Does Huygens’ principle apply to sound waves eu,0/c qv/gdw+jc ck;? To water waves? Explain.

What is the evidence that light is engsgu 92no /vwr/:j /nfergy?

Why is light sometimes described as rays ankyrn mx6ad*),e js))ieq i.h -d sometimes as waves?

We can hear sounds around corners, but we cannojef 6vmjx2 jx*pgan y6:k-k/d3 akd 57t see around corners; yet both sound and light are waves. Explain tk dk2m*dfjygae6j5x/6 -3 ak:7njp x vhe difference.

If Young’s double-slit experiment were submerged in u6f o1d /ggvc63e na6gwater, how would the fringe pattern be changed1gv e6 6ggc u/of6a3nd?

Monochromatic red light is incident on a double slit, andsx1y1 y+f)mqp-kc3 tv the interference pattern is viewed on a screen some distance away. E11mq-p3t +)kyvcxs y fxplain how the fringe pattern would change if the red light source is replaced by a blue light source.

Two rays of light from the s 8hggve/3d -nkq-xxb3ame source destructively interfere if their path lengths differ by hnb338kxdg -/ev-hg x qow much?

Why was the observation of t c)q 0sc)zzbj(he double-slit interference pattern more convincing evidsj)0c c(zzbq) ence for the wave theory of light than the observation of diffraction?

Compare a double-slit experiment for sound wavj h*4zkbv/j2: gse -kues to that for light waves. Discuss the similarities and digsh j j4:eb*-k uk/2zvfferences.

Why doesn’t the light from the byh kwg)nf)j6/h4k.ptwo headlights of a distant car produce an interfejg y.4f hwk)k6phbn /)rence pattern?

Suppose white light fasy +)y +gy(aihlls on the two slits of Fig. 24–7, but one slit is covered by a red filter (700 nm) and the other by a blue fi) iyy a+sh(+gylter (450 nm). Describe the pattern on the screen.

When white light passes through a flat piece of window glass, it is not broken .eo i xb0hzz8:down into colors as it is by a prism. Ex :8 oz0zhex.biplain.

For both converging and diverg +stpjl2a-fsu8upvk8m tv0./ ing lenses, discuss how the focal length for red light differs froap uvs.t+tk8-jpfmu0svl/28m that for violet light.

A ray of light is refracted through three different materials (Fig. 24–55)ahdpc1 zq/51 a. Rank the materials according to their index of ra1p51zqa d /chefraction, least to greatest.

Hold one hand close to your zwzufota0c 1,u9z64z eye and focus on a distant light source through a narrow slit between two fingers. (Adjust your fingers to obtain the best patt1 zot4uz6ua c z9zf,0wern.) Describe the pattern that you see.

What happens to the diffraction pattern of a si,u wxq7tgmnt3xl/9u 7ngle slit if the whole apparatus is immersed in (a) water, /7,n m 9lqtwx3utu7xg (b) a vacuum, instead of in air.

For diffraction by a single slit, what is the effect of increasf-;uhzl8l )rzing (a) the slit width, and (b) the wavelrl- zf l8;hu)zength?

What is the difference in4-u.wofrkyr 1 the interference 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 ci:yy uvp0lu bf;24lglq312j slits, (b) closely spa;: y0ql23yp2lucfluigvj 4 1b ced slits?

White light strikes (a) a diffraction grati gmw9f/.,p 4whn gz:ring, 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 razh.rwm4ng w 9f:i/, gpinbow in each case? Explain.

For light consisting of wavelengths between 400 nm and 7ms (uq8a f)u,y00 nm, incident normally on a diffraction grating, for what orders (if any) would there be overlap in the observed spectrum? Does your answfyas(qm) 8u ,uer depend on the slit spacing?

Why are interference fringes noticeable only for a thin film li n7 tqb::,a2q iqbuxx+ke a soap bubble and not for a thick piece o:b, q xqn7taiux+:qb2f glass, say?

When a compact disk (CD) is held a m2h) -,zuvyz9 fp:diwt an angle in white light, the reflected light is a full spectrum w,uzv2h )p :yi 9fmzd-(Fig. 24–56). Explain. What would you expect to see if monochromatic light was used?

Why are Newton’s rings (Fig. 24–31) closer together farther frov307mms mcajc3.pe1/ yuuu g.m the center?

Some coated lenses appear greenish yellow when seen by ref gt4;s/n vob:clected light. What wavelengths do you suppose the coating is designed to transmit completely?oc /gv; 4t:nbs

A drop of oil on a pond appearsoi8yjc,gkya.i2 tx -qn ;w8( q bright at its edges, where its thickness is much less than the wavelengths of visible light. What can you say about the index of( kq int2,ax8y-ywq.j ;og8ci refraction of the oil?

What does polarization tell us about theybl6/6pbu ,7a:dtz( 3hmtp jb nature of light?

Explain the advantage of polarized ss by(jvb4(uu5bbx6xew :on n4:*)qmfunglasses over normal tinted sunglasses.

How can you tell if a pair of sunglasses is polarizia*fdv ncv wkru)7k)**ng or not?

Two polarized sheets rotated at an angle 7k d+tv q-zo1mof 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 atmosphere?*9 lyv y,+73gjpru ubb

If the Earth’s atmosphere were 50 toq jv:a-oac4 g8:sk.fkipka(0mu )6 kimes denser than it is, would sunlight still be whsocvokaa-i f80kmk6 kg: (4 p q)j:au.ite, or would it be some other color?

  Monochromatic light falling on two slits 0.016 qr ;qt8 mnyu).zvca9h46 t*c6z*pomdatw m)+mm apart produces the fifth-order fringe ;pw .h4cyo+ ttum86vm9d*)a tnqmra6*)qcz zat 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 observed a0e cf3irc pq61n g1w0,iswz( et an angle of 18$^{\circ}\,$ when the light falls on two narrow slits. How far apart are the slits?    $\mu m$

  Monochromatic light fallet*w n26f4 dyds on two very narrow slits 0.048 mm apart. Successive fringes on a screen 5.00 m away are 6.5 cm apart near the center of the pattern. Determine the wavelengt d6d*4nwytfe2 h and frequency of the light.
$\lambda\;=\;$    $m$
$f$ =    Hz

  A parallel beam of light from /5hu )3aiyl orzgmn/2 a He-Ne laser, with a wavelength 656 nm, falls on two very narrow slits 0.060 mm apart. How far apart are the fringes in thei lz2/m3o nha5u gy)/r center of the pattern on a screen 3.6 m away?    cm

  Light of wavelength 680 nm falls on two slits and pr6 rhutpen9rus-zfj ,ke381q0tbuazx 7 0r )p-oduces an interference pattern in which the fourth-order fringe is 38 mm from the central fringe on a screen 2.0 m away. What is the separa,h ner8rst3 6u-qu-z0j f 90btepzkpu)7a1xr tion of the two slits?    mm

  If 720-nm and 660-nm light passes through two slits 0.5pxz2a 2yqe0 xyh) t7/d8 mm apart, how far apart are the second-order 7yxt dq 2 yx)e2/hp0azfringes for these two wavelengths on a screen 1.0 m away?    mm

  In a double-slit experiment, it is found that bluh*lv/-vjv obm ak)z;;e light of wavelength 460 nm gives a second-order maximum at a certain location on the screen. What wavelength of visible light would have a minimum at the same locatio)m*;zbvkl/jha- v vo ;n?    nm

Water waves having parallel ovr zd qh0n.-/crests 2.5 cm apart pass through two openings 5.0 cm apart in a board. At a point 2.0 m beyond the boa/0nv o.- drqhzrd, at what angle 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 tn s6+k a*d)u;(iwdvinm. a,sc he lower slit in Fig. 24–7 so that the two wave+s*(, n nidavsw;ad6kc.m ) ius 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 lighq2tq(c5 p nuq4t 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-n4(cu 2 qqtqp5order maximum of this light be located?    mm

  Two narrow slits separated by 1.0 mm are illuminated byj u1aag.ju mo; :9lyi:e/ 8zrm 544 nm light. Find the distance between adjacent bright fringes on a screen 5.0 m from the slzuu8:yml /:gi om;.a1jjr9a e its.    mm

  Light of wavelength 480 nm in air falls ovabv blb)jays; 4ofr :v/62q5 n 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 of3jy4z4otb gi c 3/yi-d plastic (n=1.60) covers one slit of a double-slit apparatus illuminated by 640-nm light. The center point on the s4/tic3b i4z yy 3gdjo-creen, 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 (7l/* ov;6 4cq.5bj:sd z1fndxhc9li tt00 nm) exceed that of violet light (400 nm* / :chzf9b l4ti;q5j61.dtc dolvsnx) in silicate flint glass? (See Fig. 24–14.)    %

  A light beam strikes a piece of glagf 4x0q- yv4vrnp7s2ueo;s y*ss 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 conta*)ov30lhjylqvm( t0 asy3 9unining 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 adgzo: ac/ ;+p;txkatn* ; fhbm 8(5kio slit 0.0440 mm wide, what is the full angular width of the central diffraction peak?zig/pd; o(; m; *:tt+ofxbhn kk8a5ca    $^{\circ}\,$

  Monochromatic light falls on a slit that is bz fa6 oa,y3:t$ 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 53oz juds+8 6huj.d5kl20 nm 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- -qvsd ibf3acm;x-, z wide is illuminated by 450-nm light. What is the width of the central maximum (in cmzbm a-fi3,-s-;xq cv d) in the diffraction pattern on a screen 5.0 m away?    cm

  Monochromatic light of wavelength 653 nm falls on a slit. If the angle between tomvsx 1v6r,7 vhe first bright fringes on either side of the centxrvov6, s 7v1mral maximum is 32$^{\circ}\,$, estimate the slit width.    $\mu m$

  How wide is the central diffractj3 (k2e5agqyvv6j1sj ion peak on a screen 2.30 m behind a 0.0348-mm-wide slit illukv61 j23svjgq5 eayj (minated by 589-nm light?    cm

  When blue light of wavelength 440 nm falls on a single sliu/,kb4iglo d4 t, the first dark bandsoi4l,db u4gk/ on either 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 ctfu 4w( wz/3 .xe aw ,ewzi*is1,/il2k(zqv jmentral diffraction peak that is 9.20 cm wide on a screen that is 2.55 m away. How wide is the slite,jw ki 4x(wzai/ u,.lzw(2 ve/ ms13f*zwiqt?    mm

  If a slit diffracts 650-nm light so that the dif0* d7xbp /pu.eam )qvifraction maximum is 4.0 cm wide on a screen 1.50 m away, what will be the w dv0/i*p7.qbx au)pemidth of the diffraction maximum for light of wavelength 420 nm?    cm

For a given wavelengtm: b0ssk i ne)tsrg, :w/x5q0.lyzv ;th $\lambda$, what is the maximum slit width for which there will be no diffraction minima?

  At what angle will 560-9-.kr8oa1 vmd * logytnm light produce a second-order maximum when falling on a grating whose slits are o go .9t8r*vdla-1k ym$1.45 \times10^{-3 }\;cm$ 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 do+/db51f 2, epzhnc*st lbw. jqes a grating have if the third-order occurs at an1bphtqs*ej lzwc 5n+/ ,df.2b 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 fallinbt:yho dj( .bb**hzj e *ip7g2g on a diffraction grating is observed ahj(.gbbtih ypo**e b 72dj* z:t 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 haso3 cmu51(jcy91cfq cxmp n8o;lh mp,( $ 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 normallu)ig;gs i y:5hy 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 sphqvf1( y8 (pt7r*jj mpectral order that can be seen if a grating with 6000 lines per cm is illuminated with 633-nm la 8q 7jhtvmyp1*f(jrp( ser light? Assume normal incidence.   

  Two (and only two) full spectral orders can be seen onhw fsksaw dtr0d t)o mr4j9z7th 923*0 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 gratinkzwmd os37f* 90tt dat 0rw4rj92hh s)g?    $ \times10^{ 3}\;lines/cm$

  White light containing wavelengths from 4 nl,ufc idcf7;, 5uvpv l8(:qx10 nm to 750 nm falls on a grating withlv8(f, fq5icnx ;:7plv u ,cdu $8500\;lines/cm$ How wide is the first-order spectrum on a screen 2.30 m away?    m

  A He-Ne gas laser which produces monor(qky5pj3 ) pschromatic 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 u31; bd50vy4s9izhkrwhoy t* 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, wl7ww 96ug(9 g 9woecdchat wavelength is most strongly reflected at the center of the outer surface when illuminated normal c79 wl96wdcougw9(g ely 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 .3t3 i)rq npjkglass plates are each 26.5 cm t .)rpnk3i qj3long?    cm

  What is the smallest thickness of a soa/5x pjg8; av+ev5qex4 a kgqztp01j;pp 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 k:4ujw pg 3*kmyellow ($\lambda\;=\;570\;mm$ 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’s19pd nsdisx61 rings (not 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 (Fsi 91xpnsd61 dig. 24–31). How much thicker is the center than the edges?    $\mu m$

  A fine metal foil separates one end of two pieces of optically flat glass, as6c(sishbumy 9cfn/)6jkia+7 in Fig. 24–33. When light of wavelength 670 nm is incident normally, 28 dark7m f6 +b)k6yscsn i hcja9iu/( lines are observed (with one at each end). How thick is the foil?    $\mu m$

  How thick (minimum) should 3 c1vsus47im (r un2yu.p+ gpvthe air layer be between two flat glass surfaces if the glass is to appear bright when 450-nm light is i 3r4 m+uu1y.up7(v isgv npcs2ncident normally?    nm
What if the glass is to appear dark?    nm

  vA piece of material, suspected +bm/,g3 c8+dda sm7n- vu+qu ry*gsojv*c9ixof being 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 rjcv,z-9r;o t f* :xed$(n=1.36)$ 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 immersed in a liquid,l,c*drtdkrbc63 13q w the diameter of the eigctkr3l6d*,c b dq 31wrhth 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 an2mr (5tp iwyw: interferometer if 644 bright fringes are pr: 5wtwi y(m2counted when the movable mirror moves 0.225 mm?    nm

  A micrometer is connected to the movable mirror of an interferometer. When the hgca0e ohljdf7.5:3hgg2b , m micrometer is tightened down on a thin metal foil, the net number of bright fringes th3o bh gdeh0a7lh,gg5jf:2cm. at 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 mirrors;7jyg-sf:8+ h lvbu f $M_1$ 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 th,l*ymgsbh(n9 rough a small glass container containing a cavity 1.30 cm deep. When a gas is allowed to slowly fill the container, a total of 236 dark fringes are counted to move past a reference line. The light used has a wsm y *l,9n(hbgavelength of 610 nm. Calculate the index of refraction of the gas, assuming that the interferometer is in vacuum. $n_{gas}$

  

  Two polarizers are oriented -el/q3gbz.en at 65$^{\circ}\,$ to one another. Unpolarized light falls on them. What fraction of the light intensity is transmitted?   

  What is Brewster’s angv ozkqokq: j9,s4 be,-le for an air–glass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s angle for a diamond sub+m ,hi*uy7f + f49ihzjk5y geimerged in water if the light is hitting the diamfihgi5 9hj,y 4 +iufz7me* yk+ond $(n=2.42)$ while traveling in the water? $\theta_{p}$    $^{\circ}\,$

  Two Polaroids are aligned so that the light passing through themk;tp,g;qn5l +xi so+ph c ,*os is a maximum. At what angle should one of them be placed qc osgx,;op5ithp n+k*,s;+l so that the intensity is subsequently reduced by half?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be placed so as to 5s fbza(nwydz ;(: 2xxreduce the int2abxz(s5 w :fyn;z dx(ensity of the incident unpolarized light to
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are oriented atcj,bk nhicd,2 9z;tr 0 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 ann8 92vmw0,:qcs m ytut 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 bexkp1+jf** bh uj:)c xevbf7d. for reflections off the surface of water for light coming from beneath the surface? Compare to the angle for total internal reflection, and to Brewster’sv7cp 1b *kx+ ).eh:ux f*jdjbf 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 ( vd6)(g,qg xxwtdy-n successive Polaroid sheets, each of whose axis mg6v- (d)t x(, wdgnxqyakes a 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength l h4m 8yyl;9n 0+wm/ymh32 v mcotwjr:$ 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 airplanesuw4s3h :)ozck can interfere with the direcow3ch zus :)4kt 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 diffractiong*j1 k7xzk8pxp dfr01w 1x6jw grating with x 017rw z6d xwkppgk1*8jjxf1$ 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 t2-afp5cl;le 2hme hp ee1rtz:wrx:.q : (7buahrough two narrow slits 0.60 mm apart. The screen is 1.70 m away. A second s2(:5aw .7 -x a1eer2f m;lz:ulbcreeph hp:qtource 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 light? $\lambda_2$    nm

A radio station operating at 102.1 MHzp;.lbe7 )ipq(6jzy pc 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 extend;p7e 6zy)bq(c. il pjping 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 outside doorw*:qy z1wmqw:u ,v8gcfay 0.88 m wide, and blows a whistle of 81:cfv,mz:w *uw q ygqfrequency 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 w.m4yg h7qhsb1 idth D at a 30$^{\circ}\,$ angle to the normal, describe the diffraction pattern.

  The wings of a certain beet40v ury zddi8 cg)7r8aw-4knm)zg j8ele have a series of parallel lines across them. When normally incident 460-nm light i rc 7g4rvzdmkn) )u8-4dzajw 088ygeis 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 gr71 pv)apwu+g cating have if there is to be no second-order spectrum for +c)gauv71wpp any visible wavelength?   $ lines/cm$

Show that the second- and third-order spectra of white light produced by a 8;,uje3o *y myz3vinso5ig f29-imsn diffraction grating always overlap. What wavelengths overlam;5fi siy 9jmeo38 ons-2uv3i yz ,*gnp exactly?

  When yellow sodium light,tkcs 5tbn()09cm(z wz $\lambda\;=\;$ 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:ij96abpikm p 4r,iu2 diffraction grating with and the pattern is viewed on a screen 22i pk , b4a9:u6pirjim.5 m from the grating. The incident light beam consists of two wavelengths, $\lambda_1\;=\; 4.6\times10^{ -7}\;m$ and $\lambda_2\;=\; 6.5\times10^{ -7}\;m$. Calculate the linear distance between the first-order bright fringes of these two wavelengths on the screen.    m

What is the index of89f m 8ta)c*hvhrll7: u wk*dx refraction 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 upon it? Do you have a choice for at*h9*xhm)fl:la8w7 cud 8vrkn answer?

  Monochromatic light of variable wave/cr+aj4ysc xhx2/ vn5i+qhm qo16lc;length is incident normally on a thin sheet of plastic film in air. The reflected light is a minimum only fhqay5; q xn c2j1cl++i4 6xo/mrshc v/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 anti-r 1jju +8zsoz bb))bg(aeflective 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) thicjdh kup / *rgop((136ca n40jct ajfe*kness for the air layer between two flat glass surfaces if the glass is to appear darkea*jj*hn/ard(po 03f ctc(4u k pg1j6 when 640-nm light is incident normally?    nm
What if the glass is to appear bright?    nm

Suppose you viewed the light transmitted tec 8 6t)lgpvi)/ d+veahrough 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 minima. Consider all possible value eecgi)6 tv/dv)8 +alps 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 t7yeugg -1lx1 )h 0juaihe horizon is the Sun when light reflecting off a smooth lake -7algjxhu1g1 y) 0ue iis polarized most strongly?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be pl*ga hl,)xij g63zen, lb.g ht1aced so as to reduce the intensity of the incident unpolarized light by an additional factor (after the first Polaroid cuts it in )hz31g bl tn e,hi.,j*ag6xlghalf) of
(a) 4,    $^{\circ}\,$
(b) 10,    $^{\circ}\,$
(c) 100?    $^{\circ}\,$

  Unpolarized light falls on two polarizer sheets whose tran9l:s 8vci 15fxjytp;z cdi*- hsmission axes are at right angles. A third polarizer is placed between the first two sc9 5ydfh:sljvic p-z ;8 xt1*io 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 wl2 mde8f8o2vg ith 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 throu,m5 0e3fumcservx7)72g 2rflfsh 7negh 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). Estimafe)f,n7gc72s el 2smu7rfr53 ex m0vh te the width of the beam when it reaches the Moon.    km

  A series of polarizers are each placed at 0lrq-uo;4y ys7g9 kpq 7s9nyfa 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 ykug thuu/kn .15z867m p*dehu*n6qt$(n=1.34)$ 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 other.k ,l +*bh;xzp1-iwyn a They are located at poiiwn* hy+ ak1pz -l,b;xnts $S_1$ 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 wa2vh1; +k zm zvv.1knpwko: -iyvelengths, 420 nm and 650 nm, enters a silicate flint glass equilateral prismz1y2vn- hw;mkv1 :kovi pz+k. (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 ony9i5p,9hvos i e( ret9e 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