Does Huygens’ principle apply to sound waves? To water waves? Explain.st/.nd78tu ; o7e exjh

What is the evidence roxo5dlpcpy (p 51aj0x-(3so that light is energy?

Why is light sometimes descyd*gj,h l qd2p:s w/4oribed as rays and sometimes as waves?

We can hear sounds around corners, but we cannot see aj)n el* wt+m8fround corners; yet both sound and light tjm ewlfn)8+*are waves. Explain the difference.

If Young’s double-slitogbp;pt3) c8d experiment were submerged in water, how would the fringe patter otc3)ppg;d b8n be changed?

Monochromatic red light is incident on a doub3xyy) ru+z-qw dz2m/ k 2m+hhzle slit, and the interference pattern is viewed on a screen some distance+) - k h 2umyrdwz/x2hz+qzmy3 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(0;z.z() q u jzxqnejv if their path lengths diffq0u(q( z)x.jzznv; ej er by how much?

Why was the observation of theis(qw4/73 o+w t wg,iiy:cm rs double-slit interference pattern more convincing evidence for the wave theory 7s4yq:( +oiwi , /gw swrmcit3of light than the observation of diffraction?

Compare a double-slit experi-c0 v1o+acylsy)q v.fz+p ceuu/ 3,fument for sound waves to that for light waves. Discuss the similarities and -), z csau1cuevlfqy+ycov0u+./p 3fdifferences.

Why doesn’t the light from the two headlights of2g, )yn4mi9 vny4:owcqesow* a distant car produce an interference i)n4*,w:yv29e wsgy nqoc4 mo pattern?

Suppose white light fal spqt )/6fk3yyy. z1ulls on the two slits of Fig. 24–7, but one slit is covered by a red filter (700 nmq uly)sy tf .3pzy61k/) and the other 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 bro 7ktz 4v3jyxa)ken dok zyj)74xt3 avwn into colors as it is by a prism. Explain.

For both converging and diverging lenses, discuss how the s t0f. u;a9q)9djjhlkfocal length for red light differs from that for violet lightk9l.;a0t q d)j sh9ufj.

A ray of light is refracted through three different mate/wc b1:-48tbxvc hd 6:tvrv nnw: ot7wrials (Fig. 24–55). Rank t/nbvvw:76oct-t d8nx: tc4 1h vw:wbrhe materials according to their index of refraction, least to greatest.

Hold one hand close tw1xs3bh:q1osr j;3 47 lcxhvu o your eye and focus on a distant light source through a narrow slit between two fingers. (Aq 1 hssb 1vx;:o7x3jhucr wl43djust your fingers to obtain the best pattern.) Describe the pattern that you see.

What happens to the diffraction pattern of a single slit if the whole a 5oqpexb rvz 6.nji8u;o:xl+4pparatus is immersed in (a) water, (b) a vacuum, i:x8 xjpbn.izeu;oo6l r54 qv+ nstead of in air.

For diffraction by a single slit, what is the effect of increvg)k vg1fb 2b3asing (a) the slit width, and (b) the wavelengg 2b b)kfgv31vth?

What is the difference in the interference patterns formed (a) by two slits qn 5h 9sp8.e: byl5fpc$^{-4}\;cm^2$ apart, (b) by a diffraction grating containing $10^4lines/cm$?

For a diffraction grating, what is the advantage of (a) madn,c in.br46gny slits, (b) closely spaced sl4,b .ig 6rnndcits?

White light strikes (a) a diffractiwj7hw+9 wl4xvz2n -xgon grating, 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 rainbow 9hg24nwxwz7vwx lj-+ in each case? Explain.

For light consisting of wavelengths between 400 nm anafa4a j 73)hwd)q /av-m+aruu d 700 nm, incident normally on a diffraction graq r-) w+ v)7aaadua4jf/a3hmuting, 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 *zppiwnarl /3 c3.*j( h) btk(lj8zi gfilm like a soap bubble and g) i *izjpc((lah8brwlj tz3*n/ k.p3not for a thick piece of glass, say?

When a compact disk (CD) is held at an angle in white light, the0* 0ruum,pwwl reflected light is a full spectrum (Fig. 24–56). Expl*0uw pmw0,lur ain. What would you expect to see if monochromatic light was used?

Why are Newton’s rings (Fig. 24–31) closer together farther frd5i9ie67t,ims : a; zo(ngblj om the center?

Some coated lenses appear greenish yellow when seen by reflectc ytt ugc (7w+;,tom-ged light. What wavelengt+gcmto tt ,gw( ;c-uy7hs do you suppose the coating is designed to transmit completely?

A drop of oil on a pond3:bz brj; wy(p appears bright at its edges, where its thickness is much less than th:b pby 3wrzj;(e wavelengths of visible light. What can you say about the index of refraction of the oil?

What does polarization tell us about the nature ll tg,slr2s1 b9 d8qvd;/d0sv of light?

Explain the advantage+;,;ov1ap hl6 ohq knb of polarized sunglasses over normal tinted sunglasses.

How can you tell if a pair of sunglasses is polariz2a-.zn38ykey smm2 y ling or not?

Two polarized sheets rotated at an angle of /.8wa xspi:q j4s mc5b90$^{\circ}\,$ 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 t6enudp8ir e22 he Earth had no atmosphere?

If the Earth’s atmosphere were 50 times denser than it is, would sunlight se33w w3q)wway till be white, or would it be sq aey3ww3w 3)wome other color?

  Monochromatic light falling :7w zzga o8g ;ji)k9bron two slits 0.016 mm apart produces the fifth-order fringe at an 8z7ia b zgkj:w8;g9)ro .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+ux3k2vkybhc/-v c ;25ochoy 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 uy2dmq9a7 uzx8i/:oe very narrow slits 0.048 mm apart. Successive fringes on a screen 5.00 m away are 6.5 cm apart near the c auxym9z2iud7e8q/o :enter 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 wavelength6tsp x y /j1yvjdw-;5n 656 nm, falls on two very narrow slits 0.060 mm apart. How far apart w1 -vs;jtn 5yydpx6/j are the fringes in the center of the pattern on a screen 3.6 m away?    cm

  Light of wavelength 680 nm f.7v iv4wf6w rqh3 ,vfialls on two slits and produces an interference pattern in which the fourth-order frinii,.fvhq7 wrv f6vw43ge 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 passes through two slits 0.58 mm apart, h y d/u )nne/n.fr2lia3i-x i(zow far apart are thezi ) 2.xl(/anr3fini en d-/uy second-order fringes for these two wavelengths on a screen 1.0 m away?    mm

  In a double-slit experiment, it is found that blue light of wavele4inv nb,/l/xfngth 460 nm gives a second-order maximum at a certain location on the screen. What wavelength of visiblb/vnx, f4lin/ e light would have a minimum at the same location?    nm

Water waves having parallel crests 2.5 cm apart pass through two openings 5 sojjip5d: 4nn77mtxfei,r8 8.0 cm apart 85,i t d mnn x:of7sr8pjj4i7ein a board. At a 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 glass is placed in front of the lower slit in Fig. yuor /q b4rt5qfh7j(/24–7 so that thehqrry4(j f5btqu /o7/ 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 maximum fb f(0d9(gxeiwt*j x8j+x ;gat aj7b.nhs60lbor 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 fr9sbftndb 6ghxe008 7j+(a jj;wi gtx (xl. ab*om 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 zx,fl5+h/ :fiyr.hvn light. Find the distance between adjacent brig+n/i5yf,hfxz:.vl h rht fringes on a screen 5.0 m from the slits.    mm

  Light of wavelength 480 nm j4w71h ntr p8vin 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=1.6i m6t8u/p7gq 4u: baqu0) covers one slit of a double-slit apparatus illuminated by 640-nm light. The center point on the screen, instead of beu6qubigu 8 t p:a47/mqing 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) excp8*cepb)qmw ;tu u,+0t. r mhfeed that of violet light (400 nm) in silicate flint g+m ,;th etfp wmp0rbu8 u)q.*class? (See Fig. 24–14.)    %

  A light beam strikes a pi907k:ya ek ff nw sf(d:mk(jm3ece 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 contarl sx7 1:3qs0o)e*plm cca2jzining 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 widt pydgb8d; *,wvh ov8;,ddg wp yb*f the central diffraction peak?    $^{\circ}\,$

  Monochromatic light falls on a slit that is e+ra gq3yj1u ,7 hsqz8$ 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;ny qvqbf:6zsd7,1 zo 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 the width of lg, 2tmje1pe5hsw. s* lc( t+mthe central maximum (in cm) in the diffraction pattern on a screen 5.0se.,g(t p251l tc*ws mh+lmej m away?    cm

  Monochromatic light of wavelength 653 nm falls on a slit. If the angle between tlekgxgf96:uod 1 b*5 vhe first bright fringes on either side of the ceb gevk:g*1u flo96d5 xntral maximum is 32$^{\circ}\,$, estimate the slit width.    $\mu m$

  How wide is the central diffraction peak f;1vsx,us5w+1g uxty on a screen 2.30 m behind a 0.0348-mm-wig+ yw txs1,xu 1f;5svude slit illuminated by 589-nm light?    cm

  When blue light of wavelength 440 nm falls on a si a*7a2qfrw6a xngle slit, the first dark bands on either s6f72qrx*aaw a ide 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 ahau:)f0svp iqx*k 1 h3 fy6t7d central diffraction peak that is 9.20 : 3y6fht1k7p)* fiqa0duhxvscm wide on a screen that is 2.55 m away. How wide is the slit?    mm

  If a slit diffracts 650-ckyi*sp 7p puakw9g7 e 8i2s;vdkv73, , t.lwwnm light so that the diffraction maximum is 4.0 cm wide on a screen 1.509t*pidpwswky ,7ev gp 27 ;3k ikuw.sl7 8cav, m away, what will be the width of the diffraction maximum for light of wavelength 420 nm?    cm

For a given wavelength:fv ,lvgx b6mdd*c:fq:-)fer $\lambda$, what is the maximum slit width for which there will be no diffraction minima?

  At what angle will 560-nm light produce a second-or2.7t2x x.rotao qu.xader maximum when falling on a grating o .x. q7r2ot2axu xat.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 cenxst9i27htl* /z zq;d (mu9 kwpsam4q)timeter does a grating have if the third-order occurs at an 18.0(pm wmz9472a i; uq xzk*lths/d9qst)$^{\circ}\,$ 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 f7t1ywq ( h4qpfig 9pa2alling on a diffraction grating is observed at a 15. a9p(yhw q2 gfi14p7tq5$^{\circ}\,$ angle. How far apart are the slits?    $\mu m$
At what angle will the third order be observed?

  A diffraction grating fsz u fr5b5y2.g(8xoxhas $ 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 a*q05cdd v4 igl,2 fl) rcoemr0 $9700-line/cm$ 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 orq)/0 ne33qjcdej nu- mder that can be seen if a grating with 6000 lines per cm is illuminated with 633-nm laser light? Asq3c dje3 nmj- )/0qneusume normal incidence.   

  Two (and only two) full spectral orders can be seen on either side ou;r7 gqulxf86 f the central maximum when white light is sent through a diffractlq ;ug 6rxuf78ion grating. What is the maximum number of lines per cm for the grating?    $ \times10^{ 3}\;lines/cm$

  White light containing wavelengths from 410 nm to 750 nm falls onnxlcol/ u p+ dt ,*yh7a:a-;yc a grating withtn:l7-x/ yy chcd aaop+;l, u* $8500\;lines/cm$ How wide is the first-order spectrum on a screen 2.30 m away?    m

  A He-Ne gas laser which produces monochromatic cqatiulcqt-x 6je73 :6t x4/dlight of a known wavelength $\lambda\;=\;6.328\times10^{-7 }\;m$ is used to calibrate a reflection grating in a spectroscope. The first-order diffraction line is found at an angle of 21.5$^{\circ}\,$ to the incident beam. How many lines per meter are there on the grating?    $ \times10^{ 5}\;lines/m$

  Two first-order spectrum lines are measunag i+,mn12hwo,bcg :red 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 str:.buw*bb(s2 j rwn1inyo7i ,zongly reflected at the center of the outer surface whi7w r wjs (*ib21ou,yb z:nn.ben 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 ts .:9e h15onkd7bp3 jf3in cyha6;tu9pi fuc*he glass plates are each 26.5 pc u 37y jea16ni cn:*9ufhd.h9o5;k3bipstfcm long?    cm

  What is the smallestjn0fw01 p6 h+ol9kgb y thickness of a soap film $(n\;=\;1.42)$ that would appear black if illuminated with 480-nm light? Assume there is air on both sides of the soap film. $t_min$    nm

  A lens appears greenish yew5b ; kxpkzg,o2s3d-rllow ($\lambda\;=\;570\;mm$ 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 counting 9tb3x2vnquk)+iz t +ithe dark spot at the center) are observed when 550-nm light falls normally on a planoconvex lens resting on a flat glass surface (Fig. 24–31). How much thicker is the center than the v2itnxz9 )q+3i+u tkbedges?    $\mu m$

  A fine metal foil separates one end of two pieces of optically flatd n90)bqteql48itz4 t glass, as in Fig. 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 9i0 l8z qdtt4n)tqe4bfoil?    $\mu m$

  How thick (minimum) should the air layer bew/(pc q9,4k7o76oq s t kyxkqp between two flat glass surfaces if the gla c/p6qpyqwt(47ok9 7ksq x o,kss 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 being a stolen x0 zuft+ab+d/f ;cph8 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*f bcq wl; (s2b. n1fttf,ngnes*6d:k $(n=1.36)$ 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 5t5robjz v7o42 swo)fin a liquid, the diameter4o5fotw)z 52s bo7j rv of the eighth 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 interferometer if 644 bright +2 cq ds vadm.thui 5sjji9245fringes arevcsah u5.m+djsjqt29d 25 i4i counted when the movable mirror moves 0.225 mm?    nm

  A micrometer is connecte2gr y-8q )icul/d.lsx a1 bo(wd to the movable mirror of an interferometer. When the micrometer is tightened down on a thin metal foil, the net number of bright fringes that move, compared to the empty micrometer, is 272. What is the thicka.q(i r2y so1w/g-8ld )culbxness of the foil? The wavelength of light used is 589 nm.    $\mu m$

  How far must the mirr80 1i,qggbp92 e9dzyfjvhb5 s or $M_1$ 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 an7nvq75 v2sm h)7lrq dp interferometer (Fig. 24–59) passes through a small glass container containing a cadvl2nrsqh7vm5qp 77) vity 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 interferometer is in vacuum. $n_{gas}$

  

  Two polarizers are oriented ab+s(gzk4t: v rt 65$^{\circ}\,$ to one another. Unpolarized light falls on them. What fraction of the light intensity is transmitted?   

  What is Brewster’s angl wh6 .:ad;4hdwx-rpdbe for an air–glass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s as td,ju5c 1wzn )6vq,cngle for a diamond submerged in water if the light is hitting the diamond1usqw dc,z5, jtvn) c6 $(n=2.42)$ while traveling in the water? $\theta_{p}$    $^{\circ}\,$

  Two Polaroids are aligned so that the p-7uxs; eg7ev o(+ei i/2vvdplight passing through them is a maximum. At what angle should onve2uv 7 d/ievp-(x+7 s;eopige of them be placed so that the intensity is subsequently reduced by half?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be placed so as tcay7t r9pd n2:o reduce the intensity of the incidend:79c2yar ntp t unpolarized light to
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are oriented4,ec :ofvjw c y5t4pj3 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. yzso7s) pz985/szf ir0$^{\circ}\,$ 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 surfacg1xwb 49o st-ye of water for light coming from beneath the surface? Compa1 st xb-ywog49re 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 fi( q7bkchdcavm* x9 3+gve successive Polaroid sheets, each of whose axis mm k9b(vcg +h*cq 73axdakes a 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength qf+i /rfcte;x8 u)nhosi8. y,;uw(ep $ 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 refleci 5wbd,v k,qh 9ba-8wtting from mountains or airplanes can interfere with the directb -9v, 5ww, diakqbh8t 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 diffractioa -qen1f1 ilf)5rfj3 ;mke/xcravj8- n grating with l- ef ik)a1fm5 -jra1vj3/;x frcn8eq$ 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 throughm1kk/,j nc i4r two narrow slits 0.60 mm apart. The screen is 1.70 m away. A second source of unknown wavelej1mk kn4, /cringth 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 fr-8 5r ubp+zjq+ roavv0om 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 in both directionzbv +ur ro5-j+a0q8vp s. 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 b yh k:co p8sf,*v*yt8 7qqc.hdack from an outside doorway 0.88 m wide, and blows a whistle of frequency 750 Hz. Ignoring reflections, estimate at what angle(s) it is nq hcvt y.oy**cqk8p fh7,8sd :ot 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 widd3. ro1i7wckaim*, vx th D at a 30$^{\circ}\,$ angle to the normal, describe the diffraction pattern.

  The wings of a certaix4,1s6hcugf / khgqr *,atz 9x9+tvwz n beetle have a series of parallel lines across them. When normally incident 460-nm light is reflected from the wing, the wing aps1f,z+gwuc/zk 9rv*xa g6x4,hh q t 9tpears bright when viewed at an angle of 51$^{\circ}\,$. How far apart are the lines?    nm

  How many lines per centimeter must a gratiznpcvn/*t w7p4.)m :eh /xk wvp8j d29jgo3ojng have if there is to be no second-order spectrum for any visible wavelengtcov*x 8v7 z4mjnn:ohd2tg 9j/w. pk)e wp3/pj h?   $ lines/cm$

Show that the second- and third-order spectra ofmvoh3ciqzj.u,i 3 y*7 white light produced by a diffraction grating always cv.qo i3*myzij7hu ,3 overlap. What wavelengths overlap exactly?

  When yellow sodium lig-emn7ub9i) egm 9lh74ifb6 vh ht, $\lambda\;=\;$ 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 diffrav.thn8tc6t; z2 /y0g*ewjco .z0 ys ogction grating with and the pattern is viewed on a screen 2.5 m from the grating. The incident light beam cons82.et6cot j y ; *tzyoh.0cw0s ng/zgvists of two wavelengths, $\lambda_1\;=\; 4.6\times10^{ -7}\;m$ and $\lambda_2\;=\; 6.5\times10^{ -7}\;m$. Calculate the linear distance between the first-order bright fringes of these two wavelengths on the screen.    m

What is the index of refraction of a clear material if a minimum of 150 6:gsu 8x,k)*fz ki5wgnvr 8 wdnm 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 an answer?)fw n8*5x6kr suik8 ,zg:dvg w

  Monochromatic light of5zno(f dsg3/ 8zfslo,q k5l1h variable wavelength is incident normally on a thin sheet of plastic film in air. 35z( sdlz8,5 lqgh o/fsnok1fThe 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-refkn 3xohp(jw36+qy x k/lective 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-lp b(a684ttt(q qe7guzero) thickness for the air layer between two flat glass surfaces if the glass is to appear dark when t6l(( 7gte48bqauptq 640-nm light is incident normally?    nm
What if the glass is to appear bright?    nm

Suppose you viewed the light transmit++.-nm;x x6ket *nt-.y)kcesywnbm cted through a thin film layered on a flat piece of glass. Draw a diagram, similar tx; wx+*.m- yenys)k .-nn cck6bmt+eto 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 compared to the maxima and to zero.
24-30
24-36

  At what angle above the horizon is the Sun whe l:fm 2.i+nuxon light reflecting off a smooth lak+i :onxlmu2 .fe is polarized most strongly?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be placed so as to reduce t,rsf,y3 vtgog q0zd* :he intensity of the incident unpolarized light by ansv0qg zg3,dt*o :ryf, additional factor (after the first Polaroid cuts it in half) of
(a) 4,    $^{\circ}\,$
(b) 10,    $^{\circ}\,$
(c) 100?    $^{\circ}\,$

  Unpolarized light falls on tvas gp -wj29p.wo polarizer sheets whose transmission axes are at right angj pgpsva.29 w-les. A third polarizer is placed between the first two so that its axis makes a 62$^{\circ}\,$ angle with the axis of the first polarizer.
(a) What fraction of the incident light intensity is transmitted?    $I_0$
(b) What if the third polarizer is in front of the other two?

Four polarizers are placed in succession w7a, ilmmuv2jvbr a1.jzb/5/ hith 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 poi3avb lc5htwt0w.dh s:2 /8wgented at the Moon, which is approximately 380,000 km from the Earth. Assume the laser emits waves of wavelength bv 3w2e l8sdgt05/hwa :cw th.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 at aqygwhas vz-/(ma+ y6 8 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 7bufobpoy6ofhza+6 f3b/a 3: $(n=1.34)$ 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 dg30gcm :ok3y:t/ jenbp,p :ehc db 14in phase with each other. They are located at poingdhb :mp4o/,:e 31 p0bgec dt cky:n3jts $S_1$ 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, 4(m kco:j6-s bd0v 2ist20 nm and 650 nm, enters a silicate flint glass equilateral prism (Fig. - t(jbv062c: dkm isos24–58).
(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 o/,s3 je/zd/ xx edoo0une 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