Does Huygens’ principle apply to sound wavesp e +5px(tulp1cj(g p/? To water waves? Explain.

What is the evidence that light i 9w.)aaoqvqqzgf0y6 .s energy?

Why is light sometimes described as rays and sometime)kxz;pqnev2 ky,+uqd,b r6p8 s as waves?

We can hear sounds around corners, but we cannot see around corners; ye6flipmg k9: rbr9)ddymc . 5-ft both sound and light are waves. Explainrl gmddcp ff.by 5r:k-i9 69)m the difference.

If Young’s double-slit experiment were submerged in water, how would the fringsgp6f,h 5r kd7b*v dv ,pl3g1au c)b(pe pattern be c1vbdfd*) 5pgcb kgarhp(,,l6p v 37us hanged?

Monochromatic red ligw he(s,loza z2l;5jhq 0:25tv;wv ps nht is incident on a double slit, and the interference pattern is viewed on a screen some distaeslns :qwwh(5 o0zja; h5v2,2 ;tplvznce 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 theizgcad:*6js nsy;a w2q.y12czr path lengths dif*nzzc162dajwca;y .sg qs2 : yfer by how much?

Why was the observation of the doss/ :)rfiq1uh uble-slit interference pattern more convincing evidence for the wave theory of light than the observation of diffraction?:1sfu ri/h)sq

Compare a double-slit experiment for sound waves tot x,)ln rwj 9n+bpr h442cv.fc that for light waves. Discuss the similarities n,h2jv+frr p c9x4b)c4tlw.n and differences.

Why doesn’t the light from the two headlights of a distant car p96b;)ny fw,j*lifhj jroduce an interference f 9jh,;jfiyb6n)jw*l pattern?

Suppose white light falls on thejrt3ya/( * m+b icdft- 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). Describe the pattern on tdb+atjmr(tyi/*f- 3che screen.

When white light passes through a flat ga jg 7y0i,jyg,s3wh2 piece of window glass, it is not broken down into colors as gw,2ya,y0sg3hi j j 7git is by a prism. Explain.

For both converging and diverging lenses, discuss n297dp z1jychhow the focal length for red light differs from that for violet lpjhdcy n2z791ight.

A ray of light is refs-tj/l/,+r gsl5 rpds7glt (oracted through three different materials (Fig. 24–55). Rank the materials accordsrlp gj /o5(,/s+rs7tld-gt ling to their index of refraction, least to greatest.

Hold one hand close to your eye and/z1gbov 2gqc* focus on a distant light source through a narrow slit between two fingers. (Adjust your fingers to obtain the best patz2g v*1/gcoqb tern.) Describe the pattern that you see.

What happens to the dd guf5p,4*v24m fr6wh cam;lriffraction pattern of a single slit if the whole apparatus is immersed in (a) water, (b) a vacuum, instead of4cu45flg m;rprdv 2 w6fm*ah, in air.

For diffraction by a single slit, what is the effectdrw p/oqd,5n( of increasing (a) the slit width, and (b) the wavele(,p r wd5nod/qngth?

What is the difference in the interference patlkd +-(px2 l+fbnf8 -b/zdig/ kilcb1terns formed (a) by two slits $^{-4}\;cm^2$ apart, (b) by a diffraction grating containing $10^4lines/cm$?

For a diffraction grating, what is the advantage of (a) many slits, (b) closm0n av 1x um(io4j9g0eely spaced slitsu0(vajgo4in9 mx 1me0 ?

White light strikes (a) a diffraction grating, and (b) a prism. A rainbowvu1 j27 z1bpps appears on a wall just below the direction of the horizontal incident beam in eacspu27 pvbj z11h case. What is the color of the top of the rainbow in each case? Explain.

For light consisting of wa/ley6m+y as1wvelengths between 400 nm and 700 nm, incident normally on a diffraction grating, for what orders (if any) would there be overlap in the observed spectrum? Does your answer depenw lme1 a/y+6syd on the slit spacing?

Why are interference fringes notilphq4 -zyapt :3 4-y+ j;ifagcceable only for a thin film like a soap bubble and not for a thick piece of glass, ;pqzt h3fa: ljy+4yp-a 4g-ci say?

When a compact disk (CD) is held at an angle in white light, the8y+jhm6ma s4* w1ij5n ape6px reflected light is a full spectrum (Fig. 24–56). Explain. What would you expect to see if monochromatic p 6+5 1nm i6ejm8s* 4phyjxaawlight was used?

Why are Newton’s rings (Fig. 24–31) closer togethe4z/rynd1a b.3s pwzp2n0 w8,y6jtzc yr farther from the center?

Some coated lenses appear greenish yellow when seen by refle5twvgu8f6 w7+q wq:te cted light. What wavelengths do you suppose thw+fg67 qu5wv :tq 8tewe coating is designed to transmit completely?

A drop of oil on a pond appears bright at its edges, wher a +iwh*t7i2lpe its thickness is much less than the wavelengths of visible light. What can you say about the indexa+ pi2w7t lh*i of refraction of the oil?

What does polarization fnwo+g m *0( a0iu+hb t-fj5nctell us about the nature of light?

Explain the advantage of polarized sunglasses over normal u am t+8s /3eyk (5a;jaqzltj;9xb*kntinted sunglasses.

How can you tell if a pair of sunglasses is pol30/mzsuk sk4p arizing or not?

Two polarized sheets rot5 kmo zpkf.u;yib c vi8xg:b.71a ,,gcated 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 Eartzgb iu21k;h +bh had no atmosphere?

If the Earth’s atmosphere wereo /3un hl,7 8i;kn1t6fqldaukemz ,6e 50 times denser than it is, would sunlight still be white, or would it be some ,8q66f n3k omui,/a1lu enthkl;ze7 d other color?

  Monochromatic light falling on two slits 0.016 mm apart prvntou86 n gmn:mo 4)4joduces the fifth-order fringmn486 n o 4n:tujomgv)e 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 9kx(q nnlv9z:-8qr)sptbq .fobserved 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 very narrow slits 0.glyg qvq7l/e; .sk o 6m00ffs-048 mm apart. Successive fringesq-eg kg0mlyf.qvo 6f07l/ ; ss 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 light.
$\lambda\;=\;$    $m$
$f$ =    Hz

  A parallel beam of light from a He-Ne laser, with -n36ym v8n 0gkeodfaswx5zkd(e5s (9 a wavelength 656 nm, falls on two very narrow slits 0.060 mm apart. How far ad5fnkgzs 5 (8eynk(sv 3x9mo06ead-wpart are the fringes in the center of the pattern on a screen 3.6 m away?    cm

  Light of wavelength 680 nm fallscc 5,h4f-zw ztvob-w) on two slits and produces an interference pattern in which the fourth-order fringofbvt ,czch-45 zw-)w e 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, how far apzc8os fk8+ ,apart are tof+zsa 8p ,c8khe second-order fringes for these two wavelengths on a screen 1.0 m away?    mm

  In a double-slit experiment, it is found that bl:is yq 8.vno0uue light of wavelength 460 nm gives a second-order maximum atiq8 nouv s:y0. a certain location on the screen. What wavelength of visible light would have a minimum at the same location?    nm

Water waves having parallel crests 2.5 cm apart pass through t3 )mspj2t5rqcu*pkur t0e.j 4wo 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 would the342r k)js0r. 5putmepu t*cjqre be little or no wave action?

Suppose a thin piece of glass is placed in front cgca1 y-(sib7of the lower slit in Fig. 24–7 so that the twog y1ai(7-cbsc 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 for light o*/xxhuzv z8kcd3/ rq 8f wavelength 500 nm is located 12 mm from thv/8d zxz/*hr3 cx8uqke 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?    mm

  Two narrow slits sepij9bbuwoo.s 8 +0 f7dn. hx3lk gm(mn5arated by 1.0 mm are illuminated by 544 nm light. Find the distance between adjacent bright fringes on a screen 5.0 m from ts9nbof(nx. 3+m8 kl h7wjd .bom0u5 gihe slits.    mm

  Light of wavelength 480 nm in air 3 xxktnl w 8,*c2g)vlvmb-ut;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) covers one slit of a double-slit a* l+:dv 9u fsxf4kruob+,yf f9pparatus illuminated by 640-nm light. The center point on the screen, instead of being a maximum, is dark. What is the (minimum) t:xbdfr 4y+9fl+v,o u*f9 kfus hickness of the plastic?    nm

  By what percent, approximately, does the speed of red light v 28uz4+7)c9yxxuvu:g rt5w/ 9g6 hea kcinro(700 nm) exceed that of violet light (400 nm) in tx296zr/augy+5vr :hg4i)89ko uxvwn c7euc silicate flint glass? (See Fig. 24–14.)    %

  A light beam strikes a v t 2 h4,vvpwu2+38cvxeoyjl-piece 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 contai2spiap6 *p)g ining 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 width o(0 ivhx;hpt(3bm0h nm f the central diffrac0tpi hb(x v h3m(nm;h0tion peak?    $^{\circ}\,$

  Monochromatic light falls r;jw(bj n,;se on a slit 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 .1cbpyabk j42is $ 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 p3zd o7u5aw)qis the width of the central maximum (in cm) in the diffraction pattern 3q)z5 apud wo7on a screen 5.0 m away?    cm

  Monochromatic light of wavelength 653 nm faly 1tm*5rap)c gfadb b; ov/(.pls on a slit. If the angle between the first bright fringes on either side of the central 1ap.tac5v ;o/pmyr)bdf g(b*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 hp(l6x 01fa nk0.0348-mm-wide slit illuminated by 589-nm light? hf kla0 p(6xn1   cm

  When blue light of wavelengvf joss.(0 (szth 440 nm falls on a single slit, the first dark bands on either side ofs ss.j(fv (0zo 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 creat b*z1 w5vfd ,pe(;4 g5 noaeflunpqa,(es a central diffraction peak that is 9.20 cm wide on a screen that is 2.55 m away. How wide is the s(e a;gb,5nf*uz4andp1 ,( wlope f5 vqlit?    mm

  If a slit diffracts 650-nm light so that the diffraction maximux+)t:cdjh0 0a i/kkdjm is 4.0 cm wide on a screen 1.50 m away, what will be the width of the diffraction maximum for light of wkc)/addxj h0it:0 k+javelength 420 nm?    cm

For a given wavelenguxd pt*)/;(oa 8 rf) r6akavzith $\lambda$, what is the maximum slit width for which there will be no diffraction minima?

  At what angle will 56w 6b z)9(:kl9pqzzkth0-nm light produce a second-order maximum when falling on a grating whose szzlwq()b: h9k k6z pt9lits 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 centimete70:l hs 3pqmidh hw6u6r does a grating have if the third-order occurs at an 18qdmh6pis36:l0u7w hh .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 fam n eyr.*z.cy-lling on a diffraction grating is observed at yyz. n-rm.ec *a 15.5$^{\circ}\,$ angle. How far apart are the slits?    $\mu m$
At what angle will the third order be observed?

  A diffraction gratinghgi9gb y 1mk*m 0/yz.d has $ 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 az,tw rgewox4;58 geps6 5lj; dr4wkf2 $9700-line/cm$ 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 sidt8rn)zs9 pb2qno6/v4vvy( y( l a)r een if a grating with 6000 lines per cm is illuminated with 63r l6z4() in( ysar)89v pyb/d ovtqvn23-nm laser light? Assume normal incidence.   

  Two (and only two) full spectral orders can *k5j*/he7lo09/ jqx lwnyrvk be seen on either side of the central maximum when white light is sent through a diffraction grating. What is0hkj rk/wn l975*xj yvol/qe* the maximum number of lines per cm for the grating?    $ \times10^{ 3}\;lines/cm$

  White light containing wavelengths from 410 nm m;b- hvu xy:)szs(sidv5o3 9vto 750 nm falls on a grating with i()h3ys5 dos v-bvmzx :9su;v$8500\;lines/cm$ How wide is the first-order spectrum on a screen 2.30 m away?    m

  A He-Ne gas laser which produces monochromatic ligh fdr-gd.8 hxv3t 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 measurv f nu 8 a/k/ily*p;z6hcjry/6ed 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 walac t);, )z,i6cmcozuvelength is most strongly reflected at the center of the oute) l)c,u; ,cz6ciamzot r surface when illuminated normally by white light? Assume that $n\;=\;1.34$. $\lambda$ =    nm ,which is an    -  

  How far apart are thb qnh4 kjf;-)ce dark fringes in Example 24–8 if the glass plates are each 26 4jbf;-kchqn) .5 cm long?    cm

  What is the smallest thickness of a soap p:9(op.ijz+ ruouv g)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 greeniz69* kep;bycen m7l(f sh yellow ($\lambda\;=\;570\;mm$ 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 ri:fli+p)up9s6bp +kvy zr6 bi-ngs (not counting the dark spot at the center) are observed when 550-nm light falbpp+zirvi96lf)-6 +sp : bkuyls 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 ezw4+hig0b z2optically flat glass, as in Fig. 24–33. When light of wavelength 670 nm is incident nzwh2+z4b i0e gormally, 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 ;jk rvnw vu0w+ 2.w-vlglass surfaces if the glass is tv+l. v w-nrjuw0;w v2ko 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- olj.kem:: 8lqtn)tsvn/lnb8ej -b 1 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 alcohol6kq2a g 5g.o.ggs.f v5m h,odv $(n=1.36)$ lies on a flat glass plate $(n=1.51)$. When monochromatic light, whose wavelength can be changed, is incident normally, the reflected light is a minimum for $\lambda\;=\;512\;nm$ and a maximum for $\lambda\;=\;640\;nm$ What is the minimum thickness of the film?    nm

  When a Newton’s ring apparatus (Fig. 24–31) is immersed in a liquid,q:b8 db8u0 -uot.xy1ceic y :6iahev* the diameter of the eighth beto. a0vuy*i8bxc:y q6 ihed:-cu1 8dark ring decreases from 2.92 cm to 2.48 cm. What is the refractive index of the liquid?   

  What is the wavelengtn2(0.adz ea awh of the light entering an interferometer if 644 bright fringes are counted when the movable mira0w e(a2.azn dror moves 0.225 mm?    nm

  A micrometer is connected to the movabx5.r*8suyvn k le mirror of an interferometer. When the micrometer is tightened down on a 5*vx8 kyrsun .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 mirrott.a.cjx o*nq.w; h8o r $M_1$ 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 glosp*g vo1k-)hj yro qr6(hx*:ass container containing a cavity 1.30 cm:xg q r )sk (o6ry-jp1h*o*ovh 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 orientef 4oy-i*ujot-d 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 uld,13co,g 2 btt0djm air–glass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s angle for a diamond submerged in water irl,a7 2j1yiur eu.m:yf the light is hitting the diamr7: ui, yljmu. r12ayeond $(n=2.42)$ while traveling in the water? $\theta_{p}$    $^{\circ}\,$

  Two Polaroids are aligned so that the light passing through them is a maxim,y y tjs s6;wi11m/,ntctt1 zium. At what angle should one of them be placed so that the intensi/yiy1t;i, wm61 1tcznts jt ,sty is subsequently reduced by half?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be placed so as to reduce the / dn.uc)5rwxwx3qli6 intensity of the incident unpolarized light to dlc5xu rwwn36)/.ixq
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are oriented a jl9nyll a3r()t 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 38.0y +4eiiz gkn7 2t.c.nw$^{\circ}\,$ 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 water for lighu(8w( r -hfp0w;lf dlmt cofwrf;plh- w0((d m8ulming from beneath 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 passesqhiwz mgr9jd 59q4m :6 through five successive Polaroid sheets, each of whose axizmj69 94r qg:im5qd hws makes a 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength xs0/5c ti6cmhm(xt* j$ 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 mou dv4ijig3vfz*u290uss g72d qntains or airplanes can interfere w*j gi9sqdv2gfz7vd04iuu2s 3 ith the direct 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 separa nz* zjempc8 lgn19c46ec x8,mte sources passes through a diffraction grating with c98j x 6,n1zlmne* 4mpc8 eczg$ 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 cu9 -7wmu; ptlscreen 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 t m;-luu9wc7 p590-nm light. What is the wavelength of the unknown light? $\lambda_2$    nm

A radio station operating at 102.1 MHz broadcasts f/vau*x bnph *v-; qh0vrom two identical antennae at the same elevav;uhv-0*v* xh bqap/ntion 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 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 doorwyzlx k .o)o9z,ay 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 the doorw.yzl),z9o oxk ay.    $^{\circ}\,$ either side of the normal.

If parallel light falls on a0hf+p eskid81 single 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 across them. -eprmh h )cs,,q:ba(c4nbt2fWhen normafm-bc4cp2st erha,)h:b(,q n lly incident 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 to be no second-or,s r0jz:h62 iugtimco94w:ua3x 9 ijh der spectrum for any visible wavei6uw x30h:rg9uo,h: iacsi mjj42 9ztlength?   $ lines/cm$

Show that the second-d(r/x.rgm7 vf and third-order spectra of white light produced by a diffraction grating always overlap. What wavelf/7rxgvd( .rmengths overlap exactly?

  When yellow sodium ligo ;/84t +b (ozdzzjz+ x:xjsb.d:kavlht, $\lambda\;=\;$ 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 wite3pu-f +g*ys hh and the pattern is viewed on a screen 2.5 m from the grating.+h *ufypg3-e s The incident light beam consists of two wavelengths, $\lambda_1\;=\; 4.6\times10^{ -7}\;m$ and $\lambda_2\;=\; 6.5\times10^{ -7}\;m$. Calculate the linear distance between the first-order bright fringes of these two wavelengths on the screen.    m

What is the index of refraction of a clear material if a minimum of 150 nm thicgs79y4hhz7o 9l/6ny )l6qp te;bv ivlkness of it, when laid on glass, is nee6l/7h7il94n syqpl e6tv;gb h)zyo9v ded to reduce reflection 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 wavelength is inx-qus i o4k. (x06hrsvcident normally on a thin sheet of plastic film in air. The0vk(ssu -6iq4r .x xho 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 coaosw b/7w/vw, blb+m5n-dwne9 ting $(n=1.38)$ 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 betgu9.- /k q9-n 0njgbwn4grxatween two flat glass surfaces if 99b-w .kt0 /4-gngrxq u gjnanthe 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 transmitted through a thin film layered on a fa+zy-1lyuch3-jivluw;+ * p ted m0p*lat 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 in 3y*pvpj10 - +* +wziauehdluy;tl-mcdex of refraction. Discuss the relative size of the minima compared to the maxima and to zero.
24-30
24-36

  At what angle above th +aj )o9hl/tgne horizon is the Sun when light reflecting off a smooth lake is polarized most)lj/9+hoa gnt strongly?    $^{\circ}\,$

  At what angle should the axes of two-nbh pq*8+u m-mvbtd8 Polaroids be placed so as to reduce the intensity of the incident unpolarized light by an additional factor (after the-htpbdm * q8n v8+mbu- first Polaroid cuts it in half) of
(a) 4,    $^{\circ}\,$
(b) 10,    $^{\circ}\,$
(c) 100?    $^{\circ}\,$

  Unpolarized light falls on two polariryoa5. ln01nxg l(jwm2 1heh8zer sheets whose transmission axes are at right angles. A third pol.nrw0nx2 8l5 gha 1 (1jyomehlarizer 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 with their axes verrv3:-k)d;*n. vmsra 8qkf rkxtical, 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 pointed at the M4y ;cb*jbg (nooon, which is approximately 380,000 km from the Earth. Assume the laser emits waves of wavelength 630 nm (the red light of a He-Ne laser). Estimate the width of the beam when it reaches the M (c*oybgn4b ;joon.    km

  A series of polarizers are eajls2v:u w 4mbun2qk80ax *w1jch 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 ck 2n+yf vn5 p;ep0x-n$(n=1.34)$ coats a piece of flat glass $(n=1.52)$ .How thick is the film if it reflects 643-nm red light most strongly when illuminated normally by white light?    nm

  Consider two antennas radiating 6.0-MHz radio waves in phase with eacb b/2vhoifo7 /h other. They are locatedv2obb 7f/h/oi 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 containing two wavele8cf zv6a myddl/3 4e/ongths, 420 nm and 650 nm, enters a silicate flint glass equilateral prism (Fig. 24/o6 m4ddvc/a3le fy 8z–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 3psb w g13xve2and 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