Does Huygens’ principle apply to sound waves? To water wav77ig l,f9yvwv2qa3cja: k bv/es? Explain.

What is the evidence that li fbz(i a (b/4dh(7ajalght is energy?

Why is light sometimes described as rays and sometimes as ts 7-e )noo-zhps6x7n waves?

We can hear sounds around corners, but wevwbl-0*9te t jd8*ipf5knc(r cannot see around corners; yet both soun5w8e(dlfvr jn* ttc *-ip90bk d and light are waves. Explain the difference.

If Young’s double-slit experiment were submerged in water, how would the friz0 dvalfib;1/(6* zj7uzn wv wnge pat wbaiz;n(7fuvzd0 1vz*wj/6ltern be changed?

Monochromatic red light is /uc zzevi9x:e ,z5 e4fincident on a double slit, and the interference pattern is viewed on a screen some distance away. Explain how the fringe pattern would change if the red light source is replz:i v/ezu5xf,eze c49aced by a blue light source.

Two rays of light from the same sour l1eo7mh akcem 1))i(wce destructively interfere if their path lengths differ by h7el)mao1mic1( w)kh eow much?

Why was the observation of the double-slit interference pattern more convi()s wmh hw5e 1lb5i xjzjg4/2xncing evidence for the wave theory of light than the observation of h2ewg/zb)( h4 ms lxwjix1j55diffraction?

Compare a double-slit experiment ieulk2+.iqbc yr, a5/for sound waves to that for light waves. Discuss the similarities and differencey lri+c.e/qkb 2ui,a5 s.

Why doesn’t the light fr/k.gqir f6fs( om the two headlights of a distant car produce an interferencefs kf6gq/.i(r pattern?

Suppose white light falls on the two slits g3psakcw k..m2w4 b .u*t+m oqof Fig. 24–7, but one slit is covered by a red filter (700 nm) and the otk a2w 43swb*co.p .m+.m utkgqher by a blue filter (450 nm). Describe the pattern on the screen.

When white light passes through a flat piece of window gl f1cduy .tg,2f*gyhk 4ass, it is not broken down into colors as it gt1d 2. ckyuy h,4gf*fis by a prism. Explain.

For both converging and diverging lenses, discuss how)o,ld4s8c fp 4/ 9dnv tbz6vca the focal length for red lightf do n6 ,4s4l9v)azbcp8/ctd v differs from that for violet light.

A ray of light is refracted thrp r1u* p1yy w70a14 7pcncplciough three different materials (Fig. 24–55). Rank the materials accopypyl1nacpcc* 71 0ip1wur74 rding to their index of refraction, least to greatest.

Hold one hand close to your eye and focus on a distant light source through a navfsn4+tg fqh. 3x(d/ arrow slit between two fi3f a.gvhqtd4+ f/ xsn(ngers. (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 thek5 n4y5bl:efb ucc p68 whole apparatus is immersed in (a) water, (b) a vacuubu :5 lpn5k4c ecy6fb8m, instead of in air.

For diffraction by a single slit, what is the effect of increasing (a) ya.d -j ag9ci 1xpx0y+rgk;s: the slit wid; y-ajp0k 19:xiax .gg ryd+csth, and (b) the wavelength?

What is the difference in the interference patterns formed-s:ni uvj me0l6 cq;i/ (a) by two slits $^{-4}\;cm^2$ apart, (b) by a diffraction grating containing $10^4lines/cm$?

For a diffraction grating,f yl*8tt51al, np.pch what is the advantage of (a) many slits, (b) closely sp8hfl*ptc l ,tn .ya1p5aced slits?

White light strikes (a) a diffraction grating, and (b) a prism. A rarj5( nqb)f :hu lu/tb7inbow appears on a wall just below the directirtuj(fb5u)n7b:ql/h on 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, incident nh 3dyyv lk3;.j4 a)jtrormally on a diffrack rlyd3h;3 ytv)j aj.4tion grating, 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 notgaqe+an, *e1o ccnu.7iceable only for a thin film like a soap bubble aenca*q7,aeong1c + u .nd not for a thick piece of glass, say?

When a compact disk (CD) is,lq- 7s2:xvix ajd5j x vpeu60 held at an angle in white light, the reflected light is a full spectrum (Fig. 24–56). Explain. What would you expect to see if monochromatic lightxvjqps2u:0j x67edi ,a lv 5-x was used?

Why are Newton’s rings (Fig. 24–31) closer tou9f8 p7bvnp7+b ulf 8tgether farther from the center?

Some coated lenses appear greenish yellow when seen by reflected ligd12a+(qwhzo e(z ir la q2qf((ht. What wavelengths do you suppose the coating is desi2(eo1( a qr( dazf(wiq2lz+hqgned to transmit completely?

A drop of oil on a pond appears bright at its edgse r6 pj /i4pp):a6gfdes, where its thickness is much less than the wavelengths of visible light. What can you say about the index of refraction of the oe)p6p ipr/gs 6f j4ad:il?

What does polarization tell us *i69yjt-36z osy wuyz about the nature of light?

Explain the advantage of pola /u4pk6 z+watyrized sunglasses over normal tinted sunglasses.

How can you tell if a pair of sunglaugo(nf2q pil+ry/iqq *zj-cjyq3/ 2 -sses is polarizing or not?

Two polarized sheets rotat*4 pwmdnj0z rj.by7l /ed 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 Earth had nomw9oiw ;o3xhfwr.-y yyu r)1* atmosphere?

If the Earth’s atmosphere were 50 times dense9z y 2mdncj 23z 5bi7hq7gmz:mr than it is, would sunlight still b7b9nzqgdh 53 ym7jz2m mzi:2ce white, or would it be some other color?

  Monochromatic light fallkx b0hng*b 7dpj5 8n2sing on two slits 0.016 mm apart produces the fifth-order bg pnhb285ks n 0d7jx*fringe at an 8.8$^{\circ}\,$ angle. What is the wavelength of the light used?    $ \times10^{-7 }\;m$

  The third-order fringe of 610 nme9yb u/u x;x3n light is observed at an angle of 18$^{\circ}\,$ when the light falls on two narrow slits. How far apart are the slits?    $\mu m$

  Monochromatic light falls on two very ffzp h rzm310*gb)5gxnarrow slits 0.048 mm apart. Successive fringes on a screen 5.00 m away are 6.5 cm apart near the center of the pattern. Determine the wavelength and frequency of the l3r 5bh* 1pgz)mfz0f xgight.
$\lambda\;=\;$    $m$
$f$ =    Hz

  A parallel beam of light from a He-Ne laser, with a wavoxpu236 f.ffk elength 656 nm, falls on two very narrow slits 0.060 mm apart. How far apart are the fringes in the center of the pattern on a suf2f6k3 o p.fxcreen 3.6 m away?    cm

  Light of wavelength 680 nm falls on two slits and produces an i(2 )4epw0iarrl(ux5 w3 ndt yrnterference pattern in which the fourth-order fringe is 38 mm from the central fringe on a screen 2y3 ra2xr wupt04( enwi)rd5l( .0 m away. What is the separation of the two slits?    mm

  If 720-nm and 660-nm light passes through two slits 0pr5igk1y 6p*zdb9ij ..58 mm apart, how far apart are6 9pi*g.p5j1z yidk br the 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 wavelength 46x:u, bj qy 6mdzrd;5/u. 3rzpe0 nm gives a second-order maximum at a certain lo /d,x;d5r:zur.3bp 6jzmey uqcation on the screen. What wavelength of visible light would have a minimum at the same location?    nm

Water waves having parallel crests 2.5 c1j+d4kk3 bib wm 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 would there be little or k 1w kd+34bbijno wave action?

Suppose a thin piece of glass is placed in i-gz( .gz ekt/ kzkw(+front of the lower slit in Fig. 24–7 sweig.(zktk zzk-(g/+ o that 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 experiment, the third-order maximum for light of wavelekh/*6nyzl zo0 ngth 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 sek h oz*y0ln/z6cond-order maximum of this light be located?    mm

  Two narrow slits separated by 1.0 mm are illuminated b2el;4z p5nav ay 544 nm light. Find the distance between av2 5zl;e npaa4djacent bright fringes on a screen 5.0 m from the slits.    mm

  Light of wavelength 480 nm zj 3yxcg6 *tw+n6)ihvin air falls on two slits $6.00 \times10^{-2 }\;mm$ apart. The slits are immersed in water, as is a viewing screen 40.0 cm away. How far apart are the fringes on the screen?    mm

  A very thin sheet of plastic (n=1.60) covers one slit ov ,0n-j;:.cdt vkglzz8-di wdf 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 n jgctk80i.d:, wdvz--d ;lzv (minimum) thickness of the plastic?    nm

  By what percent, approximately, does the speed of red light (700 nm) excl o pk92hm.na)eed that of violet ligpnh)l9oak. m2ht (400 nm) in silicate flint glass? (See Fig. 24–14.)    %

  A light beam strikes a piece of e9s59gt8avtgal.8:e :j2fk yd 7eyhf 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 lik *v3fj-h1+fea+yvb pght containing 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, wh(8lfu z5 dyq7yat is the full angular width of the cen7 f5u8yyzl (qdtral diffraction peak?    $^{\circ}\,$

  Monochromatic light falls dta7weg: ad: re jfc:bw9+b7(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 sliorr0 qh3.1:jd k 6flggt 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 widthb q-6lquv i 2u6e,z)+jcvruf( of the central maximum (in cm) ivbrjqv cu6 l-2+( qzu6)fe,u in the diffraction pattern on a screen 5.0 m away?    cm

  Monochromatic light of wavelength 6 8li) +hzktuh353 nm falls on a slit. If the angle between the first 8h3+u i)kzhlt bright fringes on either side of the central maximum is 32$^{\circ}\,$, estimate the slit width.    $\mu m$

  How wide is the central diffracte +ny u(hrwn,v-wgd: e0rgh-f1 vvx**ion peak on a screen 2.30 m behind a 0.0348-mm-wide grfvy*d*h-e(h ngue 10 vwn x:w,+rv -slit illuminated by 589-nm light?    cm

  When blue light of wavelength 440 nm falls on a single slit, the first dark pm wi3myn b0.8bands on emn .mb8p0wy 3iither side of center are separated by 55.0$^{\circ}\,$. Determine the width of the slit.    $ \times10^{-7 }\;m$

  When violet light of wavelength 415 nm vrsn3 -2 sasoo lweqw+zp2;*5h94ddafalls on a single slit, it creates a central diffraction peak that is 9.20 cm wide on a scrlnevwho+;w 2ra4p soa9q5z3s- *2ddseen that is 2.55 m away. How wide is the slit?    mm

  If a slit diffracts 650-nm light so that(ehj/ ;c z/(upeul*ry the diffraction maximum is 4.0 cm wide on ace p*y;(e z/ jrh(luu/ screen 1.50 m away, what will be the width of the diffraction maximum for light of wavelength 420 nm?    cm

For a given wavelengtxjh/lw)xwa+ 3.ez8s iq)srp9h $\lambda$, what is the maximum slit width for which there will be no diffraction minima?

  At what angle will 560-nm light produce a q++g 4qimci khs4e e18second-order maximum when falling on a grating w8kqegc4ie+ s 14q+i mhhose 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 iw1qf9 fmj;t; df the third-order occurs at an 18.0ffjq td1;;wm9 $^{\circ}\,$ 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 diff2h2ul1v;b s kpraction grating is observedkhbp ;1ls2 v2u 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 haqu7npqz l7- i(s $ 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 tqx6gggu:vcx s7:n(mt--(f x $9700-line/cm$ 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 f3x;egj d n7g2tqpg9u2/*vw qbe seen if a grating with 6000 lines per cm is illuminated with 633-nm laser light? txqfgwe7gv9 q /gpu*j3d2 2;n Assume normal incidence.   

  Two (and only two) full spectral orders can be seen on eithpys q ..vhq:g/er side of the central maximum when white light is sent through a diffraction grating. yv: . gphsq/.qWhat is the maximum number of lines per cm for the grating?    $ \times10^{ 3}\;lines/cm$

  White light containing wavelengths from 410 nm to 75 mf0gj;u. i*lb a)z3gr0 nm falls on a grating with *g 3.0firbl)z j;maug$8500\;lines/cm$ 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 kn(3nru3r du(m eown 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 spectrc2.x-tm*vha:i hbzyk8 qcn9f v *c u+6um lines are 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 mos7q6l tq ak)2+fbj* cxmt strongly reflected at the centerjm7q*tbl2) 6c ka q+fx of the outer surface 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 plates are eaq* aex9y/ bt1-lngj-dix4 / mxch 26.5 cm long? l* igxejxx-9/b1dyqa-mn 4 /t    cm

  What is the smallest thicknt rh80mz4;atb ess 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 zw0/ ntto.bkz ykn kv+r7u,48n- q6sf 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 Newto d:/y(tc.izqx n’s rings (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 (F(ytq/zic .:dx ig. 24–31). How much thicker is the center than the edges?    $\mu m$

  A fine metal foil separatem13bdf jklb:hh1 (r)p s one end of two pieces of optically flat glass, as in Fig. 24–33. When light of wavelength 670 nm is incident normally, 28 dark j1mdfhk(b)rlp h1 3b :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 glass surfac zgs,pd99f5qe 3uw r;ies if the glass is to appear bright when 450-nm light is incident no;wf9gudz53 i s p,9qerrmally?    nm
What if the glass is to appear dark?    nm

  vA piece of material, suspec.cc3 gbulh9t 8ted 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 alcohol 7gvyb5a0 yop)fatj8 0 $(n=1.36)$ 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 immerse ,j,z8n573 npn- dvvuw qos:lid in a liquid, the diameter of the eighth i3:,j vwlnpu5 -vso8 nq7dn z,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 b ;l8yalqdw,3 bright fringes are counted when ,lwy3 l8ad b;qthe movable mirror moves 0.225 mm?    nm

  A micrometer is connected tf(.g te:n. usxo the movable mirror of an interferometer. When the micrometer is tightened down on a thin metal foil, the net number of brige.(nfux. : tsght 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(i.unua2 ht, g $M_1$ 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 interferometep2qy.t0gqc wev;s u- (r (Fig. 24–59) passes through a small glass container containing a cavity 1.30 cm deep. When a gas is allowed to slowly fill the container, a total of 236 dark fringes are counted to move past a reference line. The light used has a waveleng(t0-2qqyu.v wes pc;gth of 610 nm. Calculate the index of refraction of the gas, assuming that the interferometer is in vacuum. $n_{gas}$

  

  Two polarizers are on30m,. acfuybooa 1 c*riented at 65$^{\circ}\,$ to one another. Unpolarized light falls on them. What fraction of the light intensity is transmitted?   

  What is Brewster’s an l 2m2nrbf x7p 1mlvl:v7q (;,qlsw.sbgle for an air–glass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s angle for a diamond submerged in water if the lign-jvbl)z g5ry6i -;w 9hkl ,ayht is hitting the diamvw y56rjy;- glh-lb)9i, anzkond $(n=2.42)$ while traveling in the water? $\theta_{p}$    $^{\circ}\,$

  Two Polaroids are aligned so that the light pas gs::p-)7acsl0vjhwg )o u1jhsing through them is a maximum. At what angle should one of them be placed so that the inte)o1w pj)gshvh:c:- aujl7gs 0nsity is subsequently reduced by half?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be placed so as to reduce o 3u)gj-tq2iis( byx 8the intensity of the incidenxobqtj-igui)8ys 2 (3t unpolarized light to
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are orientmu tx.7 u(ivf.k (bjl,ed 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.jhbul dnv1- .th8+++t8i7 5hflweqen0$^{\circ}\,$ 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 lightz. 8wpj7 cp7 *h3f2afx g3mc8tmem3 ot coming from beneath the surface? Compare to the angle for total internal reflection, and to Brewster’s angle from abow t pm8hpm 3m7a8*e c j37.cxff23gtzove 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 Polaroid sheets, each 3 om/vhkja(jc*- x 4rfof whose axis makes x j /or m(c*34-akfjhva 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength i8 /ng(ehli p2$ 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 rngh/2j1teuqea 3s:z : eflecting from mountains or airplanes can interfere with thegt juh 1e3/: aqzne:2s 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 separate sources p07,ryjs0o z. tk:er mhasses through a diffraction grating with z,o0msytr.j h: 0kre7$ 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 s7 +,6 kmdqds7jd eo9tnm passes through two narrow slits 0.60 mm apart. 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 9qod7,ss7d dj t+k6emthan the 590-nm light. What is the wavelength of the unknown light? $\lambda_2$    nm

A radio station operating at 102.1 MHz broad/s6q 25yqu aoycasts 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 along the midline, perpendicular to d at its midp s2qyu6a 5yqo/oint and extending horizontally in both directions. If the midline is taken as 0$^{\circ}\,$, at what other angle(s) $\theta$ is a maximum signal detected? A minimum signal? Assume all measurements are made much farther than 8.0 m from the antenna towers.

  A teacher stands well back from an outside doorway 0.88 m wide, 4 elm*;vn.kagfww-; a and blows a whistle of frequency 750 Hz. Ignoring rmwaf ;l;v*ek wa-.4gneflections, estimate at what angle(s) 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 single l)w5ozo;hzgyh(o5 4y: gqkn8slit 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 linj;* qfwjij;1cl3v u7les across them. When normally incident 460-nm light is reflected from the wq7; jj l ivfu;*3jlw1cing, 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 gratihobd0d):s mpe +/fpr9zlcj 2dkl( .b3ng have if there is to be no second-order spectrum for any zbj9s(k:+fbp 3pdhl0d m/ der.)o2lcvisible wavelength?   $ lines/cm$

Show that the second- and third-order spectra of white light prodsr3 rj4tuoi* a*8lf4m uced by a diffraction grating always overlap. What wafr us4ti4*jrlm 8o3*avelengths overlap exactly?

  When yellow sodium light, )w * ydwulioxfv/.m4,$\lambda\;=\;$ 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 + k-/ogrwhbgq 0xauzm- 3dn 74a diffraction grating with and the pattern is viewed on a screen 2.5 m from the grating. The incident light beam consists o-xg4wr g0zkq/nuh bo m -+ad73f 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 minimbwgb52d v1bs9xxf93,mrm9faum of 150 nm 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 cho91wbm5rb 9g 3,v ds9 fxfmb2axice for an answer?

  Monochromatic light of variable wavelent1a b alaj+rjxa; 69 7 eptya7fca/7a)gth is incident normally on a thin sheet of plastic film in air. The ref/apr9ca) be+7 xaaf7j1a;laat 7 tjy6lected 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 alpfdn:o.s d .f-hc0e71 1 x:xg*y .ogvsv) jrvnti-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-z je4y/6vb zmn:)- xdb gfcxf*/ero) thickness for the air layer between two flat glass surfaces if the glass is to appear d x/zxb6dn4c*-)gfefvj bmy /: ark when 640-nm light is incident normally?    nm
What if the glass is to appear bright?    nm

Suppose you viewed tlfn s luatn7v jjg81qh6/f ;2ril9 18che light transmitted through a thin film layered on a flat piece of glass. Draw a diagram, similar to Fig. 24–30 or 24–36, and descricjlrv2uq sf7 jn6ta9;8l18 gh 1in/fl be 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 when light refle8dz(gsb+ 6jfbcting off a smooth lake is polarized most strongly? gdf+bjz6bs(8    $^{\circ}\,$

  At what angle should the axes of twoffk hceev8o2hc7g)1au gpf+w l4v,0/ Polaroids be placed so as to reduce the intensity of the incident unpolarizev,)4e 28efgfl0fhah v + /ucco7 kgwp1d 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 onzz1 rdyh+e+7e two polarizer sheets whose transmission axes are at right angles. A third polarizer is placed between the7+ze+hyz red1 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 ver ya6)r+l5 pimktical, 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 Moon, x1x;kdzzr. xa:aks3rn3 :n p4which is approximately 380,000 km from the Earth. Assume the laser ax1pzxn3:3:;d4srxkzar .n kemits 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 ,s( hl:h// fa3 ntshhoare each 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 ozp7*us4 kupq rw+l58e 3-xou$(n=1.34)$ 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 radia7 znlq6m1sj r3ting 6.0-MHz radio waves in phase with each other. They are locate1jlq67z3n mrs d 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 wavelengths, m8 qs7+dfsvsww+d3if s2j +:t420 nm and 650 nm, enters a silicate flint glass equil+m8 tsqdf3 7w2+di+fjwss vs: ateral 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;5;nugdspd0 luv9dlpoxl 3 5atn)f50 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