx c,c +y5g6hyi4uinterference pattern is viewed on a scre,iyoh4+yck56xu + c guen some distance 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 destru5(rce: cuy2s+ qcz1xvctively interfere if their path lengths differ by hc+r(ces5:uc1v qyx2 zow much?

Why was the observation of the double-slit interference pattern more c/sin ff;/lo3convincing evidence for this/ocff 3/; lne wave theory of light than the observation of diffraction?

Compare a double-slit experimay(h7 rxt)dqm 36a l+ment for sound waves to that for light waves. Discuss the similarities and differencemlq6xa+)( mtday r7h3s.

Why doesn’t the light froh, ,gn/pugf.gm the two headlights of a distant car produce an interfgf un ,gg/.h,perence pattern?

Suppose white light falls on the two slits of Fig. 24–7, but one sliu i :0s-qior9 yyih3y7t is covered by a red filter (700 nm) and the other by a blue filter (450 nm). yy o9iiuh:r7 s0-yqi3Describe the pattern on the screen.

When white light passes through a flat piece of window glass, ij;,ff zwhdi:c7r)h v1 p*dwi0t is not broken down into colors as it is by a prism. Explain,ddp;c1fw0)ir wzivhhf : 7 j*.

For both converging and diverging lensl 3 ahiz8d;v-oes, discuss how the focal length for red light differs from that for violeda;zhol38- vit light.

A ray of light is refracted through three different materiaej 1ei.hu/0b mls (Fig. 24–55). Rank bu.ej e/mi01h the materials according to their index of refraction, least to greatest.

Hold one hand close to your ey4mojzmda/q) 7e and focus on a distant light source through a narrow slit between two fingers. (Adjust your fingers to obtain the best pat)4m o/zjda m7qtern.) Describe the pattern that you see.

What happens to the diffraction pattern of a single slit if the whole av whp83/vc;1mnrh ,xzpparatus is immersed in (a) water, (b) a vacuum, instead of in aic; vhxz/rv 13n ,wmp8hr.

For diffraction by a single slit, what is the effect of increasing (ayj l+)4bjvj*1j9 vd k6;begpt) the slit width, and (b) the wavelengge; jj)v lv1b6t4 b9+pjjdy*k th?

What is the difference in the interference patterns .82s3n ldt8df4)rru 8 gxggecformed (a) by two slits $^{-4}\;cm^2$ apart, (b) by a diffraction grating containing $10^4lines/cm$?

For a diffraction grating, what is the advantage of (a) manyfv- zvux4q / g5kftf3, slits, (b) closely spaced-v /xk uqf5z3 4fgv,tf slits?

White light strikes (a) a diffraction grating, and (b) a prism. e dk;tzgm 76:yA rainbow appears on a wall just below the directet ;dkzg:67ym ion 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 wavelew-bzd7z.q wq*rvr 6 citdb1;9 ngths between 400 nm and 700 nm, incident normally on a diffraction grating, for what orders (if-.* i 6z;rtrcwbdd71qq9vwzb any) would there be overlap in the observed spectrum? Does your answer depend on the slit spacing?

Why are interference fringes notdo*sx6i w,. dciceable only for a thin film like a soap bubble and not for a thick piece of glassx cd*.6io,dsw, say?

When a compact disk (Cw 00v b7arfv u.)fp;9/vkf*q8jvk oy gD) is held at an angle in white light, the reflected light is a full spectrum (Fig. 24–56). Explain. What would you expect to see if monochrom.b7rqof wku)9 gjavk y 8;f/*f vpv00vatic light was used?

Why are Newton’s rings (Fig. 24–31) closer together farther from the cs6u 6yk jgg/d;enter?

Some coated lenses appear greef,4hp id-j6t mrlrzw+i7c3 x*nish yellow when seen by reflected light. What wavelengths do you suppose the coating is designed to transmit completelyr6, mh d4-z 7wclxp f*3itrij+?

A drop of oil on a pond appears bright at its edges, where its thickness is muc6a9u(ydsw.qm nuxt uy-;c2k,m - wf l+h less than the wavelengths of visibm6us, 9 ntqcl fdymwax +--ukuw.(; y2le light. What can you say about the index of refraction of the oil?

What does polarization tell us about the nature of lby6x 1. :fezk)ljic9r 9 igmz 2uj:w:fight?

Explain the advantage of polarized sunglasses over normal tinted zdb 2x z1,8czi0rkvw4sunglasses.

How can you tell if a pair of sunglasses is polarizzkab(f29m *sklp)t :+os j)ywing or not?

Two polarized sheets rotated at an angle of p /00zn5 n4s3rvjv kbkeuem1(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 Eartm hr24 +7hrqjkh had no atmosphere?

If the Earth’s atmosphere were 50 times denser than it is, wouldrsx)/z sn w107i2cophbw)e0 o sunlight still be white, 0)hi eo2 w1 nsbs)czxp7r0ow/or would it be some other color?

  Monochromatic light falling on two slits 0.016 mmx1+dn f7y9uuq apart produces the fifth-order fringe7uu 1xn dy9f+q at an 8.8$^{\circ}\,$ angle. What is the wavelength of the light used?    $ \times10^{-7 }\;m$

  The third-order fringe of 610 nm ;t utqk, ly3n,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 narrow slits 0c vo e1sn4,hznn;,n/ b)h4zqd.048 mm apart. Successive fringes on a screen 5.00 m away are 6.5 cm apart /bvheo,hcnn q 4; n4z),z s1dnnear the center 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, wh8 -wjtp)p x.x mfs. wivk+d; i0u)vb9ith a wavelength 656 nm, falls on two very narrow slitsw 8fxpk-) ij.budx +vm .)vi09 sh;wpt 0.060 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 falls on two slits and produces an interferk:a i2 6*kpp1d uxscr6ence pattern in which the fourth-order fringe is 38 mm from the central fringe on 6pr6u kakcds1ipx:2* a screen 2.0 m away. What is the separation of the two slits?    mm

  If 720-nm and 660-nm light passes through two slits 0.5+;dw p pnb0s. ztk1q(h8 mm apart, how far apart are the second-order fringes for these two wavelengths on a scrkpw+t.1qb d 0 p;hnsz(een 1.0 m away?    mm

  In a double-slit experiment, it is found that blue light of wavelength 460 nm gy 6yu6v11ihlhdc4;fmives a second-order maximum at a certain location on fd46vhyu1yh mi l;c61 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 5.0 cfcc8jgf+p 8j 22udpg 2m apart in a board. At a point 2.0 m beyond the board, at what 8 gp+28 pf2cjjfu gd2cangle relative to the “straight-through” direction would there be little or no wave action?

Suppose a thin piece of glass is placed in front of the lower slit l4p zbow swq+s5e ipo.,45h6 gin Fig. 24–7 so that the two waves enter the slit.ipbog s5hpq46 s w+,oelz 5w4s 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 ms*d5q*m4oh fa )z/kcbaximum for light 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 tkhfdcqm4 /bza 5s*o*)he 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 1.1:ty9w(e6 l jf8 vpz9v4tem)kdr,ucg0 mm are illuminated by 544 nm light. Find the distance between adjacent brfwk (uztg 98e4v dlc e,)vm9pr6:y1tjight fringes on a screen 5.0 m from the slits.    mm

  Light of wavelength 480 nm in air f wpbvm:6k7 ag67o1w oballs 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 slit of a double-slipk1pwm1dl 6hmuh1h lf+- /h (ht apparatus illuminated by 640-nm light. The cente6hmhp11+1hhpwhk u-fl l(m/dr 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 o 7behucj6eh9.f red light (700 nm) exceed that of violet light (400 nm) in sieceh7bu .j9 6hlicate flint glass? (See Fig. 24–14.)    %

  A light beam strikes a piece of qx uz3n; *8eekglass 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 containing two wavex *-k4z4x6oo syur d9xlengths, $\lambda_1\;=\;450\;nm$ 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, whan dyc q54;ghgi/xcws cr60 6b)t is the full angular width of the/w;46hqc5 isbc6g n0c)ydr xg central diffraction peak?    $^{\circ}\,$

  Monochromatic light fall c1+zty7*36ic8pk i nse 6yvngs 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 fall2jycq4nd ) mp:s 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;o(b:o ymhhq( zl*8 8 8vftp/5atoygps-pa5 y is the width of the central maximum (in cm) in the diffraction pattern on a scqp*a;8t(sv / oyfbyamz5 (:5tp8hogh o8p-y lreen 5.0 m away?    cm

  Monochromatic light of wavelength 653 nm falls on a sli9 atv+8m bibx-t. If the angle between the first bright fringeab-9tm iv 8xb+s 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( bonyq4 da3b4.30 m behind a 0.0348-mm-wide sln4qdoab y43( bit illuminated by 589-nm light?    cm

  When blue light of wavelength 440 nm falls on a single slit, thyw.jrc/p22mhmn (su*2 4g 4p 1 nagctle first dark bands on eithgl a.c ynp4jn r /*m(1msuwc24gtp2h 2er 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 a single slit, it creates a cenzak2pv84e kvsrb ; nq,h+o)i7 tral difzrpne8kkv,4 q;ao) s+72hvibfraction 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 maximum is 4.0 c9m:gftcb) .lhm wide on a screen 1.50 m away, what wi:c .hlmt) bfg9ll be the width of the diffraction maximum for light of wavelength 420 nm?    cm

For a given wavelength(440i, 3taaujd cqvux $\lambda$, what is the maximum slit width for which there will be no diffraction minima?

  At what angle will 560tpm-0g*-iqgr6 v jn4p-nm light produce a second-order maximum when falling on a grating whose slits 4 jmirvg- t-qppn*g06are $1.45 \times10^{-3 }\;cm$ apart?    $^{\circ}\,$

  A $3500-line/cm$ grating produces a third-order fringe at a 28.0$^{\circ}\,$ angle. What wavelength of light is being used?    nm

  How many lines per centimeter does a grating have if the third-order occu* fmfaje-x6c/t.,j k0h -znebrs at az - nte6afm-e0.*,kjhf cjx/bn 18.0$^{\circ}\,$ 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 obs q7ha w)i0z,3 xf0xdojerved at a 1o 3jz,iqxdx0 h0)7wfa5.5$^{\circ}\,$ angle. How far apart are the slits?    $\mu m$
At what angle will the third order be observed?

  A diffraction grating hasotnp3w f+8k5 /rkro:wa .ah0a $ 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 normall/wkmfxt0 p ,+jy 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 ca.p)h 8 4aqre5ux3lt4* v akea grating with 6000 lines per cm is illuminated with 633-nm laser light? Assume normal rq au*)k lte543 e cv84xaa.phincidence.   

  Two (and only two) full spectral orders can be se /arvte05h3h/+jabbx 5e7p:x difs- w en 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 grat x3r /hade:5/wix+vp-0b7j5s fh be ating?    $ \times10^{ 3}\;lines/cm$

  White light containing wavelengths from 414 fgyca0c;u q00 nm to 750 nm falls on a grating with 4qu0f ;c0 aygc$8500\;lines/cm$ How wide is the first-order spectrum on a screen 2.30 m away?    m

  A He-Ne gas laser which pro) rg gx9b/*g7vrbv/k8ibnf)xduces monochromatic light of a known wavelength $\lambda\;=\;6.328\times10^{-7 }\;m$ is used to calibrate a reflection grating in a spectroscope. The first-order diffraction line is found at an angle of 21.5$^{\circ}\,$ to the incident beam. How many lines per meter are there on the grating?    $ \times10^{ 5}\;lines/m$

  Two first-order spectrum lines are measuredv8,(ax cds0b z 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 13 4js7k/.duw yxr/j rg4pkp2 )b0qcsh20 nm thick, what wavelength is most strongly reflected at the center of the outer surface when illuminated normally by white light? Assume thatqpp4brkr2/j.y4 /khs)s u0c3d gw7j x $n\;=\;1.34$. $\lambda$ =    nm ,which is an    -  

  How far apart are the dark fringes in Example 24–8 if the glass plates are ec;z0fk0e.u tvach 20 tezkc; 0fv.u6.5 cm long?    cm

  What is the smallest thicknes9s p85z83wzuik8govv s 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 yellow (jfh6c e/,ft y0o3z(er $\lambda\;=\;570\;mm$ 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 dar5 x8kruu *gfdh e*y,k/9rova) k Newton’s rings (not counting the dark spot at the center) are observed when 550-nm light falls normally on a planoconvex lens rd8r*ax5g,huo9)ef y *k kv/uresting 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 e9;/m ksy1 iwhlnd of two pieces of optically flat glass, as in Fig. 24–33. When light of wavel9iykm; s/wh1length 670 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 1bo :ru7lr/rzsurfaces if the glass is to appear bright when bru/o: 71z rlr450-nm light is incident normally?    nm
What if the glass is to appear dark?    nm

  vA piece of material, suspected of being* c(b i+glls7z 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 alcohol sbfxy.-m1:o n$(n=1.36)$ 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 apyz/88xl(+z b xdil+geparatus (Fig. 24–31) is immersed in a liquid, the diameter of the eighth dark ring decreases from 2.92 cm to 2.48 cm. What is the refractive index ox+x(/ 8lyz8bdg+e z lif the liquid?   

  What is the wavelength of the light entering an interferometer :jjvbmm t(7*bqwp6f7 if 644 bright fringes are counted when the movable mirror moj*vf:7bp qtmw b (jm67ves 0.225 mm?    nm

  A micrometer is connected to the movable minev9amuv(pk c27a- fo3gi 9ox :q5 -kzrror of an interferometer. When the micrometer is tightened down on a thin metal foil, the net num5-v7q9xno-9 ak:vc pk23azfig oeu(m ber of bright 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 mirpi1hslnz / sg8p3m 11xror $M_1$ 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. 24–54t9hw:jm g dqrz /.u 1.ve,pau9) 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 a9zmht : 4aed.v ujrpg.,/quw 1re 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 65ra2g: (pzvm 1k$^{\circ}\,$ to one another. Unpolarized light falls on them. What fraction of the light intensity is transmitted?   

  What is Brewster’s angles pjd zujex.-e:/2 ec; for an air–glass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s angle for hs h3l hnq6shol4 j* t2wf2 (kg2-yyrxu 5(xq2a diamond submerged in water if the light is hitting the l(u5ghw6x qjxh2sf 3tknqsh- 4(l22h 2ryoy* diamond $(n=2.42)$ while traveling in the water? $\theta_{p}$    $^{\circ}\,$

  Two Polaroids are aligned so that the light passiou3cs1b 4c(ploueoea0)5gf : ng through them is a maximum. At what angle should one of them be placed so that the intensity is subsequeguo c)cu0oep1 s54b lfao e(3:ntly reduced by half?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be placed so as to reduce t cwzfaw/g we ag3br0390 .8kbfhe intensit/cf e9 30bkb.ga 8g0wz3fww ray of the incident unpolarized light to
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are oriented at 4ezhoq 0; bn2+c0$^{\circ}\,$ 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 oriente rjx2(qqgf s 4ffvu,n 4y)c)8ed 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 reflec dddj6ggvxneb3-ex956r uy.4 tions off the surface of water for light coming from beneath the surface? Compare to the angle for total interna.r9d -6u yx 4gx5d6v3 gdbeejnl 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 who8f8 z twl b80wi)wz(hcse aw f8c wbtz lhzw)8(i08xis makes a 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength -q0 e6 td3irva$ 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 frws3gy/ uflt )jo; 6f/.lu9jlxom mountains or airplanes can interfere with thl u6ys/g9jux.3o j)w l;tf/ lfe 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 throuz zmg7/zp j6,9c(8enumofb9 ,nw k 8twgh a diffraction grating with wk cf/m uo wp8n,zz6e7g9 z ,bnt9j8(m$ 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 e7 nud)*ye+wf 590 nm passes through two narrow slits 0.60 mm apart. The screen is 1.70 m away. A second source of unknown wavelength produces 7udnwe *)ef+y 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 operating at 102.1 MHz broadcasts from two identical antennae arith4r0e2 2cy uim2ln;fp )b ywq1u-(t 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. If the utmn2h);2e2 -qcrp1i 40bifwuy r(ylmidline 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, ebm1m.x c,t ay4tx;a9and blows a whistle of frequency 750 Hz. Ignoring reflections,ma yxtbea 9c m,t14;x. estimate at what angle(s) it is not 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 slit of wid ns71-zm5xzxg th D at a 30$^{\circ}\,$ angle to the normal, describe the diffraction pattern.

  The wings of a certain beetle have a series of parallel l9xyy2t2mf7uzns8 5 ro ines across them. When normally incident 460-nm light is reflected from th mx5rs 7 yt2on92fy8uze 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 jt(5*bovb+o)g h*he qgrating have if there is to be no second-order spectrum for any 5johb evb+hq()*g *to visible wavelength?   $ lines/cm$

Show that the secondphgu3s-2hyp 2ldvm4 - - and third-order spectra of white light produced by a diffraction grating aph4ypg2l-dm 3s-u2v h lways overlap. What wavelengths overlap exactly?

  When yellow sodium lighsmknla y:1u 7)t, $\lambda\;=\;$ 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 m dq/xy*qw hm ((jl9;nthe pattern is viewed on a screen 2.5 m from the gqdm; m*xj/9 qlny((whrating. 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 1 8i*i2: pqtgt jv,z8xs50 nm thickness of it, wixt2t z ,8j:vp g*is8qhen 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 ef* yf3,za c*r9ijkn4variable wavelength is incident normally on a thin sheet of plastic film in ai9f, ai f3ycjn**z4kerr. 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 1w-pgk hdtlv+b4i1 (lf2fi-* d e f/eyneeded 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 r. b:g4nel6 f6j8p7vv9oesoc two flat glass surfaces if the glass is to appear dark when 640-nm lib4l o6on.gc8p svee:6 fjrv9 7ght is incident normally?    nm
What if the glass is to appear bright?    nm

Suppose you viewed the light transmitte m7r 9:e8t *yvuaijk0nd through a thin film layered on a flat piece of glass. Draw a diagram, similar to Fig. 24–30 or 24–36, annv9 ir0ay8e j *mu7:ktd 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 4z26(h6yacrjxj c 1ma is the Sun when light reflecting off a smooth lake 2c1(jj66mc h xyaraz4 is polarized most strongly?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be placed so as to reduce n*3*yjzeg zc;1 rmqmu610eu0p ;rsg: ewib8zthe intensity of the incident unpolarized light by an additional factor (after 0bews6e ji3 m g r*0e u:q1*czyn8u;gp1zzrm ;the first Polaroid cuts it in half) of
(a) 4,    $^{\circ}\,$
(b) 10,    $^{\circ}\,$
(c) 100?    $^{\circ}\,$

  Unpolarized light falls on two pom)j pi+ )lvnj5larizer sheets whose transmission axes are at right anglesl )mj5+)p jvin. 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 placed in succession with their t c jo xiveivo5c6,a,7/ /31gexg7jvtaxes 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 i;cqzb7 *6ml xrs pointed at the Moon, which is approximately 380,000 km from the Earth. Assume the laser emits waves of wavelength 630 nm (the redc ; 7r*qmlz6bx light of a He-Ne laser). Estimate the width of the beam when it reaches the Moon.    km

  A series of polarizers aryizs9/duxfvlvq; q*u5;( :q r e 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 uc v ;7czf3;ix kv48newqy7 2g$(n=1.34)$ 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 rad)t n8j 0ni xy*b9ycq,uiating 6.0-MHz radio waves in phase with each other. They are locate8u cy jx9b)i,nq*t0ynd 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 wre*d vm epd olg0t.qmmn ary6xm30:- e+5+e e1avelengths, 420 nm and 650 nm, enters a silicate flint g6q31mm:xree d r0e5olnypa* me-g0+d+em v. t lass equilateral 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 planoconvexfz/a3 :a/hro2 z rh xvke;0g4d lens 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