Does Huygens’ principle apply to sound waves? To watery:mw8fqb- +xnh65/,l q ayeu g waves? Explain.

What is the evidence2f p42fsvd5wn*3saj c that light is energy?

Why is light sometimes desc.hm1(6jsckiblv0 3 gyribed as rays and sometimes as waves?

We can hear sounds around corners, but we ck - e 3e,ne* .a bsobk//gvg9ae*v9fsrannot see around corners; yet both sound and light are 9 nf kekg-ea.gavo*/ vb9,3 serbes/*waves. Explain the difference.

If Young’s double-slvn/ .wg)uevjt.wr 6f8it experiment were submerged in water, how would the fringe paewvt8.wv f) /urn.jg6ttern be changed?

Monochromatic red light is incident on a double slit, and the interfg;62q7 fp78l 5 ccvm fplljb; vweq;*serence pattern is viewed on a screen some distancbvpp *e;;g7l7f 2 ;cm6lfjvc w58qqsl e 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 destructively interfere if their ej n: c:-55m;c 6)yiav:cmh ,ptfcmjypath lengths differ by how mnfcpcme-imjc,6 mc :5v h::j)5tyya ; uch?

Why was the observation of the doublxs1;z9kj 3 1u:ih ycrpe-slit interference pattern more convincing evidence for the wave theory of light than t ys3x r:h1jp9;kiuz c1he observation of diffraction?

Compare a double-slit experiment for cf2b9k 5j g(zasound waves to that for light waves. Discuss the similarities and dif 5zb2ck jag9(fferences.

Why doesn’t the light from the two headlights of a distant car p w qu,oiqxi5avwi)v6pnw,-:1 roduce an interference pato) p,qww -,xiuqi:aw5i61v nvtern?

Suppose white light falls on the two slits of Fig. 24–7, but one slit i n6q n6 kpu1,t)veae9hs covered by a red filter (700 nm) and the other by a blue filter (450 nm). Describe the pak)n1eqa e, ph6ut6v n9ttern on the screen.

When white light passes through a flat piece of wma g8ar mas3m-5uj7y 7. auw,xindow glass, it is not broken down into colors as it is by7,a 7gax3awaum- m. smjyu8r5 a prism. Explain.

For both converging and diverging lenses, discuss how the fu 6 t qif* g(lvips44(:vd7glvocal length for red light differs from that for violet lp6 vql(7 idgf4ti* (s:g4 lvvuight.

A ray of light is refracted through three different materials (Fig. 24–55). Ranabd3v27-pxaw r dw4.ovuh)a: k the materials according to their index of refraction, l:4 db)vuv2o-7r .x d3a pawahweast to greatest.

Hold one hand close to your eye and focwh,z bde9c9b 8us on a distant light source through a narrow slit between two fingers. (Adjust your fingers to obtain the w 9hed,cb89z bbest pattern.) Describe the pattern that you see.

What happens to the diffraction pattern of a single slit i r9yto2ad))h d-agrwtk(q9(vg(1oo mf the whole apparatus is immersed igw)()(-9qo(m1 h2 tya ktv orodd9a rgn (a) water, (b) a vacuum, instead of in air.

For diffraction by a single slit, what is the effect of incgytcz *bc ntw0w2y./ 9reasing (a) the slit width,2zy*/twc90yb. c gtw n and (b) the wavelength?

What is the difference in the interference patterns formed (as(n2 bst-7atrl0 .j+ rnw*gxg) by two slits $^{-4}\;cm^2$ apart, (b) by a diffraction grating containing $10^4lines/cm$?

For a diffraction grating, what is x 4vei+emy7.ub/ san* the advantage of (a) many slits, (b) closely spaced slits?7name.*e/ v s4+uixyb

White light strikes (a) a diffraction grating, and (b) a prism. A rainbow app(; erxykyd,pbo48y1;k s bci8ears on a wall just belo(8sd1 o;cpx8ebr k,i;k byyy4 w the direction 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 wavelengths between 400 nm and 700 nm, incidv6k4fa. 0i*f* z pipfcent normally on a diffraction grating, for what orders (if any) would there be overlap in the observed spectrum p*k* iiz0pa. fcf6v4f? Does your answer depend on the slit spacing?

Why are interference fringes noticeable only for a thin filmgx liig0 3:bv7 like a soap bubble an70li:b xvig3 gd not for a thick piece of glass, say?

When a compact disk (CD) is held at an angle in whiteii*d1u3v3) d kvrbjmg( k4sm, light, the reflected light is a (vjm iim31r d*,sukd g vkb43)full spectrum (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 frodp pg) rv*gjj-,o1kmw0,zjt-m the center?

Some coated lenses appear greenish yellow whey;e y4 j6y8vro)2opq en seen by reflected light. What wavelengths do you suppose t 8pre;j6y)qy4 v oyo2ehe coating is designed to transmit completely?

A drop of oil on a pond appears 2lwy lt;l.v4zs vd 3l/bright at its edges, where its thickness is much less than the wavelengths of visible light. What/ldztvv2 llys; . 4l3w can you say about the index of refraction of the oil?

What does polarizatie4hmp *) gdzs6on tell us about the nature of light?

Explain the advantage of polarized sunglasses over normal tinte7 :lr8a eiikw+vxau*)2tq)c ni; +soed sunglasses.

How can you tell if a pair of sunglasses is polarizing or no )c 9uofqmm06et?

Two polarized sheets ro)/elik hyav9 j+j1*v jtated 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 co6)jqd6wc ;o zvlor of the sky if the Earth had no atmosphere?

If the Earth’s atmosphere were 50 times denser than it is, would sunlo7 q(krhoid b576n*jpight still be white, or would it be somen7r5qh7kd*o iobp (j6 other color?

  Monochromatic light falling on two slits 0.3 qf rqj19d 9n3v/q 9ncr(o*ybn nivt+016 mm apart produces the fifth-order fringvd+1ft3b/n* q(rjci9qn no3 q ynv99re at 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 at an angle o10g 6jxmvv( fq2d5 immf 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 0.048y2 r :sp;vh;ne mm apart. Successive fringes on a screen 5.00 m away are 6.5 cm apart near th ;:rvhspyn2; ee center of the pattern. Determine the wavelength and frequency of the light.
$\lambda\;=\;$    $m$
$f$ =    Hz

  A parallel beam of light from) m/yonod*m.i a He-Ne laser, with a wavelength 656 nm, falls on two very narrow slits 0.060 mm apart. How far apart are the frn/). oomd*imyinges in the center of the pattern on a screen 3.6 m away?    cm

  Light of wavelength 680 nm falls on two slits and produceudy4 *k3aw;aws an interference pattern in which4da;*u y3w awk the 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 light passep(7x g68 m/ki nutse5us through two slits 0.58 mm apart, how far apart are the second-order fringes for these t8uu57 tsm(igeknx/6 pwo wavelengths on a screen 1.0 m away?    mm

  In a double-slit experiment, it is found that blue g:a :nv+yj ,m)vl 0ce/fsp1nulight 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 locationl evcmy+1p:nv)/ug fs: j,0an?    nm

Water waves having parallel crests 2.5 cm apart pass through two openi l;c8s4hwb j,ai)kk(r ngs 5.0 cm apart in a board. At a point 2.0 m beyond the board, at what angle relative to the “straight-through” direction would thj; a(hs8i)l rwc kk4,bere be little or no wave action?

Suppose a thin piece of glass is plg ev d/z-eze1+czq/0 faced in front of the lower slit in Fig. 24–7 so th evd0qfze ec1-z+//g zat the 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 expeld,7j,c ohcc, riment, the third-order maximum 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 p ,h7jc c,,doclrojected through the same slits. How far from the central bright spot will the second-order maximum of this light be located?    mm

  Two narrow slits separated by 1.0 mm are illuminated by 544 nm lig:ezdih (fod8x:y05iinif- 1e ht. Find the distance between adjacent bright fringes on a screen 5.0 m from theezi8dfi i- 1yd h i0xof:n:(5e slits.    mm

  Light of wavelength 480 nm in air falls on two slits bynz1hpksvb) tm;90 xwv g2s28dr5 .q $6.00 \times10^{-2 }\;mm$ 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 onhp1foue 6y8g 0e slit of a double-slit apparatus illuminated by 640-nm light. The center point on the screen, instead of being a maximum, is dark. What is the (minimum) thickness of the pl68fhug01p yoe astic?    nm

  By what percent, approximately, does the speed of re.brpc:7pwui; sulo9 7hv 1(x;2hlpc sd light (700 nm) exceed that of violet light (400 nm) in silicate flint glasoi 9s7 :pc2s( .;7ppl w uhb1hrluc;vxs? (See Fig. 24–14.)    %

  A light beam strikes a piece of glass at a 60.00vf +6)dqhk9wd+gqj1: jyr1r gu *u g2u$^{\circ}\,$ 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 wavelengt l.m/; qy)qck9q/wp+6 r ie;ioxrys9u.ej *ps hs, $\lambda_1\;=\;450\;nm$ 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 full692ge *bsoy zdc78cto ;ja:l1enhyz 2 angular width of the central diffraction peak: coa;z2oe 6j2y b nytg7l hz8s9e*d1c?    $^{\circ}\,$

  Monochromatic light falls on a slit tha eojle ;z 4fsjav(27 n)t:ned(t 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 52(7i bb3o ,qdzd0 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 wide is illuminated by 450-nm light. What is tm9u .r04)f0afgtgasvhe width of the central maximum (in cm) in the d0afavgt m)fur940 .sg iffraction pattern on a screen 5.0 m away?    cm

  Monochromatic light of wavelengtuc0v3krl 30r tqh8r,hh 653 nm falls on a slit. If the angle between the first bright fringes on eithe cr8trulqh0v hk0,3r3 r 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 behef:brq3j,w 8 4sa cg+k*k b4ilind a 0.0348-mm-wide slit illuminated by 589-nec4 s8kkf igj:4lb r3b+*aqw,m light?    cm

  When blue light of wavelength 440 nm falls on a single slit,jj c3g r.,jg6t the first dark bands on either side of t36grjg ,j.cjcenter are separated by 55.0$^{\circ}\,$. Determine the width of the slit.    $ \times10^{-7 }\;m$

  When violet light of wavelengtyu.l km-n- czwvvx(g)nbg9w-y49 a.kh 415 nm falls on a single slit, it creates a central diffraction peak that is 9.20 cm wide on a screen that is 2.55 m away. How wide is the vc9kbl .4xgy-(y k9a)u wwv gm--zn.nslit?    mm

  If a slit diffracts 650-nm light so that thegq4 k(g -a5vyg diffraction 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 -(qy4 vgkg5a gnm?    cm

For a given wavelength j b ue5n(ekmnh)9sc;: $\lambda$, 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 maximum oiw4a) 02q:d 5-q(hogdqyw yan7;ya vwhen falling on a gratin0qyy5qia7qdwyg n ah; d4ow2)o a(:-vg 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-orgnq/nk (p5; ajder occurs at an 18qn (g /;anjk5p.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 dyrvo +p+n2* )l, epmgciffraction grating is observed+lc py)pvo mg+2e,n*r at 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 has g0x,s .jr:eup$ 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 onyml caq,6:i 4a2wy29n .mrgad 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 se0n4nmye3a( m:dw71t3h, fj wyqulg+uen if a grating with 6000 lines per cm is illuminated witd w 3: yqfhleam4gwu jt70muy3(n,1n+h 633-nm laser light? Assume normal incidence.   

  Two (and only two) fuzull0m*, - fjjll spectral orders can be seen on either side of the central maximuj ml0-,u*jlfzm when white light is sent through a diffraction grating. What is the maximum number of lines per cm for the grating?    $ \times10^{ 3}\;lines/cm$

  White light containing wavelengths fr -k8n*dasnye 3n:n *xtom 410 nm to 750 nm falls on a grating with *a txens3n: nk-8*ydn$8500\;lines/cm$ How wide is the first-order spectrum on a screen 2.30 m away?    m

  A He-Ne gas laser which produces monochromatic lightkd.-qe3vr:v mnfe(qd 5 (h y,keh 6)l x;g(ddu 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 areg+*5 ov-c kzvj 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 l 7mkra1x: 4(n/uk:ak lg3xqbstrongly reflected at the center of the outer s4 k lm 3/1:a7ar(lgxx qbk:uknurface when illuminated normally 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 pl sb ji6+tg7/x9rhe h9lates are each 26.5 cm67jg/hieb9+xhs lt r9 long?    cm

  What is the smallest thickness oa7vzvjyr ev8i;e u0g ;4z (2cmf 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 yw7/4l aj.yki)xg am *xellow ($\lambda\;=\;570\;mm$ 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 rinrt41q6yp; a fpgs (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 (Fig. 24–31p ;6f4apqty1 r). How much thicker is the center than the edges?    $\mu m$

  A fine metal foil separates one end of two pieces of op;vvwo.l yl;q7ns()z ) pja r/jtically flat glass, as in Fin ;l(saz/o.p7qrj )j vyw)l;v g. 24–33. When light 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 be betwee tsf0bi;weu1.n two flat glass surfaces if the glass is to appear bright when 450-nm light is incident norma0u;stw eif.1blly?    nm
What if the glass is to appear dark?    nm

  vA piece of material, suspected of being a xdt+)na(9 tv9it t;i4gxxw k *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 alcoho:o*bt0 fef c.tl $(n=1.36)$ 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) i 4(qzx7bp0v chlqg;* xs immersed in a liquid, the diameter of the eighth dark ring decreases v q;phcb(*x7l0zgxq 4from 2.92 cm to 2.48 cm. What is the refractive index of the liquid?   

  What is the wavelength of the light entering an interfero3kjfn a) vn,:fmeter if 644 bright fringes are counted when the movable mirf:nj)a,nk f3 vror moves 0.225 mm?    nm

  A micrometer is connected to the movable mirror o aw,czol25hbs86f 0 :fp p2bapf an interferometer. When the micrometer is tightened down 8l 2pc5p6aswa0zp,hfbo f2: bon 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 mirror sed*7hvc82 fl $M_1$ 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) pu-9z; esgemnwj ;p 1b3asses through a small glass container containing a cavity 1.30 cm deep. Wh;m pze b3ej ;-ug1snw9en 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 interferometer is in vacuum. $n_{gas}$

  

  Two polarizers are oriented j 3 wqrqgh)aw(uudws/(w19; cat 65$^{\circ}\,$ to one another. Unpolarized light falls on them. What fraction of the light intensity is transmitted?   

  What is Brewster’s angle fo psb-b2 5c i e6l2qgqwpb8rp.2r an air–glass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s angle for a diamond submxnou vi+ :ttq o/6:a-merged in water if the light is hitting t/tmn x:uooq6a-v:ti+ he diamond $(n=2.42)$ while traveling in the water? $\theta_{p}$    $^{\circ}\,$

  Two Polaroids are aligned so that the light passing through the .jc 5q, zla0o2rpiz)qm is a maximum. At what 5zl,.c2rjoq0qz ip a) angle should one of them be placed so that the intensity is subsequently reduced by half?    $^{\circ}\,$

  At what angle should the axes of two Polarojpa4j 88viv c;ids be placed so as to reduce the intensity of8ijv vj;ca 84p the incident unpolarized light to
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are oriyu wn*9gmv77 jented at 40$^{\circ}\,$ to each other and plane-polarized light is incident on them. If only 15% of the light gets through both of them, what was the initial polarization direction of the incident light?    $^{\circ}\,$

  Two polarizers are oriented at 38.0l h6):q-lw or+bk3v vx$^{\circ}\,$ 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 an,(hrf3af kv(qgle be for reflections off the surface of water for light coming from beneath the surface? Compare to the ang(vhqrk (3ff,ale 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 successive Polaro )z;5d5hvhjtt:+ 5t li5ahi bsid sheets, each of whose axt :ahst5h+i)i jzl5 ;5hvd5tbis makes a 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength i gveq/t.wf hzdvx0ve34.2 w($ 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 reflectusbhp 6ogxk o)h h9 138z0is(eing from mountains or airplanes can interfere with the direct ss(9so px bok8hg 60u )izh1h3eignal from the station.
(a) What kind of interference will occur when 75-MHz television signals arrive at a receiver directly from a distant station, and are reflected from a nearby airplane 118 m directly above the receiver? Assume $\frac{1}{2}\;\lambda$ change in phase of the signal upon reflection.  ----待选择----constructivedestructive 
(b) What kind of interference will occur if the plane is 22 m closer to the receiver?  ----待选择----constructivedestructive 

  Red light from three separate sources passes through a diffraction gratin m-sy-+d4qz2r q ado f;4iz 9ebcvd(l*g with asr yl;z-qdqd4vzbo+4c2eid f *9-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 590 nm passes through two narrow slits 0.60 mm mw5iqj5jdn /; h)oi g5- (vvqmapart. 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. Whaiq5 5/oimd mn wj5;gh j(vvq)-t is the wavelength of the unknown light? $\lambda_2$    nm

A radio station operating at 102.1 MHz bror 6soj799id xcadcasts 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 co697x9dj siralong 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 wid: 1r hvej9 r;v,vjfez2e, and blows a whistle of frequency 750 Hz. Ignoring reflections, estimate at what angle(s) v fvze h1j:err;2jv9,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 singao8po 8 syg; bsv0fg0*le slit of width D at a 30$^{\circ}\,$ angle to the normal, describe the diffraction pattern.

  The wings of a certain beetle have a series of parallel lines acrosc9l yo q/-.dpzulv5* ts them. When normally incidentyv- qp zt .c5ulo*dl9/ 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.op6-bi oajvbp h+ x/0 grating have if there is to be no second-order spectrum for any vpoja6 +bpi0o x- h/bv.isible wavelength?   $ lines/cm$

Show that the second- and third-order spec ej(b)r (jbw+0vh6-vk*odgwttra of white light produced by a diffraction grati )t6r((h*jv+w obkwg0dejvb - ng always overlap. What wavelengths overlap exactly?

  When yellow sodium light, ac8t(8-alsuk/v m5 kf$\lambda\;=\;$ 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 g 8 dwth r4xujp*sxaehi777lrn, ka7f6 -*4 rn and the pattern is viewed on a screen 2.5 m from the grating. The incident light beam consists of two njw fa 84 7e7xrdu r-h6*,l*7 g aitxsrk4pn7hwavelengths, $\lambda_1\;=\; 4.6\times10^{ -7}\;m$ 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 u6aj bp ex2q hjz(,k/h)8f xn3150 nm thickness of it, when laid on glass, is needed to reduce reflekbu fxz28 h/(6a3pj),x hjnqection to nearly zero when light of 600 nm is incident normally upon it? Do you have a choice for an answer?

  Monochromatic light of variable wavelengtf81g38qz,o;qazh jov h is incident normally on a thin sheet of plastic; o1gfhqqj,o 8vz83az 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-reflective cm+) -ktcbwjwy. b160xg 5j- oihz;mjkoating $(n=1.38)$ 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-g.f70go caq tz8;fv :nzero) thickness for the air layer between two flat glass : f 7;zat0gv c.qgf8onsurfaces if the glass is to appear dark when 640-nm light is incident normally?    nm
What if the glass is to appear bright?    nm

Suppose you viewed the light trangpsw-p/w 4dy5t ./bz8oinqp ;smitted 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. Consider all possible values of index of refraction. Discuss the relative size of the minima comb 5 nowwti -sdpqp.g; 4z8//yppared to the maxima and to zero.
24-30
24-36

  At what angle above the horizon is the Sun when light refleuf*czn 1ie xc ta1u1/6cting off a smooth lake is polarized most str /cet1xiczu6 n1f*1ua ongly?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be placed so as t. ,bg6swlwsg2wk -x a8o reduce the intensity of the incident unpolarized light by an additional factor (after the first Pb8k26gswxs la . gww-,olaroid cuts it in half) of
(a) 4,    $^{\circ}\,$
(b) 10,    $^{\circ}\,$
(c) 100?    $^{\circ}\,$

  Unpolarized light falls on two polarizer sheets whose trxcfu( -jyw69zv32 lg eansmission axes are at right angles. A third polarizer is placed between the first two so thatfvey9l-2g3 z cwj(ux 6 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 the w467 w/gozzd z-xnti1ir 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 cmmx6wi. ;x*t(9mtcfn d ,q5ftj and is pointed at the Moon, which 9x n.w6mmjfxct;q(, tt*f di5 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). Estimate the width of the beam when it reaches the Moon.    km

  A series of polarizers are eac)4 ap7n.t9ohoin5p dz.qcp ;7hw: seqh 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 )tn7 t5nj 0wjw$(n=1.34)$ 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 i: 4pr5-p:gj9uat hqya n phase with each other. Thapr 4hp:j9yt5q u-g :aey are located 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 containfud47 5+k6no zg,vx-:suulb fq.y-agihq, b4ing two wavelengths, 420 nm and 650 nm, enters a silicate flint goyvi,qg z6h u.: 4,x-7f-bl gu54fdqnkba+su 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 planoconvex lens has one flat surface and one with pu73 cefh7 ahhw ue71($R\;=\;18.4\,cm$ 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