Does Huygens’ principle apply to sound h7n9 7o165gotapjkke waves? To water waves? Explain.

What is the evidence that light is energyod-zh l b1h3;n?

Why is light sometimes described ajyxx(k f.-o4,m ,t 5jcfh3br bs rays and sometimes as waves?

We can hear sounds around corners, but we cannot see aroun1x3ksa 1es;o9 d4 *zz7dt2 zorywa ve.d corners; yet both sound and light are wavw329x eo4*str z1.zyk1 sdzeao7 a dv;es. Explain the difference.

If Young’s double-slit experiment were suy3b cya r.y 8h4nsx6)abmerged in water, how would the fringe pattern be change a.b ny hcaxs4)ryy386d?

Monochromatic red light is incident on a double slit, and the interference patte shy6vuk q53jnl ,/d* km9fdz9rn is viewed on a screen some distance away. Explain how the fringe pattern would change if the red ,nkqhf9d/3ykj9l *6v zu 5dms light source is replaced by a blue light source.

Two rays of light from the same f9dgvi0rh u 2e0wd52fsource destructively interfere if their path lengths5 dg0hr2d iw0 29uefvf differ by how much?

Why was the observation of the dogg i.j/nh:qr9uble-slit interference pattern more convincing evidence for the wave theory of light than the observr :n/j q9ig.hgation of diffraction?

Compare a double-slit experiment for sound waves to thatxc*4ku:bnl a-f:lk- k5pdos- for light waves. Discuss the simifl: u* kdxk-c 4solp--:5kb nalarities and differences.

Why doesn’t the light from the two headlights of a distant car produce an intao5sl4a/b ;+2-qnkj lzfaq,i erference pat5azbfk4lo +j ls;,qnqa ia /2-tern?

Suppose white light falls on the two slits of Fig. 24–7, but one s0n1eb r max+nkrc4ns;1d- 2k llit is covered by a red filter (700 nm) and the other by a blue filter (450 nm). Describe the pattk;sdn0xa4+be 21rlkrc- 1 n nmern on the screen.

When white light passes through a flat piece of window glass, it is not brok s9l)cq7:xbao.0ynzien down into colors as it is )no7cz0.y isq:x alb9 by a prism. Explain.

For both converging and diverging lenses, discuss how pr1ld9p*cq0a6 (n kkvthe focal length for red light di1( kc l*dk qvnapp096rffers from that for violet light.

A ray of light is refracted through three different max+ zz(zkxs+5f;ix/ gjterials (Fig. 24–55). Rank the maisz ( /;5kxzfjg++zxxterials according to their index of refraction, least to greatest.

Hold one hand close to you0bc o:i*n- ubn0:oa9tf mis6dr eye and focus on a distant light source through a narrow slifiu icodoa*:9 s6 bnnm0-b0:tt between two fingers. (Adjust your fingers to obtain the best pattern.) Describe the pattern that you see.

What happens to the diffraction pattern xcr(4 jmd*9pb of a single slit if the whole apparatus is immersed in (a) wjd m9bp*x4c(rater, (b) a vacuum, instead of in air.

For diffraction by a single slit, what is the effect q q*tkxt7e*n +t,nlb(vcl 94z of increasing (a) the slit wid4*(bcq q xvl*,t+9tnez7t kl nth, and (b) the wavelength?

What is the difference in the ic/3m 5 ufatt0x6e )hv xxy l3+gq5svm9nterference 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 ;q w832il:ty; wgibgz3n qhf1advantage of (a) many slits, (b) closely spaced sliqt3wbwy g:i2;8qf3 n hizl1;gts?

White light strikes (a) a diffraction grating, and (bcd/ bv1t t4ev/) a prism. A rainbow appears on a wall just below the direction of the horizontalvtvdt e/b41/c incident beam in each case. What is the color of the top of the rainbow in each case? Explain.

For light consisting of wavelengths between 400 nm and 700 nm, incident nor57g9ipl c p*gymally on a diffraction grating, for what orig5* ypcp7lg9 ders (if any) would there be overlap in the observed spectrum? Does your answer depend on the slit spacing?

Why are interference fringes nfs8efdmh+cd34g;2 0h p jr )kkoticeable only for a thin film like a soap bubble and not for a thick piecd3jk2hdk804f+;cm s hpgr)efe of glass, say?

When a compact disk (CD) is held at an angle in white light, tu4 n3yzyi*dy 2he reflected light is a full specy d*uiny 3y42ztrum (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 frb r78/9;m3wglfqrrsqynim/6 om the center?

Some coated lenses appear greenish yellow when seen by reflected light. W1.zfwmh9c w. tkgou4g w9s)c4hat wave 1sz9cw t)ug4.m o4kwf ch9g.wlengths do you suppose the coating is designed to transmit completely?

A drop of oil on a pond appears bright at its edges, wher jt-fqp 4ssftn o/56+de its thickness is much less than the wavelengths of visible light. What can yojf4/5-sf tsq +don6ptu say about the index of refraction of the oil?

What does polarization tell us about the nature of eh cn9 pf8g/o4light?

Explain the advantage o ,;r.e 8tslm1h:gpjgw3owpdm 00jz- pf polarized sunglasses over normal tinted sunglasses.

How can you tell if a pair of sunglasses is polarizing or ne7+zh wym 83czot?

Two polarized sheets rotatuht trol6zp+3(xu ou((j 4jn 9ed 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 th ci: 0k2z7ifepe Earth had no atmosphere?

If the Earth’s atmosphere were 50 times denser than it is, wo4ha)la. *p-d /c.o broybczn ) lkjy.7uld sunlight still be white, or would itrl cc) .)*./kn pbla4.od 7oz-hbyajy be some other color?

  Monochromatic light falling on two slits 0.016 mm apart produces the b cu v(3uim88jvhl:xvj)k/q;fifth-order fringe at an 83vcv : 8k;i (/hj8bmquxv ju)l.8$^{\circ}\,$ angle. What is the wavelength of the light used?    $ \times10^{-7 }\;m$

  The third-order fringe of 610 nm light i(gygk4q yl4o) s 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 veo ie91)dy7d gpv2x. ygry 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 wavelength and frequency of the lie y17y2)igxo . gpdv9dght.
$\lambda\;=\;$    $m$
$f$ =    Hz

  A parallel beam of licb8mru- o0p 3bght from a He-Ne laser, with a wavelength 656 nm, falls on two very narrow slits 0.060 mm apart. How -8b0urb 3copm 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 slit7 pl1*r0;l sz fi3qfyjs and produces an interference pattern in which thpyf17j zsfir03l;l *qe fourth-order 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 lighllw-qcrz .91/;g;g .lplxqa mt passes through two slits 0.58 mm apart, how far apart are the second-order fringes for these two wavelengths on a screen 1.0 mrz- la/p;q.;9.lql1mgcwxl g away?    mm

  In a double-slit experiment, it is found that blue light of wavelength 460 nm g,yg;42 qnj qynives a second-order maximum at a certain location on the screen. Whatyng;24j nqyq , wavelength of visible light would have a minimum at the same location?    nm

Water waves having parallel crests 2.5 cmnk,-81anakn)n m x la8 apart pass through two openings 5.0 cm apart in a board. At a point 2.0 m beyond n1kk,)ana xmanl8n8- the board, 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 the lower slr)bjydp e *im o,:6(coit in Fig. 24–7 so that tho,m 6 jey b:ri*(dcpo)e two waves enter the slits 180$^{\circ}\,$ out of phase (Fig. 24–57). Describe in detail the interference pattern on the screen.
24-7
24-57

  In a double-slit experiment, the third-order maximu 4n 51vcs1ms qh.el2uim 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 the same slits. How far from the central bright spot will the second-order maximum of this light be located? m1el .c nhq2v1u4iss5   mm

  Two narrow slits separated by 1.0 mm are illuminated by 544 nm liunmv0*a3z oas13i ( zyght. Find the distance bet i3uzyaas*v03nmo 1z( ween adjacent bright fringes on a screen 5.0 m from the slits.    mm

  Light of wavelength 480 :tf3 2nhwse u.r1w (s:wy cg5jnm 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) cove +ne6idyer+;mrs one slit of a double-slit apparatus illuminated by 640-nm light. The center point on the sey+ r+ i6n;mdecreen, 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) exce *cfh*8p7pu qky evh61 7or(dhed that of violet light (400 nm)v o*ph (freydhc867*7p1 uqkh in silicate flint glass? (See Fig. 24–14.)    %

  A light beam strikes a pa, 32jiajs e:ji.vhe0 iece 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 containinu3pzm q6 9ae2gsyf5w6g 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 angular wio/ ughu* +7j;aazk8w i yosnnb--*9y edth of the cenub*8 ou ; ogawy-n-/9ena 7 zsiyjkh*+tral diffraction peak?    $^{\circ}\,$

  Monochromatic light falls on a sli9 0(c7 (42kgcxa vnejcz3;q vvj 0yewet 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 slit that i3d e/cl3pz6d8:ud fi as $ 3.20\times10^{ -3}\;mm$ wide. Estimate how far the first brightish diffraction fringe is from the strong central maximum if the screen is 10.0 m away.    m

  A single slit 1.0 mm wide is illuminated by 450-nm light. What is the widzk-/f(m wm-eeth of the central ma m/-e-efm (kwzximum (in cm) in the diffraction pattern on a screen 5.0 m away?    cm

  Monochromatic light of wavelength 653 nm falls on w. e2w0ccwj2la slit. If the angle between the first bright fringes on either lc02jwew .cw2side 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 ;wjnafp nn i q2r(d)n*xs4-e5 0.0348-mm-wide slit illuminated bp*-n; ifq 54wnxj(ras2 dn)ney 589-nm light?    cm

  When blue light of wavelength 440 z8i bza 8t;./hrow936b o,tfw ;pjggtnm falls on a single slit, the first dark bands on either sido;tzjr86 t.9ww8it3fbgohz/ b, a;g p e 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 crwtd/za42g/m. zm c*xveates a central diffraction /c.m zzwmt2gv 4a*/x dpeak 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 lighti++iacr moh ;4 so that the diffraction maximum is 4.0 cm wide on a screen 1.50 m away, what will be t++h mo ci4;irahe width of the diffraction maximum for light of wavelength 420 nm?    cm

For a given wavelengk1+x ktx /ap mtts3-u0th $\lambda$, what is the maximum slit width for which there will be no diffraction minima?

  At what angle will 560-nm light produce a second-order mf**7 yay*vtr 2x: uzxtwa)0is aximum when falling on a grat ***)uir2vs7 xx:tyfzya 0wating 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 centimb mf*yxr )k0k6eter does a grating have if the third-order occurs at an 18.0 xrf 6yb)k*0mk$^{\circ}\,$ 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 lpaa gocn6/y(.j7*e18yhp ; b-b a hrkoight falling on a diffraction grating is observed at a 15b*a-rh86o cnyb;pagp k a/ o.hy1je7(.5$^{\circ}\,$ angle. How far apart are the slits?    $\mu m$
At what angle will the third order be observed?

  A diffraction grating has *r8efnagnsj,a ie9lo 9(4 +nu$ 6.0\times10^{ 5}\;lines/m$. Find the angular spread in the second-order spectrum between red light of wavelength $ 7.0\times10^{-7 }\;m$ and blue light of wavelength $ 4.5\times10^{-7 }\;m$.    $^{\circ}\,$

  Light falling normally on ayul 4i t52wm-3jq) lc lb0, ,pbgdu-ml $9700-line/cm$ 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 sesixmp1z jq 669en if a grating with 6000 lines per cm is illuminated with6q1m x6z9i spj 633-nm laser light? Assume normal incidence.   

  Two (and only two) full spectral orders can be seen oe,d9kv a7)cmc+kk9 pkn either side of the central maximum when white light is sent through a diffraction grating. What is the maximum number of lv c ,p)9amkck7d +ek9kines per cm for the grating?    $ \times10^{ 3}\;lines/cm$

  White light containing wavelengths from 410 nm to 750 nm falls on a grating :s3zjflrm7q f;gt6ia: 7fk/ywithrffkjy f:ig mz77ls;6:3/at q $8500\;lines/cm$ 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 waveleng7g *0c. lpi,aasuv:pk th $\lambda\;=\;6.328\times10^{-7 }\;m$ 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 measured byg )g1m w6uo8yr 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 12* - x;swz:mktp t;gn/zw8a-i i0 nm thick, what wavelength is most strongly reflected at the center of the outer surface when illuminated normally by white light?8sagzzi; mw/ - :t kx*;nwit-p Assume that $n\;=\;1.34$. $\lambda$ =    nm ,which is an    -  

  How far apart are the dark fringes in Example 24–8 if the glass plates are each5v dc7g -gktx6 26.5 cm lon 7dgtx-gkv5 6cg?    cm

  What is the smallest thickness of a sgdu ho1t7ehcr 8ew00 ,oap 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 (cj3d/oen ,h) bjf(86vei . biv$\lambda\;=\;570\;mm$ is strongest) when white light reflects from it. What minimum thickness of coating $(n=1.25)$ do you think is used on such a glass $(n=1.52)$ lens, and why? $t_{min}$    nm

  A total of 31 bright and 31 dark Newton’s rings (not countifeg: ,cbp b dh7jadq1sqq 27-:ng the dark spot at the center) are observed when 550-nm light falls normally on a planoconvex lens resting on a flat glass surface ca:77,h- dqeg: dpjb1 fsqqb2(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*lej*8 dhun; -mrly-hj ithl*ev3q;4 optically flat glass, as in Fig. 24–33. When light of wavelength 670 nm is incident normallyt ;mjhi 8r- ;ln3ll4eyu dv*h** qjhe-, 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 glassua*8).xsdamq8b/ sc c surfaces if the glass is to appear bright wc.) ubma8 d8xq*s a/cshen 450-nm light is incident normally?    nm
What if the glass is to appear dark?    nm

  vA piece of material, s xg+s g wug.(gi-,xhl.t57taguspected of 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 alcohiu0 j:4 qkz03s:bkkw6su x, rzol $(n=1.36)$ 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)*zvsk+v0 ;chd8s7p d y is immersed in a liquid, the diameter of the epdkcvz+* s0 y8 ;dvh7sighth dark ring decreases from 2.92 cm to 2.48 cm. What is the refractive index of the liquid?   

  What is the wavelength ofo)5tiwm h)t3x sli;*ft6o 7 tbz1u:o f the light entering an interferometer if 644 bright fringes are counted when the movable mi6i )ttozfsmttuo53 w l1i *o:x7h b;)frror moves 0.225 mm?    nm

  A micrometer is connected to the movable mirror of an inteu2 nv,g1)p1k,6 baxcc1d p5ne-hf jln rferometer. When the micrometer is tighgdbp1jeav15 cxu, nfnp-1k)n2h lc ,6tened down on a thin metal foil, the net number of bright fringes that move, compared to the empty micrometer, is 272. What is the thickness of the foil? The wavelength of light used is 589 nm.    $\mu m$

  How far must the mir)e8r6tv u cwe*ror $M_1$ 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 i8wojw q7l.u n/x;3 +9bbdfprbbq k48s nterferometer (Fig. 24–59) 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 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 interferometerrb/xosq8bq w8puk +fl7b nw3;9.4db j is in vacuum. $n_{gas}$

  

  Two polarizers are oriented ahn3kub+n m42 xt 65$^{\circ}\,$ to one another. Unpolarized light falls on them. What fraction of the light intensity is transmitted?   

  What is Brewster’s angleo2(3juxl kq me z-;-qalzf(* s for an air–glass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s angle for a diamk -pr t cn 3mj;;r5qls(fl-1 xzwxbh))ond submerged in water if the light is hitting the diamon-t)msxhqfkzw -nrlp;);x1bj5( clr3 d $(n=2.42)$ while traveling in the water? $\theta_{p}$    $^{\circ}\,$

  Two Polaroids are aligvxw ;xy -ul7,86ialj 0zmq8ug ned so that the light passing through them is a maximum. At what angle should one of them be placed so8v ziuyqa-;ml x 8,uljxg706 w that the intensity is subsequently reduced by half?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be placed so as to reduce t, b qqj9)eoe8whe intensity wq,)je q9 eb8oof the incident unpolarized light to
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are orientedv0w 7 kjn6m,ps4rjdzpq 56b-5/q . mo m-zuwph 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 orie4tug+55ic duep;,zk pnted 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 reflections off the surface of zyt b-.ry49e mgd,aj) o/fg, lwater for light coming from beneat.,/tflr maod9zeyg ,4gb )- jyh the surface? Compare to the angle for total internal reflection, and to Brewster’s angle from above the surface.
If the light is coming from water to air, $\theta_{p}$    $^{\circ}\,$For the refraction at the critical angle from water to air $\theta_c$   $^{\circ}$ If the light is coming from air to water $\theta_p'$   $^{\circ}$

  Unpolarized light passes through five sp0tza9dx g7*ku 77frv uccessive Polaroid sheets, each of whose axis 7dp*gr uft90azvk7x 7makes a 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength vrfw(8+rz/lf $ 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 airplanes can interfpd )blbbfaj 6ef6-.q(ere with the direct signal 6b)q fdfl6b-p(e. a bjfrom 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 thrqj7vf(;npjc .:*jvucl ly/ ;wough a diffraction grating with c*w(;vl7pn vjj .ufj;y/lq :c$ 3.00\times10^{5 }\;lines/m.$ The wavelengths of the three lines are $ 6.56\times10^{-7 }\;m$ (hydrogen), $ 6.50\times10^{ -7}\;m$ (neon), and $6.97 \times10^{ -7}\;m$ (argon). Calculate the angles for the first-order diffraction lines of each of these sources. $\theta_{h}$    $^{\circ}\,$ $\theta_{n}$    $^{\circ}\,$ $\theta_{a}$    $^{\circ}\,$

  Light of wavelength 590 nm passes through two narrow slits 0.60 mm apart. The 41akf yh) hs+tscreen is 1.70 m away. A second source of unknown wavelengthsa41hy kf)t+h 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 MHz broadcasts from two identical n5dtaq*8e t 1r/bg wg;antennae at the same elevation but separated by an 8.0-m hrt5gd ne w/g;aq8t 1b*orizontal 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 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 wdtd7ik 72gec(.x ep .vhistle of frequency 750 Hz. Ignoring reflections, estimate at what angle(s) it is not possible to hear the whistle clearly on the playground outsidevdketxe2.(7 p7 idc g. the doorway.    $^{\circ}\,$ either side of the normal.

If parallel light falls on a single slit of widthu /22 ygrpcii;p:.qz8zrj j:r D at a 30$^{\circ}\,$ angle to the normal, describe the diffraction pattern.

  The wings of a certain beetle have a sgr9eeq /qr*zio6 ( ln)eries of parallel lines across them. When normally iei(/o*l6gn)eq qrz9rncident 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 have if there is tdjr/ubtp:+ d9i7beg :o be no second-order spectrum for any vibg e9ju:7d/ +:br dpitsible wavelength?   $ lines/cm$

Show that the second- and third-order spectraxt4o dg-)t1vj of white light produced by a diffraction grating always ov- tjv4dx1)ogt erlap. What wavelengths overlap exactly?

  When yellow sodium light+ax*zfx*j dj9, $\lambda\;=\;$ 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 on pr,xn y 36 hk4su*2gbta screen 2.5 m from the grating. The incident light beam consists ysgh246 k*3,tnb urpxof 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 152w.y7t/a n :3vv/ek zw nro2ig0 nm thickness of it, when laid on glass, is needed to reduce reflection to nearly zero wwo/n :/ewv 27zy aik. gr2nt3vhen light of 600 nm is incident normally upon it? Do you have a choice for an answer?

  Monochromatic light of variable wave.ki.ep gwq nm(0;vj0lxdl.n 3 length is incident normally on a thin sheet of plastic film in air. The reflected(0qg vl.jnix. 0 m e.pkd3nwl; 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 th8khsb :zko:(u/d4 g vxickness needed 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) th4)ykdg2i*f m+( q 3uit zof,auickness for the air layer between two flat glass surfaces if the glass is to appear dark when 640-nm lig i o2qizk(,4y )mf3+aud*tfu ght is incident normally?    nm
What if the glass is to appear bright?    nm

Suppose you viewed the light transmitt z jn0iwsut*af/p/y.9 ed 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 minima. Coni s a.wy9tnzuj /0f*p/sider all possible values of index of refraction. Discuss the relative size of the minima compared to the maxima and to zero.
24-30
24-36

  At what angle above the horizon is the Sun when ligh6 5* iinyznapgot-06 ct reflecting off a smooth lake isgt0n6 pzc*ni-5 oiy6 a polarized most strongly?    $^{\circ}\,$

  At what angle should the axes of two Polakj /p/ad)p+1nj :akkqn:wk+dx*3r krhc(t 0u roids be placed so as to reduce the intensity of the incident unpolarized light by an additional factor (after the +1:*kh+dr)/ p3c dwa0kpxkj/ktjunak n: q(rfirst Polaroid cuts it in half) of
(a) 4,    $^{\circ}\,$
(b) 10,    $^{\circ}\,$
(c) 100?    $^{\circ}\,$

  Unpolarized light falls on two polar syq27 ;.yuzoiizer sheets whose transmission axes are at right angles. A third polarizer is placed between the first two i.;yo zusq72y 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 plac38rr hg xr-y.ged 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 kglhmf1 /tlqwe-v bm3 mk0)9,t0wba, a slit of width 1.0 cm and is pointed at the Moon, which ifl3bqkg w,0mv9 ma/m, w)h -te0t1 kbls approximately 380,000 km from the Earth. Assume the laser emits 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 are each placed.x8o hn8 i z.db,t2ikk 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 ir-n sbz9q ,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 i kgu7t82tqgpt +fww m-tv:( 8radiating 6.0-MHz radio waves in phase with each other. They are located at pf:mkt w-(vq8 p u 2i8ggtwt7t+oints $S_1$ and $S_2$, separated by a distance $d\;=\;175m$, Fig. 24–61. What are the first three points on the y axis where there will be destructive interference? (Destructive interference in this case means that a radio receiver placed at that point would pick up no signal).    m    m    m

  A parallel beam of light containing two wavelengths, 420 nm :8daq pu*3ttr and 650 nm, enters a silicate flint glass equilpa rd*3u 8tq:tateral 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 an rebnunj v3/5d. iyd58d 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