Does Huygens’ principle apply to sound waves? To water waves? Explai /x 3h6u cxc;:y2lrdtp; i9hfdn.

What is the evidence that light is energlc7vw1cb.z 7+ /qpyexy?

Why is light sometimes described as rays and ri.i+ ytprvn 7* 8hautu ;-pbl6)/fpt sometimes as waves?

We can hear sounds around corners, but we cannot see around cormrfe744uulac6n nzwl1v/4jm+nn0 8.yq q i(qners; yet both sound and li0ml (vuj/. fmn ur+y17 qe4q8a nnnl46q4zicwght are waves. Explain the difference.

If Young’s double-slit experim4 82cytf.k jg,n2o pkfda+-vjent were submerged in water, how would the fringe pattern be chf84 cf2j tko. yav dp,nk+-j2ganged?

Monochromatic red light is incident on a double slit, and thk5 e73l skkm2ve interference pattern is viewed on a screen some distance away. Explain how the frine35ls kk7k2vmge pattern would change if the red light source is replaced by a blue light source.

Two rays of light fromnuc-jv ;y5w) l the same source destructively interfere if their path lengths dif c5)w;uny -ljvfer by how much?

Why was the observation of the double-slit interference pattern more ckf(h4 / kd3vrie zeit 487ub;jonvincing evidence for the wave theory of light than th47b ed fv8ie kki;hujz/t3r(4e observation of diffraction?

Compare a double-slit experiment for s72e de9zc- 77 ktjdectound waves to that for light waves. Discuss the similarities and differenc 7d7e-jze2 7ekt ctcd9es.

Why doesn’t the light from the two headfbn :8kz e(mtgw 374kjlights of a distant car produce an interference pattern4zt: 7(3kke wbgnfj8 m?

Suppose white light falls on the two slits of Fqn 85cqi2n z.bma7rc* ig. 24–7, but one slit is covered by a red filter (700 nm) and the othrcnb nq78a*c z2 5miq.er 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 broke)ka( 0u:lb)ksj 3rtzui rr y)p(bf7 y:n down into colors klt b u ))urzr0)ys( pbjf7: iy3akr:(as it is by a prism. Explain.

For both converging and diverging lenses, discuss how thn:zt,5 ,k6 jw5aye2x wfu h*/m bmfso9e focal length for red light differs from that for violet lig auhw25 j:oxk96 bz,ef,w/5f ymt* smnht.

A ray of light is refracted through three different materials (Fig. 24–55). Raj7 otjtt,wl8)nk the materials according to their index ofo)8t 7jtwtjl , refraction, least to greatest.

Hold one hand close to your eye and focus on a distant light source througwodicrgr -5r6h2/ jla7 -k77r qu,ilgh a narrow slit between two fingers. (Adjust your fingers to obtain the best pattern.) Des da i7l2gh57lugjr/-irc -o,wk76r rqcribe the pattern that you see.

What happens to the diffraction ) p3z/bl9ff v4+nhsmp6zhvh8pattern of a single slit if the whole apparatus is immersed in (a) wathpzvbmp4n 6hs+8f z/ vh l93f)er, (b) a vacuum, instead of in air.

For diffraction by a single slit, what is th pt+9h:d+.re m qng,jfe effect of increasing (a) the slit widt n. fh+,e9+:g qrtdpmjh, and (b) the wavelength?

What is the difference in the interferenci d8tv-al ( y,g)ub6gue patterns formed (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) many slits, (wh.j lderud3 qk3t0r* bb671lb) closely spaced slibr w deqb67 k3ju 0rdl3t*hl1.ts?

White light strikes (a) a din)wx4n u y*+ l4d1tpnyffraction grating, and (b) a prism. A rainbow appears on a wall just below the direction of the horizontal incident beam in each ) tw441nyndu+*yxnlpcase. What is the color of the top of the rainbow in each case? Explain.

For light consisting of wavelengths between 400 nm and 700 nm, inn .urs7h 9hw7w;t9n rxcident normally on a diffractionursn wtx79 r;h9nh7. w grating, for what orders (if any) would there be overlap in the observed spectrum? Does your answer depend on the slit spacing?

Why are interference fringes noticeable only for a thin film like a s6boaat,6hi1d v */qoloap bubble and not for a thic h 6do*l,/q1ava6 tbiok piece of glass, say?

When a compact disk (CD) is held at an angle in whsnu oe 477uy6*0 hdp w9cbv:dpite light, the reflected light is a full spectrum (Fig. 24–56). Explain. What would you expect to see if monochromatic sb9:up46ye *dvwc p7u dn0h o7light was used?

Why are Newton’s rings (Fig. 24–31) clod i5 ye8x+kxhc (5vs*ki-az6jser together farther from the center?

Some coated lenses appear greenish yellow when seen by reflected ligui2uf2*koudl1 k+kc84s4luxue3 tg; ht. What wavelengths do you suppose the coating41x2u+g*; ie38u4utuukfds 2k ck lol is designed to transmit completely?

A drop of oil on a pond appears bright at its edgelgytms :yaae) ,33cc 6s, where its thickness is much less than the wavelength3 y:a)3c ,l csgytmea6s of visible light. What can you say about the index of refraction of the oil?

What does polarization tell us about the nature ofs sw, ir7,3n-serukk6( 8 evb -av2xyl light?

Explain the advantage of polarized sunglasses over normal tinted sundv ,t8kk2 me:nzh s 8)movbd*5glasses.

How can you tell if a pair of sunglasses is polarz 1,fw/c+. kg+fhzxzg : ;pqemizing or not?

Two polarized sheets rotate ph)y0*h cbxq.d at an 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 no at52vws1zr3ag vumj, 7: g jtqfy7uah*9mosphere?

If the Earth’s atmosphere were 50 times denser than it is, would sunlight stgdtvnzto,2 :4ill be white, o ,nv:o dzg24ttr would it be some other color?

  Monochromatic light falling on two slits 0.016 mm apartc;yegr6p c 55e produces the fifth-order fringe a ey6g;pc55ecrt an 8.8$^{\circ}\,$ angle. What is the wavelength of the light used?    $ \times10^{-7 }\;m$

  The third-order fringe of 610 nm light is observeq)o) :xdfa(1f v nq0vqd 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 mm apart. wcib qplj7 :.s n. w5+pje(pz)f) ikx0Successive fringes on a screen 5.00 m away a :flcb qjw5x.z +iep)jki 7p0) n(.spwre 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 from a He-Ne laser, with a wavelength 656 nm, falls on2x)d,vv -s uugimwdw./hz(2e two very narrow slits 0.060 mm. d,-sivv2x ) edgzwuwu2/(mh 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 interferenckb-i r;e r(8j85y0op /l2ikpjjj5tz f e pattern in which the fourth-ordejk j52i/y 8krjpro5pb e(it 0fljz;-8r fringe is 38 mm from the central fringe on a screen 2.0 m away. What is the separation of the two slits?    mm

  If 720-nm and 660-nm light p,+p yra2 9uafsasses through two slits 0.58 mm apart, how far apart ar p 2safaruy,9+e the second-order fringes for these two wavelengths on a screen 1.0 m away?    mm

  In a double-slit experiment, 0w,nwlidsi ,m c)k6 0xit is found that blue light of wavelength 460 nm gives a se) silxw,kn ,6d i00wcmcond-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 p* q6 d/cxohct3ass through two openings 5.0 cm apart in a board. At aco3q/6*ct dh x point 2.0 m beyond the board, at what angle relative to the “straight-through” direction would there be little or no wave action?

Suppose a thin piece of glask qr iyk1f597gqlxuv:: bf1)ps is placed in front of the lower slit in Fig. 24–7 so that the two waves enter the slits 1ub15:9yqf:lrkqv7xf k p)gi 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 waveleng0lzyqf. hug,: th 500 nm is located 12 mm from the central bright spot on.fh: q ,lyg0zu 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 illuminate rdy/b g5ud(ry:*p9p2 gjbs;ad by 544 nm light. Find the distance between adjacent bright fringes on a screen 5.0 m from thap b /y*;rjd :gp2ydbs5(ug r9e slits.    mm

  Light of wavelength 480 nm in air falls on twoc.z;j ,;p 1 vbuj3qllj 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-slit a1s)klsky)qq eh-;g g 1pparatus illuminated by 640-nm light. The center point on the screen, instead of being a maximum, is dark. What is the (minimum) thi;q1q-kgs s 1h) kegy)lckness of the plastic?    nm

  By what percent, approximately, does the speed of red light (700 nm) ev-1gza1e;cc4ap8 j kmxceed that of v maz1c kj8pace41;g- violet light (400 nm) in silicate flint glass? (See Fig. 24–14.)    %

  A light beam strikesk9fr*p(qx p) e a piece of glass at a 60.00$^{\circ}\,$ incident angle. The beam contains two wavelengths, 450.0 nm and 700.0 nm, for which the index of refraction of the glass is 1.4820 and 1.4742, respectively. What is the angle between the two refracted beams?    $^{\circ}\,$

  A parallel beam of light containing two wave pr3le,hyk0nn .ky;i glln,,: lengths, $\lambda_1\;=\;450\;nm$ 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 l-m0luqbj3s - wide, what is the full angular width of the centr-j 0ml3ls-qbual diffraction peak?    $^{\circ}\,$

  Monochromatic light falls onu 72j hrx:xy+g:8cgzw 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 falls ona- rurfxa,. )h 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 ligh4dw na u lyv,;sp3;xh*t. What is the width of tsd;hly,u*xp v ;4naw 3he central maximum (in cm) in the diffraction pattern on a screen 5.0 m away?    cm

  Monochromatic light of wavelength yzznon d7r)m z s+7,o5653 nm falls on a slit. If the angle between thr)5m+s dnozonyz7z7,e 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 0qy*v4nnua 87jr y f71cx7r. te.0348-mm-wide se t qv4jy7*1aru7cf nx.nr8y7lit illuminated by 589-nm light?    cm

  When blue light of wavelength 440 nq: swr1mk6 tx1s 2kxg*m falls on a single slit, the first dark bands on either side of center arex: wstk 1gk26xr 1s*qm separated by 55.0$^{\circ}\,$. Determine the width of the slit.    $ \times10^{-7 }\;m$

  When violet light of wavelength 415 n ( ., jzj n*enva0lwgwww-9ed2m falls on a single slit, it creates a central diffraction peak that is 9.20 cm wide on a screen that is 2.55j en a9zw2n,j *(wv0g.dwe- lw m away. How wide is the slit?    mm

  If a slit diffracts 650-nm light so that the dif+n8**jny wv-)au aapq fraction maximum is 4.0 cm wide on a screen 1.50 m away, what will be the width of the diffraction maximum for light of wavelength 420 nmu-n a 8n)vy*p *+jaawq?    cm

For a given wavelengcu8bc x16mw c:th $\lambda$, what is the maximum slit width for which there will be no diffraction minima?

  At what angle will 560-nm light produce a second u+(tah yus.a2-order maximum when falling on a gratinguys2ah.+tau ( 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 grating have if the third-order kpw:/6 jo.p fpzt6ie(occurs at an 18.0p6p it /wpo.ez(6k f:j$^{\circ}\,$ 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-npwrk3gy01b;m ap) 3zbm light falling on a diffraction grating is observed at a 15r3apb; w) g0pbyz3k 1m.5$^{\circ}\,$ angle. How far apart are the slits?    $\mu m$
At what angle will the third order be observed?

  A diffraction grating has da lq,42nc -rs$ 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 normallyx:; h3;tsdyx p/s5iggb lii/rrd 4 9t4 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 jue/nn (;dba) x k 5ifspx)z7g;qp9n :spectral order that can be seen if a grating with 6000 lines per cm is illuminated with 633-nm;u;gen9xqn)djs:7 iap (n5x/ b k pfz) laser light? Assume normal incidence.   

  Two (and only two) full spectral orders can be seen on ei3dzusl ) a nl,-29g:7lniyzbk ther side of the central maximum when white light is sent through a diffraction grating. What is the maximum -, dln g:793)uklnz z2ba liysnumber of lines per cm for the grating?    $ \times10^{ 3}\;lines/cm$

  White light containing wavelengths from 410 nm 1zt ohxk) k/5pto 750 nm falls on a grating with /kzo5 )hkx t1p$8500\;lines/cm$ How wide is the first-order spectrum on a screen 2.30 m away?    m

  A He-Ne gas laser which produces monochromatic light of a known wav--6mno.e ms r r8.rm) es* rdmemk1nk,elength $\lambda\;=\;6.328\times10^{-7 }\;m$ 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 li fqyn1mdit-(/a e0cc-nes 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 xp9 nsp+kjzod47zlemj4p8msd -5 *5p strongly reflected at the center of the outer surface when illuminated normall* 4jd8ps5psz9+ x pmjl-d7z 5oe4mkpny 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 platesuiy7a)kr5 k wggt+/ 0g 1.qtzb are each 26.5 cm0 qa/yrkz+ i7.tb 5ggt1u )gwk long?    cm

  What is the smallest thickness of ahdczer+r;x 8 * 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 yelloph/ on ttya.6*1rc:uhmf. mg 0w ($\lambda\;=\;570\;mm$ 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’0rpff1m ozg+m)i 3q t0s rings (not counting the dark spot at the center) are observed when 550-nm light falls normally on a ) mip1+r00zmf og 3qftplanoconvex 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 end of two pieces of or b:e r-q5/v 1gxjqt6pptically flat glass, as in Fig. 24–33. When ligh xqtgr5vq -rj:b 16pe/t of wavelength 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 be4)cwd-w q 2mc1c)j*hru /peqz between two flat glass surfaces if thdzu* )wjcmhew q cp4r)1/2-c qe glass is 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 bein pg2(k 2 9tnv(ihd6b27kylwgxg 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 alcohong -t5)fv aejk p1:2wrl $(n=1.36)$ 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 hjzmjf8 h1/a/v 2b7e:ifk 0mdapparatus (Fig. 24–31) is immersed in a liquid, the diameter of the eighthmfvbh j8h2 ked:iafmj//z 71 0 dark 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 entering an inqwpz.m* qf6z dr6h:a .terferometer if 644 bright fringes are counted when arp*q.q.dmzh z:f 66wthe movable mirror moves 0.225 mm?    nm

  A micrometer is connected wepjp38wwu,*s 0i v5 sqm q-3f8m obq3to the movable mirror of an interferometer. When the micrometer is tightened down on j pums w, m3boqwips38eq5 0-w vq83*fa 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 light used is 589 nm.    $\mu m$

  How far must the mirr --8*b01bwdhsp namvxor $M_1$ 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 acb7c z fg3y1 8:ejyrg, 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 zjyc 8:r e,f ggc71y3bfringes 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 65m hw b4+(fvh n+(xf(uz$^{\circ}\,$ to one another. Unpolarized light falls on them. What fraction of the light intensity is transmitted?   

  What is Brewster’s a.+ev etf3 01 mcq9imwv r4/otsngle for an air–glass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s angle for a diamond submerged 9feo b5)vsd bi/ (lv)pin water if the light is hitting t9pbv(feb ls) /)i5ov dhe diamond $(n=2.42)$ while traveling in the water? $\theta_{p}$    $^{\circ}\,$

  Two Polaroids are alignfa)uv l 8*wwo7ed so that the light passing through them is a maximum. At what angle should one of them be placed so that the intensity is subsequently reduced by hal)u vw7 fwa*8olf?    $^{\circ}\,$

  At what angle should the axes of two ivgtfanx +-yd5 -2i3vj t70jz Polaroids be placed so as to reduce the intensity of d3ai -n f57vi+t02vzy xt-gjj the incident unpolarized light to
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are oriented at-)stf7z: 1:(rrm mpc zwitcp v2rtv/; 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 orie/fx+kol -t3na nted 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 zv:4ay- vdz.+kiph-/ fd*t 5t u5egcygej4d: reflections off the surface of water for light coming from beneath the surface? Compareet v v taj5cfg -/z+d:h4dykg zp.-ie u:*5d4y 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 cc4q - wwis)gqj +1u+bfive successive Polaroid sheets, each of whose axis ma1wqig j)+ubcsq-+ w4ckes a 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength etlnn5b (2df /f5arpvod4t/ ; $ 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 airplen2r.pg+gh f :anes can interfere withhe .pg2nf+rg : 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 di80(lrypfy8(k r(uahgffraction grating with 8r0lgk (r8(( uphfayy$ 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 thr/m6n(0 gvyt1zym7ruhough two 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 than the 590-nm light. What is the wavelength of the unknown limnvzh 6ym 7uy r0t1(g/ght? $\lambda_2$    nm

A radio station operating at 102.1 MHz broadcasts frgx) przuq1yd8 4* pz+ l/nhuc/om 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 +)g /pznl4 u8ydqh/p*c xr1zuin both directions. If the midline is taken as 0$^{\circ}\,$, at what other angle(s) $\theta$ is a maximum signal detected? A minimum signal? Assume all measurements are made much farther than 8.0 m from the antenna towers.

  A teacher stands well back from an outside doorway 0.88 m wide, and blows a wh 1eez fx(r yonz5)irt9z04mhl1/e h;cistle of frequeert(m iyzhcre fn1x054;1o ) ez z/h9lncy 750 Hz. Ignoring reflections, 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 width D at ia3w (fyv ( +4zavvrw)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. W dhj;q8,f7bramulkze+* 7k- j- 9g zuahen normally incident 460-nm light is reflected from the wing, the wing appears brirkalj a7 79;k uzg* zeb+8 qd--fj,hmught when viewed at an angle of 51$^{\circ}\,$. How far apart are the lines?    nm

  How many lines per centimeter must a grating have if there is to be no ) xxw i) l24gvlt7o,oksecond-order spectrum t2l)io7lk vowxx)g,4 for any visible wavelength?   $ lines/cm$

Show that the second- and third-order spectra of white light pf+0.rpda 1 f,itobgx,+ 5rqnkya7 / aeroduced by a diffraction grating /rxq1f5yoa7,b . e+gnid0 +aak tr,fpalways overlap. What wavelengths overlap exactly?

  When yellow sodium lig4(:p r nta2:eghziw5eht, $\lambda\;=\;$ 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 rjw,ov 7bmc08diffraction grating with and the pattern is viewed on a screen 2.5 m from the grating. The incident light 0r8j w,7bmvco 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 refractio6gqw u2-j2cdhz iz ymz 6;96gan of a clear material 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 incident normally uponui266qdj g yzgaz9whc-6m;z2 it? Do you have a choice for an answer?

  Monochromatic light of variable wavelength is incident normall((nh.xwgf 3ihln; wvkw(u6 (vy on a thin sheet of plastiw 6 nhx(nl(fw ;iv (3hw.kgv(uc film in air. The reflected light is a minimum only for $\lambda\;=\;512nm$ and $\lambda\;=\;640nm$ in the visible spectrum. What is the thickness of the film $(n=1.58)$? [Hint: Assume successive values of m.]    nm

  Compare the minimum thickness needed for an anti-6 yu wq;yb 07wja9goa: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 flze 3dm.zlnz +58xgs6dat glass surfaces if the glass is to appear dn6 dsxz3z md8 lgz5e+.ark 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 t0/n oinxdzl9 1hin 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 minima. Consider a0 oxlzn9id n/1ll 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 horizonr96hub p nzo19gz*hc--z q2gj is the Sun when light reflecting off a smooth lake is polarized most stror bg -c*99 qh 6pz2-hzjguzn1ongly?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be p ;l0:egrxb(v*lcxe )zlaced so as to reduce the intensity ovx ezgex*)c:b0lr l;(f the incident 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 falls on two polarizer sheets whose transmission axes a eatfw 7d15;gtt2c/rrre at right angles. A third polwr at2t1t /defg7c;5rarizer 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 succizbhx.iwgc +t)srut3i5xp0 -/q8v+ e ession with their axes vertical, at 30$^{\circ}\,$ to the vertical, at 60$^{\circ}\,$ to the vertical, and at 90° to the vertical.
(a) Calculate what fraction of the incident unpolarized light is transmitted by the four polarizers.
(b) Can the transmitted light be decreased by removing one of the polarizers? If so, which one?
(c) Can the transmitted light intensity be extinguished by removing polarizers? If so, which one(s)?

  A laser beam passes through a slit of width 1.0 cm and is+l +z:wec 5vhlibw::xgjq,0j8df wr: 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-w i+:8z0c,+r::dx l5:wjb e vwlfjqhgNe laser). Estimate the width of the beam when it reaches the Moon.    km

  A series of polarizers are each placed at6no:l ;2c8jxqs s lx:t 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 /g/ g5ra/yn-hy l )wjrsq79c d$(n=1.34)$ coats a piece of flat glass $(n=1.52)$ .How thick is the film if it reflects 643-nm red light most strongly when illuminated normally by white light?    nm

  Consider two antennas radiating 6.0-MHz radio waves in phase with each otherxd o h/h;8tc /b+mxbi8. They are located at p8t;ohhb 8xx bi/m+ /dcoints $S_1$ 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 q-ck)z 3e00vp8;gpapkn e8t4h w3r-o iqwoo4 wavelengths, 420 nm and 650 nm, enters a silica)w0 8k3r3hpqpo8w -i 0 c; qeoo vzekptng-4a4te flint glass 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 planoconvex lens has one flat surface +t)t-bn9y x ivand 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