Does Huygens’ principle apply to sound l6tsa,rp : g80zwi5abmosytw8 1)oa6waves? To water waves? Explain.

What is the evidence that light is enerlxtz- 0 txwd+/gy?

Why is light sometimes described as rays and sometimes as waveg7n(omtc06z/c5o e lep ijtq/*a.0yy s?

We can hear sounds around corners, but we cannot see around corn 69/ovn7hol5 vr7afyfers; yet both sound and light ar75/n lovvo6ah9fy f7 re waves. Explain the difference.

If Young’s double-slit experiment were submerged in water, + 9;exg2ujx *p etoc.phow would the fringe pattern be changed?*tgo.;c 9j xpeu2 e+xp

Monochromatic red light is incident on a doub/ :*mcu:e/sxnv *;) 9vtenas bxfp5 yrle slit, and the interference pattern is viewed on a screen some distance away. Explain h9*)p e/te vfsvxa:;cxbu*n /nm5y:rsow 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 interfereka,1hvvu z8dp *w+dea9v6(+utwh6 ocj/r- kl if their path lengths d +uvakh kjv ww1pev+,hd-c6o(z*l d6 u /89artiffer by how much?

Why was the observation of the double-slit interference pattern more cop3n19 m5s pydpbw4h 6bnvincing evidence for the wave theory of light than the ob5bp1hy s9dmp6pn 43wbservation of diffraction?

Compare a double-slit experiment for sound waves to that for light w,ym8e tko/ oc+h5i,wmaves. Discuss the similarities and die/ m5hwtk,m 8y,oco+i fferences.

Why doesn’t the light from the two headlights od7 hpu-k 72w jzbs1etn4,au4a f a distant car produce an interferjtus7bhp zedk-na wu41 ,74 2aence pattern?

Suppose white light falls on the two slits of Fig. 24–7, but one slit is covep 5dgkp:lg( xwojs 6(3red by a red filter (700 nm) and the other by a blue filter (450 nm). Describe the pattern on the scred(g6(g3p5o:wxkpjls en.

When white light passes through a flat piece of window glass, it is not broken g88 .owxml-lw ;c ea)odwl8mw)8-c ag .loxoe; own into colors as it is by a prism. Explain.

For both converging and diverging lenses, discuss how thrkz1c-l oj- +pe focal length for red light differs from that for vio clo-+zkj-1rp let light.

A ray of light is refracted thka /r8 n(cpyn4rough three different materials (Fig. 24–55). Rank the materials accordycn(n8/4r pka ing to their index of refraction, least to greatest.

Hold one hand close to your eye and focus on a distant ligf81ar yv0 cqx6 8vo-4 wnsng8nht source through a narrow s wao18-q8 8yrnxc f g6ns4vn0vlit 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 the whole ap 97p1ykddbjyti(q,b3 paratus is immersed in (a) water, (b) a vacuum, ins iq y91py ,kdbjd7b(t3tead of in air.

For diffraction by a single slit, what is the effect of it2l9fs ytdc:w rf)i-7ncreasing (a) the slit width, and (b) the wavelengtlt-idfyc )tfs r:29 w7h?

What is the difference in the interference patterns formed (vg- jsyq.( ku6a) by two slits $^{-4}\;cm^2$ apart, (b) by a diffraction grating containing $10^4lines/cm$?

For a diffraction grating, what is the advantageor(c+-gbn4gjk al-ytf , (// c hyp(; izg.bkv of (a) many slits, (b) closely spaceg+r - z/pjc(,vib.fkcty nbhk;ga-(ly(/ g 4od slits?

White light strikes (a) a diffraction grapnd 1/ -a+xvbgting, 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 gbvdx/np + a1-the rainbow in each case? Explain.

For light consisting of wavelengths between 400 nm and 700 nm, incid)ic9g 1lfkq3 fs -e3xiz 1s0snent normally on a diffraction grating, for what or91nqek- ffl) zx i1 c03ssgs3iders (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 tg29n: 2-tdenps t+swpwf*c d8+ pce n3hin film like a soap bubble and not for a thick piece on nptdp+c wst 8+29* :pfwesg3e nd2c-f glass, say?

When a compact disk (CD) is held at an g pp(:tf ;unhilrnz69607 w:6owndiu angle in white light, the reflected light is a full spectrum (Fig. 24–56). Explain.uh;n unz(6 wgr9 :iwof 0:tn 7l6dpp6i What would you expect to see if monochromatic light was used?

Why are Newton’s rings (Fig. 24–31) closer together farh ;y.(m l6msjbther from the center?

Some coated lenses appear greenish yd:2eiv(r (vx17hp pxt7pw;iehw nh1u( ;p/cyellow when seen by reflected light. What wavelengths do you suppose the coating is designed 1id:2hpuwh ;7 x e7c((pytwxhipr( n/vpv1 ;e to transmit completely?

A drop of oil on a pond appears bright at t8d9z-r:(b u0 mcm0:ghil zvtits edges, where its thickness is much less than the wavez cb0tmu m9:tvdl zi8-:0h rg(lengths of visible light. What can you say about the index of refraction of the oil?

What does polarization tell usxfeut8n0x +ccwd))5i about the nature of light?

Explain the advantagec0ahh /am1 uo ;yn.-sa of polarized sunglasses over normal tinted sunglasses.

How can you tell if a pair of sunglasses is polarizing or n79zc4 c fts* a*fb3txlot?

Two polarized sheets rot*r9fgb86wj p rated 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 9.r cgu7;l 7ktzrotkqbu1uj1rt33 5n of the sky if the Earth had no atmosphere?

If the Earth’s atmosphere were 50 times denser than it is, would :)g)6lx2kw:b)nk 7v2gfntpo kqs4 sdsunlight still be white, or would it be ) )dxo qs gn4pgbfs:kk ):ln v2726tkwsome other color?

  Monochromatic light fallin1durl8 hwkj /+jb5if( wdzsqu: b-8u ;g on two slits 0.016 mm apart produces the fifth-order fringe at an 8. kbww5 +rzb-ufl du:q/s;dh1( 88jiu j8$^{\circ}\,$ angle. What is the wavelength of the light used?    $ \times10^{-7 }\;m$

  The third-order fringe of 610 nm light is okl0;mfm g v(7t+ujp8b bserved 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 onts9 zt2pp 6li1.yhxs4 two very narrow slits 0.048 mm apart. Successive fringes on a screen 5.00 m away are 6.5 cm apart near the center2si.1txs6 hp t zl4py9 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, wvyv2(xi: hl fnncg 9(l-1bct9f6 d5cb ith a wavelength 656 nm, falls on two very narrow slits 0.060 mm apart. How far apart are t cif n(tcl 5fvvcgnb :1yx9d2b9l6 h(-he fringes in the center of the pattern on a screen 3.6 m away?    cm

  Light of wavelength 68+38tlt zlvnsa)x ( wf00 nm falls on two slits and produces an interference pattern in which the fourth-order fringe is 38 mm from the central fringe on a screen 2.0 m away. What is the sepanzs v)(alx8 3+ft0wtlration of the two slits?    mm

  If 720-nm and 660-nm light passes through two slits 0.58g) 61.ub ffbmc mm apart, how far apart are the second-order fringes for these two wavelengths on a .ufmcbg6b1f) screen 1.0 m away?    mm

  In a double-slit experiment, it is found that blue light of waveltif,z:ca+f)r ength 460 nm gives a second-order maximum at a certain location on the screen. What wavelength of visible light wourt)z:,af c if+ld have a minimum at the same location?    nm

Water waves having parallel crests 2.5 cm apart pa3o:6bchy )pwm : cuav1ss 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 twu b:1) ahv3c:po6cymhere be little or no wave action?

Suppose a thin piece of glass is placed in front of thei1ckf4zn6j ,p )k0ggo lower slit in Fig. 24–7 so that the two wa0g no6 ) zgfij,k1kc4pves 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 wavelengthfnzrq2(c :/0fp( ko5d +p uxc5jzj(io 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-or(quj i5 k/jz (fn fxr52 +cc0zpdo:p(oder maximum of this light be located?    mm

  Two narrow slits separated by 1.0 mm are*kim i)z8w6 xa 4lz*ae illuminated by 544 nm light. Find the distance between adjacent z al*zii)a6mx*8kew4 bright fringes on a screen 5.0 m from the slits.    mm

  Light of wavelength 480 nm in air falls on two ;x)zapg40 m/k5npdox pp t(y)nal6w) 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 w.umx65xr lb*one slit of a double-slit apparatus illuminated by 640-nm light. The center point on the screen, instead of being axrxlwm * bu56. maximum, is dark. What is the (minimum) thickness of the plastic?    nm

  By what percent, approximately, does the speed of red light (700 nm) exceed s/,c pme-r q6pkwb1y+that of violet light (400 nm) in silicate flint glass? (kmep 6/qr,cy-+p sw1bSee Fig. 24–14.)    %

  A light beam strikes a piece of 1(qdv(g,wxvtobly8 lw29w s :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 containipd0i mqbi5,0u ng 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 fu6l j*br+caw35yx6f s vll angular width of the central diffraction peakyvxbslja 65 6cwr 3*f+?    $^{\circ}\,$

  Monochromatic light falls on a sl:itqoop3cq ,u v0r2:git 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 f+ilidsc /l7)c alls 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 b::y9 d i 9iacbwch1pu3y 450-nm light. What is the width of the central maximum (in cm) in the diffraction pattern on ap9h:3 adc 9uc yiw:b1i screen 5.0 m away?    cm

  Monochromatic light of wavelength 653 nm falls on a slit. If the angle brg/,bf3n,d)lbf -ica-oha 7j etween the first bright fringeslnj,-h ,oafgcabd-b7)/fi 3 r 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 2.30 m behind a 0.0348-mm n hh3ysk1wc (i;gsz+5-wide slit illumn(y53h;z+s1hgks iwc inated by 589-nm light?    cm

  When blue light of wavelength 440 nm falls on a single slit, the fiotio)i- 1yk2 )bmuyw+rst dark bands on either side )bio-1wyuk) i2t+m o yof 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, zr -6py q+)+okmvyo .ncdgw( *it creates a central diffraction peak that is 9.20 cm wide on a screen that is 2.55 m away. How wide is the slip)g oz+w.ro6+cq v *myd(n-kyt?    mm

  If a slit diffracts 650-nm light so that the diffractiyq*m4eo iowj 8( p1q+jon maximum is 4.0 cm wide on a scwqji 41ej*(q+8mopo yreen 1.50 m away, what will be the width of the diffraction maximum for light of wavelength 420 nm?    cm

For a given wavelengtu2 jy z276ehgyp,em:9 lrg jd4h $\lambda$, what is the maximum slit width for which there will be no diffraction minima?

  At what angle will 560 ,/shei7dlbcfgt:3y9 -nm light produce a second-order maximum when falling on a graf t97c: dyg/s,3i hbleting 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 t+m0 6cktkfr myrc*1zbjk 7m99he third-order occurs at an 1ymr* f 0b169z k+7cmtkkj9 crm8.0$^{\circ}\,$ angle for 630-nm light?    $ \times10^{3 }\,lines/cm$

  A grating has $8300\;lines/cm$. How many complete spectral orders can be seen (400 nm to 700 nm) when it is illuminated by white light?   

  The first-order line of 589-nm light falling on a diffract,0 2bo k7dgn)nncib ;tion grating is observed an2ktng,7b;c0i nd )obt a 15.5$^{\circ}\,$ angle. How far apart are the slits?    $\mu m$
At what angle will the third order be observed?

  A diffraction gratinw-grumz oe ;rti z ty39(xd;-+g 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 y42ctvdm*pb4 on 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 56bmweadf 5ij/ga- u;with 6000 lines per cm is illuminated with 633-nm laser ligh-5ia/ ewmd5;6b fu jagt? Assume normal incidence.   

  Two (and only two) full s zkcg-5 ltbm45 zii68wpectral orders can be seen on either side of the central maximum when white light is sent through a diffraction grating. What is the maximum number of lines pertc65 bl8 g i4kw-z5imz cm for the grating?    $ \times10^{ 3}\;lines/cm$

  White light containing wav3m( hnzk4u0h delengths from 410 nm to 750 nm falls on a grating withhk43h md (z0nu $8500\;lines/cm$ 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 agm*a; d8qg 9l;ee/pwa 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 measured bv-4ac8ekn0 8wzno; v uy 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 strongly reflectc5pxy8z0 ey 9s7pp j+ded at the center of the outd7 y+ 0ep sxp59yzp8cjer 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 pla p cnrcv )//peyzs;, +kz43sxgtes are each 26.5 cm e ,yx; /+szcnp v4/)scpz krg3long?    cm

  What is the smallest thickness of a so vbd 6 5ok ra8bk5yfp26d+ro7a cci6v5ap 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 greeni*k-06xua d ynish 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 7( zdea0s y1z7by1vlsand 31 dark Newton’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 glayydzvas sbz1717e0 l( ss surface (Fig. 24–31). How much thicker is the center than the edges?    $\mu m$

  A fine metal foil separat -(pnewvqd/)6jt4 eo ues 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 lines are observed (with one at each end). o twvj-nud(qepe6 /)4 How thick is the foil?    $\mu m$

  How thick (minimum) should the air layer be 2hq(ebg u xr.x x5nq l01p+b6nbetween two flat glass surfaces if the glass is to appear bright when 450-nm light is incidex1bne62ubx(qnx p . g0hl q+r5nt normally?    nm
What if the glass is to appear dark?    nm

  vA piece of material, suspected vexlr0iax uj4eb *k,f+ o 81b2of 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 ox t8ho x2br4tog0texs/-;b 7ol $(n=1.36)$ 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 ic zhxlmi6g ri w2:).-,nm:xtzn a liquid, the diameter of the eig icmhzgir.x62)-:zm wn, t: lxhth 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 interpf /k8-0 css31rejg enferometer if 644 bright fringes a1/jr-80pfss3 gkcnee re counted when the movable mirror moves 0.225 mm?    nm

  A micrometer is connected to the movable mirror of an intmnd+2rds-3o se*e lu 8erferometer. 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 thickness of the foil? The wavelength of light used is 589 nn8* 3+rl-2omed d ussem.    $\mu m$

  How far must the mirjko;,b k-m:e-cg9 ktzror $M_1$ 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) passes9o8 uw )9(hsa.x bk2h-wzz pac through a small glass contawku 9 chh)sx p(z.a-z9o w2b8ainer 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 oriented at uqs1v- x a;e+h6 *vwba65$^{\circ}\,$ to one another. Unpolarized light falls on them. What fraction of the light intensity is transmitted?   

  What is Brewster’s angle for ;3ee zri2me7oa* ;ygfan air–glass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s angle for a diamond submerged in water if the light is n-k/,qe zh; kyhitting the diamond;k,e -hq znk/y $(n=2.42)$ while traveling in the water? $\theta_{p}$    $^{\circ}\,$

  Two Polaroids are aligned so 42(hz txhi6dtthat the light passing through them is a maximum. At what angle should one of them d4h i(t6x2 tzhbe placed so that the intensity is subsequently reduced by half?    $^{\circ}\,$

  At what angle should 556pvmuacyt 0 the axes of two Polaroids be placed so as to reduce the intensity of the incy6ma 5pcv0ut5ident unpolarized light to
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are orientedu osh8y,6ev/al j n 3a+gas7z+ 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 orien +hx:6teauabq* w2iu 4ted 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 water for 2 6iq4kuyj k*xlight coming from k4k iqxj62u y*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 passes through five successive Po la 712tzr; kco nc59xgjl(uh:laroid sheets, each of whose h7l;u t(n2kgjoc la:rcz1 9x5 axis makes a 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength coqcu5qa h8:pwz 7(tq6y)ul. $ 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 n*s(kyp,fxx :uj5 gl, can interfere with the direct signal from the station(kx p,*s f njlgux,5y:.
(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 dyyj vhgfo, k *1js ie x/ph6*1agh-r;,iffraction grating with yv6 jxi-hagj hseh ;*o/rg* f,,1 kyp1$ 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 narp+. v8 ri8,eoiihvm/srow 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 than the 590-nm light. What is the wavelength of the unknown light? .oi+8i8h/vrpi,sem v $\lambda_2$    nm

A radio station operati( xyt9h.ab3wg rao 3a+ng at 102.1 MHz broadcasts from two identical antennae at the same elevation but separated by3+ayw9a. (gta3o hxrb 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 doorway 0.88 m wide, and blows ji13+ ah xftt*a whistle of frequency 750 Hz. Ignoring reflections, estimate at w*1it xf3at jh+hat 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 slit of widt4+9v,a r7jt+.iduol-bg x es hh D at a 30$^{\circ}\,$ angle to the normal, describe the diffraction pattern.

  The wings of a certain beetle have a series o8xj9 a 5mscy0+pvv.urf parallel lines across them. When normally incident 460-nm light is reflected from the wing, the wing appears bright u5+0pcymvx8 .9ra j svwhen 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 seconiua-opu7y5o 5v); heraz ,;kya i3r.xd-order spectrum for any vir.io-5 ;yrkop7 v i5u)3,hua ayzea;xsible wavelength?   $ lines/cm$

Show that the second- and third-order spectra of white *dsm)e. po93 on;zgoflight produced by a diffraction grating always overla3g o*;o 9zd nmofs)ep.p. What wavelengths overlap exactly?

  When yellow sodium le 50m/7 (fgdq 0l 8ibsg t01ogokpwga)ight, $\lambda\;=\;$ 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 a6q7or lv7l4o pnd the pattern is viewed on a screen 2.5 m from the grating. The incident light belq 7o67 lop4vram 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 refractiq x/ qpt506d*xmzn .2wt,tbih *9ansk on of a clear material if a minimum 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 choice for an am6qzxn*d0 an*hk.p9w, xt sqb25ti t/ nswer?

  Monochromatic light of variable wavelen:q+ +;tncrer kgth is incident normally on a thin sheet of plastic film in air. The reflected light is a minimum only for +nqc+;ktr e:r$\lambda\;=\;512nm$ 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-reflgb4n2:,m;qc c g)mfj 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-zero) thickness for the aiwnr 6y0m5i/w yr layer between two flat glass surfaces if tyw50rnwim/ 6y he 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 lqx; ,i ss kelki9-w-nbo+j;tr -e1 e/jight transmitted through a thin film layered on a flat piece of glass. Draw a diagram, similar to Fig. 24–30 or 24–36, and describe the conditions required for maxima and minima. Consider all possible values of index of refraction. Discuss the relative size of the minima compared to th toj 1s-e- k+;jxlseinbqi kr9-e;/,we maxima and to zero.
24-30
24-36

  At what angle above the horizoa.a bzrw c0pfdch3 3-+n is the Sun when light reflecting off a smooth lake is polarized most strongph3. carbdz3a fc+w- 0ly?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be placln2nnk um d( q :1hq4aqwndd(-;nn:u 5ed so as to reduce the intel:24 d nadumqnwn(:-khqduq ;(5n1nn nsity 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 shebs 9(stp9(ldpv2+c euets whose transmission axes are at right angles. A third9lu ed(b+v2ts p9pc(s 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 with their axes ver8n*j) pzmte67) bmdko tical, 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 a8 che1 i,o)f8algs 2:vcvo+zand is pointed at the Moon, 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 reachevl8 o,1)go eah:zvc ci8a+sf2s the Moon.    km

  A series of polarizers are each p(:bg* k,uz5as -qp43ve bnbng laced 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 /mtrqw8;:ho4 lw (c el$(n=1.34)$ coats a piece of flat glass $(n=1.52)$ .How thick is the film if it reflects 643-nm red light most strongly when illuminated normally by white light?    nm

  Consider two antennas radiating 6.0-MHz radio waves i*xachg 4tpdvu op78-ni 9f); rn phase with each other. They are located at popprd h7ci ga)4 9fv- tnux8;o*ints $S_1$ 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, 420 nm /. cuf qg//m4hmb7trqand 650 nm, enters a silicate /c 4/m qqm.tghfr7bu/flint 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 fl o6p4iy(f5 yilkr:yf8 d ,;sm2yrrjh(at surface 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