Does Huygens’ principle apply to sound waves? To water waves? Explaip7m s4,t2 z4gx5i 4(rnffsagdn.

What is the evidence thjoe5 6 z:xlz56 s3cqzqat light is energy?

Why is light sometimesg7 :+q6icarl/3rmg.t2v wvd o described as rays and sometimes as waves?

We can hear sounds around corners, but we cannot see around corners; yet bothr1uc5 o jx njsc.6(wa+ sound and light are waves. Ewjn+6 jcocr1. xu a(5sxplain the difference.

If Young’s double-slit experiment were submerged in lt1,qyolvj9; bk9h x2 water, how would the fringe patter 9lbvkjtho; 2,q 9xy1ln be changed?

Monochromatic red light is incident on a double slit, vs *ule*4kj0d ;4g hv.k+xfu +s-rbg- 7eg oqdand the interference pattern is viewed on a screen some distance away. Explain how the fringe pattern would change if the red lighthgkx0 +qgs- jdd+loks rg4 b 4*.v7;fe euv*-u source is replaced by a blue light source.

Two rays of light from the same so;8(oo;;m.tdcri ffbzrr , j5vurce destructively interfere if their path length z(vt8rimjor. ;db c;ro5;ff,s differ by how much?

Why was the observats9gipn5xf-qzob ;y54 ion of the double-slit interference pattern more convincing evidez9yfgqobx np-is4;55 nce for the wave theory of light than the observation of diffraction?

Compare a double-slit exp .mgtfq91pv r8eriment for sound waves to that for light waves. Discuss the similariti 1vt.qm grp89fes and differences.

Why doesn’t the light from the two headlights fmi* vu ed, vtri)iph+1t i+)/of a distant car produce an interference pat))r+ u1i if/m*ph+tidet, vvi tern?

Suppose white light falls +:9jso51)e dsovug 9 3pbyaqpon the two slits of Fig. 24–7, but one slit is covered by a red filter (700 nm) and the other by a blue filter (450 nm). Describg9 v9:) uoye31da+ po5p qjbsse the pattern on the screen.

When white light passes through a flat piece of window glassfwgf4,kinj*q ; e: w-tqnwj51eg m;-a, it is not broken downnf5*g1g4j;tk,ww nei--fj w e:qm; qa into colors as it is by a prism. Explain.

For both converging and diverging lenses, discuss how tif 398gl8pd2g go (awirz9 g,mhe focal length for red light differs from that for violet lig gl 893g z8,r9wo(afdmg ig2piht.

A ray of light is refracted through three different materials (Fig. 24–n rg1 dd;w7z2eb5cl a 4vfe)3fze9o.u 55). Rank the materials according to their index of refraction, le9v5ew7d c g1oz.ba4f 2 ;n3zr)eul edfast to greatest.

Hold one hand close to your eye and focus on a distant light sourc, (g ,/dgsljobe through a narrow sl/b(ljg g,,sodit between two fingers. (Adjust your fingers to obtain the best pattern.) Describe the pattern that you see.

What happens to the diffraction pattern of a single slit if y zlm coim t02b:vmc2ya6c :13the whole apparatus is immersed in (a) water, (b) a vacuum, instead mc:3lyo6t0 mbvcic12 m2z :ayof in air.

For diffraction by a s3cn0m-y 0gm9 ws-hhgbingle slit, what is the effect of increasing (a) the slit width, an-90n gc-ybhsg3 m hwm0d (b) the wavelength?

What is the difference in the interference patterns formed (a) by tw 2lwq7ls e,ep 7;azwly9t -g/wo slits $^{-4}\;cm^2$ apart, (b) by a diffraction grating containing $10^4lines/cm$?

For a diffraction grating, what is the advantage of z 8-pcj,kjv) q(a) many slits, (b) closely spacej-8qkvzjc) ,p d slits?

White light strikes (a) a diffractionlve7-gg orpf j+y/seec+0- g0 grating, and (b) a prism. A rainbow appears on a wall just below the direction of the horizontal incident beam in e+lo jv+/fgr0gegs-pece-y07 ach 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 normally lva( bvgu4nfvw3g109(t6 pia on a diffraction grating, for what orders (if any) a3( vt0wi v(puf ag 16n9gv4blwould there be overlap in the observed spectrum? Does your answer depend on the slit spacing?

Why are interference fringes noticeable only for a thin rw vbw6*3qgp/film like a soap bubble and not for a thick pie */36wqrb pvgwce of glass, say?

When a compact disk (CD) is held at an anvo -mdep dl+619 qv-vjgle in white light, the reflected light is a full spectrumpvd9ejv-m1 vq l d6-+o (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 farthh50 p 9a3ljyq +*jzpbt x n;,og7spq-xer from the center?

Some coated lenses appear greenish yellow when seen by reflected light. What wa96r9 a,49 yibbbxxf4cbz9 azivelengths do you suppose the coating i6rx aaz9i9b4bbc,499ifx b zys designed to transmit completely?

A drop of oil on a pond appears bright at its edges, where its thickneuu :ifmjc6+.m 96szbi ss is much less than the wavelengths of visible light. What can you say about the index of refraction ou+jcm6um :i6sizb.f9f the oil?

What does polarization tell us about the nature of ligupcav 6v-l x6/aw3 wc8 vbs;;hht?

Explain the advantage of polarized sunglasses ove awu*lif(n1i vc i289ur normal tinted sunglasses.

How can you tell if a pair of sunglasseplidu ojj7n ( dr:7;xlz) 2gw9s is polarizing or not?

Two polarized sheets rota -s /kzlukyo0;ted at an angle of 90$^{\circ}\,$ with respect to each other will not let any light through. Three polarized sheets, each rotated at an angle of 45$^{\circ}\,$ with respect to each other, will let some light through. What will happen to unpolarized light if you align four polarized sheets, each rotated at an angle of 30$^{\circ}\,$ with respect to the one in front of it?

What would be the color of the sky if the Earti spt2z 6u(o1b0ud jk2h had no atmosphere?

If the Earth’s atmosphere were 50 times denser than it is, would sunlight 8ei a+ eo*mu08bls+mfstill be white, or would it be some otib 880me+*moeaulsf + her color?

  Monochromatic light falling on two slits 0.016 mm apart produces0uv8 f qsfim9cpxl / x;/.vd(e the fifth-order fringe adp9 vfx;0 s(.xlcveqif/u/m 8t 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 a nrf:uc,: 6i c6:6(iuiuu asoan angle of 18$^{\circ}\,$ when the light falls on two narrow slits. How far apart are the slits?    $\mu m$

  Monochromatic light falls on two very narrow slits 0.048 mm apart. S*.o9+;eoffjot1te 5z7* nyqsed v ;rb uccessive fringes on a screen 5.00 m away are 6.5 cm f t *.ro7f;tbz*nyqs eeev+9;ojdo51 apart near the center of the pattern. Determine the wavelength and frequency of the light.
$\lambda\;=\;$    $m$
$f$ =    Hz

  A parallel beam of light from a He-Ne laser, with a wavelengar9wsf 27rdm )th 656 nm, falls on two very narrow slits 0.060 mm apart. How far apart are the f7a 2fw)9rrdms ringes in the center of the pattern on a screen 3.6 m away?    cm

  Light of wavelength 680 nor +a+z+/( qp-xp)dpiw(hzyum falls on two slits and produces an interference pattern in which the fourth-order fringe is 38 mm from the central fringe on+((zpp dx+ q u-/owaihrp+zy) 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 0.5twhf21d/mw x, td3f 9k8 mm apart, how far apart are the second-order fringes for these two wavelengths on a wxdfmd,whft9 3k/2t 1screen 1.0 m away?    mm

  In a double-slit experiment, it is found tg 2tvt2: :wkty*smg )lhat blue light of wavelength 460 nm gives a second-order maximum at a certain location on the screen. What wavelength of visible lig:mt: 2swk*2gy) tvg ltht would have a minimum at the same location?    nm

Water waves having parallel cr(0tcjz jfa e 3yn6k8/qests 2.5 cm apart pass through two openings 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 wofcj 6k(0/a t8n zq3yejuld there be little or no wave action?

Suppose a thin piece of glass is placed in front of 2+se a9 sbu*)u ntrq(ac s+w)gthe lower slit in Fig. 24–7 so that the two qgatnc)us +se9as+ 2 *b)r(uwwaves 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 experroc xz(. ggbmkjj/,*35c8rjt* rn hq-iment, 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 projected through the same slits. How far from the central bright spot will the second-order maximuc c 83g5q*. * xorgtmjz,bkrr(/j h-njm of this light be located?    mm

  Two narrow slits separated8zj,i: td l1ic by 1.0 mm are illuminated by 544 nm light. Find the distance between adjacent bright fringes on a screen 5.0 m from the slits. i z8jt ,cl1i:d    mm

  Light of wavelength 480 nm in air falls on two s4f .zhl*6 t os2kazwp6ym0gh(lits $6.00 \times10^{-2 }\;mm$ 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 onez475g xgd -bnxzu5s5x 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 plasu bx7szx5nd4gx55g z -tic?    nm

  By what percent, approximately, does the speed of red light (700 nm) .h9oa ncqi46dqmo5s;77efh 7ms pnh, exceed that of viol5 h;h7oc, 4mao q6pnsshdi.n 9qe7f7met light (400 nm) in silicate flint glass? (See Fig. 24–14.)    %

  A light beam strikes a piece of x;p7ar8 :tilkcb2t*l 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 contayy*h0ovo1 1 onj7oz*l3m2aflining 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 thel3 qg 5)i)rjgfjv pa2, full angular width of the centr q) 3pjiv5r2fal)gg,j al diffraction peak?    $^{\circ}\,$

  Monochromatic light falls on a slit th2oy,d16bxjou8wbhko 8j )-c+ouu w1k at 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 i ) ev*/krtsg.ps $ 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 illumi60qzj3u qr7i v+5,idad klce2 qbvl2:nated by 450-nm light. What is the width of the central maximum (in cm) in the diffraction pattern on a screen 5.0 m awayd:q3 qe7va lbidizju 5 rcq62+k02l,v ?    cm

  Monochromatic light of wavelength 653 nm yjnpue47 )oa -n/dnkzz(x s64falls on a slit. If the angle between the /(zopz)n axy4nn7e-4 6 kud jsfirst bright fringes on either side of the central maximum is 32$^{\circ}\,$, estimate the slit width.    $\mu m$

  How wide is the central diffraction peak on a screen 2.3ct*b /qj3su +i0 m behind a 0.0348-mm-wide slit illuminateds j/t bui*c3+q by 589-nm light?    cm

  When blue light of wavelength 440 nm falls on a single slit, the firsm (wp9d:bf, gan ch4n:t dark bands on either sid,9bghn4w:pn f m :ac(de 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, id4kn 8rg(mv5 ut creates a central diffraction peak that is 9.20 cm wide ok58u4m(rvngd n a screen that is 2.55 m away. How wide is the slit?    mm

  If a slit diffracts 650-n whm8/l2 z;kf2cq/ms zgj3x2 wm light so that the diffraction maximum is 4.0 cm wide on a screen 1.50 m away, what wi 2 wk/sflx23gjmz /zhm2w 8cq;ll be the width of the diffraction maximum for light of wavelength 420 nm?    cm

For a given wavelengt ngbik4() /niih $\lambda$, 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 when fall tl -qj l+u.7j,ykh o:ws+*fhfing on a gratih-lw:7 jtsqkflh f.,+*o+u j yng whose slits are $1.45 \times10^{-3 }\;cm$ apart?    $^{\circ}\,$

  A $3500-line/cm$ grating produces a third-order fringe at a 28.0$^{\circ}\,$ angle. What wavelength of light is being used?    nm

  How many lines per centimeter does a grating have if the third-order og(gub9t i/f72o p xl4occurs at an 1 9ulgf oo b4i7pgt(/2x8.0$^{\circ}\,$ 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 irsvc qj01vg:uu ;n94 falling on a diffraction grating is observed 1v ; u0:s4gj vurcnqi9at 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 hyfpgmxo3 p5*6 as $ 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 (rfvc23 o3kn rav6l4 won 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 seen if a grating with 6000 xx. l/6pig:z3fhhdvk k km+53 lines per cm is illuminated with 633-n pxhdkm+ 36ilxgf h k5/kz3v:.m laser light? Assume normal incidence.   

  Two (and only two) full spectral orders can be seen ovg8n utu 5p:6hn either side of the central maximum when white light is sent through a diffraction grating. What is th:6u5hp v8nut ge maximum number of lines per cm for the grating?    $ \times10^{ 3}\;lines/cm$

  White light containing wavelengths from 410 nm to 750 nm fgi90)wwnf 5x kiuw3b7alls on a grating with5gw wx7 3wbf0i n9kiu) $8500\;lines/cm$ 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 wavegfg6*qq *g jk+length $\lambda\;=\;6.328\times10^{-7 }\;m$ 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 measurl xz8*l hq ojth09816sa6 eyired 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 8p tlm76id -im120 nm thick, what wavelength is most strongly reflected at the center of the outer surface whel- p76id8mtm in illuminated normally by white light? Assume that $n\;=\;1.34$. $\lambda$ =    nm ,which is an    -  

  How far apart are the dark fringj *ci/k :pqm/ho//xpses in Example 24–8 if the glass plates are each 26.5 cx mh/:qs /pipj/c*o/km long?    cm

  What is the smallestpbh+ it,s)fh pf90w* ms:9 gov 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 yelllqk,.sm9:p4y dv5y w fow ($\lambda\;=\;570\;mm$ 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 the dark spot a l9g4i*fo(m):,sn j xge 2vuztt the center) are observed when 550-nm zm slj4go(xn ugi92v t*:)ef,light falls normally on a planoconvex lens resting on a flat glass surface (Fig. 24–31). How much thicker is the center than the edges?    $\mu m$

  A fine metal foil separates one end of two pieces of optically flat glass, (5qyin k9zhk; as in Fig. 24–33. When light of wavelength 670 iz (kq5 kh;9ynnm is incident normally, 28 dark lines are observed (with one at each end). How thick is the foil?    $\mu m$

  How thick (minimum) should /odapk(j *h l51u kee+the air layer be between two flat glass surfaces if the glass is to appear bright when 450-nm light is incident normapejk d/h+eo 1lk u5a(*lly?    nm
What if the glass is to appear dark?    nm

  vA piece of material, suspe 4jtw;5r/m w (pn+oslfcted 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 alcoh xn,8k,1apitonnz9u* ol $(n=1.36)$ 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) .k8w ,8xlimfcp *u :zfis immersed in a liquid, the diameter of the eighth dark ring decreases from 2.92 cm to 2.48 cm. What is the refractive inde.uikm8zx8l :pf*w fc,x of the liquid?   

  What is the wavelength of the light entering an iyj9un v4 yjx-5nterferometer if 644 bright fringes are counted when the movable mirror moves 0.225 mm? vujx j y5yn4-9   nm

  A micrometer is connected to the movable mirror of an interferometer. Wag 1 /nfe+q/gdhen the micrometer is tightened do/1g +gaqedf/nwn 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 mirror avcyq/0 ft/u +$M_1$ in a Michelson interferometer be moved if 850 fringes of 589-nm light are to pass by a reference line?    mm

  One of the beams of an interferometer (Fig. 24–59) passes through a small glas1 lt82om0 m.z haqd4ycs contac oy ztm.dh2am48q 01liner 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 interferometer is in vacuum. $n_{gas}$

  

  Two polarizers are orie abn0*yd a0(y+4oxcp ented at 65$^{\circ}\,$ to one another. Unpolarized light falls on them. What fraction of the light intensity is transmitted?   

  What is Brewster’s angle for an ai ,ygha2y) eiejiad1;.r–glass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s angle for a diamond submerg9., ffjcnq ,,;gjdwfbd;0 wzged in water if the light is hitting bfgdw . cg9qd0 j,j,wz ,;f;fnthe diamond $(n=2.42)$ while traveling in the water? $\theta_{p}$    $^{\circ}\,$

  Two Polaroids are aligned so that the light passing thrzlzv /mq g)l 5+cli-6cough them is a maximum. At what angle should one of them be placed so qlzmvc c/)+zg 5l6-ilthat the intensity is subsequently reduced by half?    $^{\circ}\,$

  At what angle should the axe spax6f )f8a+cs of two Polaroids be placed so as to reduce the intensity of the incident unpolarized +xas fpac6)f8 light to
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are orientediz 1dlpsr0li )sgw,f3+gx;h ( 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 orient5g6 x8c: pkxwbed 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 ,iq rn9a36tayo6th9 h water for light coming from beneath the surface? Compare to the angle for total internal reflection, and 6i6r9qh9aha t,t 3 ynoto 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 eek :n8 fxg*d*Polaroid sheets, each of whose axis make e d*f8ne:g*xks a 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength m)6cyrr yr7iftw gw2v8gi. *3$ 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 interfei 8m0vj8/ z:8r*lvdhu zcbvwu1u/ p e-re with the direcvlu m81v:8u8*v ec/wr piu0zb -dh /jzt 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 diffraction grn nq )p36 *oyen3p;r +4ifvp0tyje gk.ating with 43r+ pyn f vteon 6;3pp*enji0y g.k)q$ 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 0.60-3f)ygk o r t2krqs7-u (iq,xz mm apart. The scur) oy k3txir- q-z2,qk(gfs 7reen is 1.70 m away. A second source of unknown wavelength produces its second-order fringe 1.33 mm closer to the central maximum than the 590-nm light. What is the wavelength of the unknown light? $\lambda_2$    nm

A radio station operating at 102.1 MHz broadcasts from two identical antennaelu9* wm1:m.cb/6t0 cyfd kejo at the same elevation but separated by an 8.0-m horizontal diym9tc .u6bdm1jk0o fc*l/ew:stance 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 doobua tux 630n/;kkm7th rx8b 2orway 0.88 m wide, and blows a whistle of frequency 750 Hz. Ignoring reflections, estimate at what angle(s) it is not possible to hear the whistle clearly on the playground outside theahxkbk7m t3u0botu n2; 8x r/6 doorway.    $^{\circ}\,$ either side of the normal.

If parallel light falls on a single slit of width D at a 3. hx6i sgqi;:x0$^{\circ}\,$ angle to the normal, describe the diffraction pattern.

  The wings of a certain beetle have a series of parallel linesns(3 ui)cxkag, /sd7u /wx8hz across them. When normally incident 460-nm light is reflected from the wing, the wing appears bright when v 8hw/sgc(7xd)saz,k n3i/xuuiewed at an angle of 51$^{\circ}\,$. How far apart are the lines?    nm

  How many lines per centimeter must a grating have if there is22rk.kb2zx gstr3 mo p+p zl7- to be no second-order spectgkm ztpx 2ol2 .3kb 2+sp-7rrzrum for any visible wavelength?   $ lines/cm$

Show that the second- and third-order spect-w2gvt *n: izlra of white light produced by a diffraction gratt- l:zng 2*wiving always overlap. What wavelengths overlap exactly?

  When yellow sodium light,.w3b, yteijf- $\lambda\;=\;$ 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 onlf q8-v/t;n2;s lwxz v a screen 2.5 m from the grating. The incident lilt;8 ;2z/ -vqvl xfnwsght beam consists of two wavelengths, $\lambda_1\;=\; 4.6\times10^{ -7}\;m$ and $\lambda_2\;=\; 6.5\times10^{ -7}\;m$. Calculate the linear distance between the first-order bright fringes of these two wavelengths on the screen.    m

What is the index of refraction of a clear material if a min 7:lm3j5ka1jhbci (ro.k5 l rpimum of 150 nm thickness of it, when laid on glass, is needed to reduce reflection t:r3alc1oj(m5.rh7 jbkiplk5 o nearly zero when light of 600 nm is incident normally upon it? Do you have a choice for an answer?

  Monochromatic light of vh2mg1i zow c:)cz+ .yeariable wavelength is incident normally on a thin sheet of plastic film inz+o)mwzhgc ecy: 2i1 . 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 needv ffj5fs 0/c;coplxj 1n:fgyj.u- p0* ed 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) thickness for the air layer between two flat gla4l;u*tz obsv8b1t -nvss surfaces if the glass is lbn 1 v8tv4*t;z-buso 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 transmitted through a thin film layered on a fla gtg.w2d/dgq x+go.xi+ 3 7myvt 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 comparg3gvd qimx.7 +2 ydxwt.o/g+ged to the maxima and to zero.
24-30
24-36

  At what angle above the horizo h)2 zwdg-gqhks;pi t-s5o80u n is the Sun when light reflecting off a smooth lake zt-is 2g8)sq-;opd0hug wk5his polarized most strongly?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be placed so as to reduce thqh *kmj +llz0al9a03;0c emlhe intensitcq ;ma3*l0+e h0jzhalk09 llm y of the incident unpolarized light by an additional factor (after the first Polaroid cuts it in half) of
(a) 4,    $^{\circ}\,$
(b) 10,    $^{\circ}\,$
(c) 100?    $^{\circ}\,$

  Unpolarized light falls on two polarizer sheets whose transmission axes ou lov9d3m067xa u2tware at right angles. A thirdxmou72l wd03 tuao96v 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 pl xqg*cpz58qh ra7p6z*aced 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 a slit of width 1fdqp+h1f. h;3g*sycx ux2s 3e o2mt.t .0 cm and is pointed at the Moon, which is approximately 38o2hcg.xxys 3 ut. ;me2t+* f13qfsdph0,000 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 pla(w.5h2trxd u2u+0tp .4t4;d apamns lye vz6eced 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 ib.8bx6.a m bs$(n=1.34)$ 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 waves7i7 rtl8i ,i(mz; 5fp.en luze in phase with each other. They pizte. 8fi75erl;liz (nm, u7are 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 cont.gm9uk w4cz-jc-o epe )pn. *aaining two wavelengths, 420 nm and 650 nm, enters a silicate fli.-ke9-uw*g.ocpemn )aczp4jnt glass equilateral prism (Fig. 24–58).
(a) What is the angle between the two beams leaving the prism?    $^{\circ}\,$
(b) Repeat part (a) for a diffraction grating with    $^{\circ}\,$

  A Lucite planoconvex lens has one flat s -dv78;fevmzvh ss+ 3g6q y6isurface 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