Does Huygens’ principle apply to sound waves? To water waves? Ex;d saz;n br;h,j manq;j 129ntplain.

What is the evidence that l. v kz4svpw.1tight is energy?

Why is light sometimes d*jyd lq b2q7ps/nw+pf4dh z1.escribed as rays and sometimes as waves?

We can hear sounds around corners, but we cannot see arounrusf4v vt v:5;.vc gr4hsq) )bd corners; yet both sound and light are waves. Explain the differenrv4brg )t4. c;f) su:v5qvsvhce.

If Young’s double-slit experiment were submerged in watezfw 3x68p pg.tr, how would the fringe pattern gf3p8w .t6zxpbe changed?

Monochromatic red light is incident on a double slit, and the int0 9plebp7 et8x wz07oxerference pattern is viewed on a screen some distance away. Explain how the fringe pattern would change if the red lighexz070 b l9t7ox8wpp et source is replaced by a blue light source.

Two rays of light from the same source destructivelhtj bj:3du r-,q9o,py/*ebg8-c q6:lmfad iq y interfere if their path lengths differ by h8y irpgq-9:-fb,:cdht l* qaj ,q bmdou/3ej6ow much?

Why was the observation of the doubl4k /nrysxb7 z*e-slit interference pattern more convincing evidence for the wave theoxb7y/z r*nk4 sry of light than the observation of diffraction?

Compare a double-slit experiment for sound wavjfb( )xxg4 ev/es to that for light waves. Discuss the similarities an (exb)fjv /xg4d differences.

Why doesn’t the light from the two headlights of a distant car produce aa6r15hyag2 c qn interference patteh1 qr2gacy a56rn?

Suppose white light falls on the two slits of Fig. 24–7, but one sf1; frtf2r l9flit is covered by a red filter (700 nm) and the other by a blue filterf1f;9f f2ltrr (450 nm). Describe the pattern on the screen.

When white light passes through a flat piece of window glass, it is notu:bp t4p1 f.un broken down into colors as it is by a prism.tn fp.uub4p:1 Explain.

For both converging and divergidlcn; .ki 6v1hng lenses, discuss how the focal length for red light differs from that for vih. ;nvkd1 6cliolet light.

A ray of light is refracted through three different materials (Fig..icli 1:ci tt/ 24–55). Rank the materials according to their index of refractiocit:c. /it il1n, least to greatest.

Hold one hand close to your o1kcan zqp,+h5d* 3v a2mod fwwe:31ueye and focus on a distant light source through a narrow slit between two fidd3*fpoz:1,hw qa5+e1amv woc ku2 3n ngers. (Adjust your fingers to obtain the best pattern.) Describe the pattern that you see.

What happens to the dax0/p.15: jll ticnr diffraction pattern of a single slit if the whole apparatus is immersed in (a) water, (5/ j10 :apn it.rlcdlxb) a vacuum, instead of in air.

For diffraction by a single slit, what is the eff8:d2n7i52gjm ,cps 0tsrd ek;+mbbcfect of increasing (a) the slit width, and (b) the wav:mdpd g7b8b;cejt+s2f0 imksnr,5 2celength?

What is the difference in k z84r *9wpwllthe interference patterns 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) clk bc /f1ze9)tyosely spacebt9 k)/yfz1ec d slits?

White light strikes (a) a diffraction grating, and (b) a prismvf4br2a4jjuz -i5 l6 j. A rainbow appears on a wall just below the direction of - 4vjlui24 j6afb jr5zthe 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 nus/kl.0md-*m 2z d t*b9n mmttm, incident normally on a diffraction grating, for what orders (if any) would there be overlap in the observed spectrum? Does your an/.u-td*m ztst bnd l* 209mmkmswer depend on the slit spacing?

Why are interference fringes noticeable only forn:,- w ndxj-:mx3 lkhlk-(x ga a thin film like a soap bubble and not for a thick piece of glass, sayk-xl :ng,jxxn-m3 lw-h(a k:d?

When a compact disk (CD) is held at an andkocsk)2nsl yep ;4 b *,fc:e3gle in white light, the reflected light is a full spectrum (Fig. 24–56). Explain. What would you expect to see if monochromatic ligb dy) ec3eo4kf:c slskp,2*n ;ht was used?

Why are Newton’s rings (Fn931ahb)a vp hig. 24–31) closer together farther from the center?

Some coated lenses appearmq*cko5u c :v2+y p/s jos;i(j greenish yellow when seen by reflected light. What wavelengths do you suppose the coating is designed to transmit p/5c:+j;ouvikc osyj q2 *ms(completely?

A drop of oil on a pond appears bright at its edges, where its thickf-cqvd7xu zy4u 7nl-2 u( s6agness is much less than the wavelengths of visible light. What can you say about the indxa(2dy7n6l gsfuuvz7 q- u4-cex of refraction of the oil?

What does polarization tell us about the ne -(tkix0 u)fj.v;2uf8k vfd;lhkud;ature of light?

Explain the advantage of polarized sunglasses over normal t-l nch w /s..i51vwnaf0c0le o 8ylsm5inted sunglasses.

How can you tell if a paiz.-i a 2-*zjwces*le er of sunglasses is polarizing or not?

Two polarized sheets rotated at an angle ofu1* g*szqo8u6 ak ae2n 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 w:ux( qcd6/vpr qo+7i. q4nzw the sky if the Earth had no atmosphere?

If the Earth’s atmosphere i1cl6 -nv 0wbjwere 50 times denser than it is, would sunlight still be white, or would it b0ni-jv6 l wcb1e some other color?

  Monochromatic light falling on two slits 0.016 mm apart rmue:/ *zm,rq ;uydz5 t +j;kuproduces the fifth-order ujmurz;r+yq/,:5*m kuetz d;fringe 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 observed ac0mciutvp79j:z q+(x3, arzet 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 0.048 mm vbb ), zsju87gapart. Successive fringes on a screenj)g7,8vzbsu b 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-Nenkb. hnp z61i.(:jlwp laser, with a wavelength 656 nm, falls on two very narrow slits 0.0606 (.:.pznljpinh kb 1w mm apart. How far apart are the fringes in the center of the pattern on a screen 3.6 m away?    cm

  Light of wavelength 680 nm falls on two slits and produces an inter4bga9v-fczhq jxx252(f li g7yn;z :ry (9jvbference pattern in which the fourth-order fringe is 38 mm from the central fringe on a screen 2.0 m away. What is the se 4hzx5x2an-gv9b jiyy (qjb7r;v ( zlcf:gf29paration of the two slits?    mm

  If 720-nm and 660-nm light passes through two slits 0.58 mm 05h-vr/ kwb uwapart, how far apart areh5w/b-uwrk v0 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 44w dit.mhipve*uxqf8o7t .- blue light of wavelength 460 nm gives a second-order maximum at a certax vih.u 4 m *p8t4diwqtef-o7.in 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 thro 34-rsr:3yyhdiid 8vuugh 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” dir ry:4viys-h83d3 u idrection would there be little or no wave action?

Suppose a thin piece of glass is placed in front of th7+7 .i5mxnzbk ) psvwfe lower slit in Fig. 24–7 so tha x7f sv)ip.+zmn5wk 7bt 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 wavelength 50 eucsf*go) d3j12m9i i0 nm is located 12 mm from the central bright spot 193uim)ocf igjde*2s 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 separated by 1.0 mm are illuminated by 544 2w:rsp ny e6t5nm light. Find the distance between adjacent bright fringes on a scree5t: 2ype6n srwn 5.0 m from the slits.    mm

  Light of wavelength 480 nm in air falls on two slitsh1iro l i( (qtu7fkt;h25 lv6 p3isft/ $6.00 \times10^{-2 }\;mm$ 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 appar5m8z/ lbiz:wy (4bgpvatus illuminated by 640-nm light. The center point on the screen, instead of being a maximum, is dark. mg(y 8b p:iblz/w 5z4vWhat is the (minimum) thickness of the plastic?    nm

  By what percent, approxi*+pw k9ak6ue6wf i 1smmately, does the speed of red light (700 nm) exceed that of violet light (400 nm) in silicate flint glass? (See Fig. 24–14.6p16+ *9ska ewumik fw)    %

  A light beam strikes a piece of glass at a 6ugtc7(td wi2(vxn qf/ .j5x t-0.00$^{\circ}\,$ 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 conn t* d6,j;o:*fia tt,/bdsrqet(9 o gmtaining 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 f :kuyd/lne:k (ga b:u8ull angular width of the central diffraction peau :n gk:kdbe:l8(ay/u k?    $^{\circ}\,$

  Monochromatic light falls on a slit tha(ewgy43oijn :t 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 is -f4sk gj0mde3$ 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. Wha ir 9try:d6i3gdu5joax3i)* nt is the width of the central maximum (in cm) in the diffraction pattern on a screen 5.0 m away?rjnt3 5orax39 gidui:y6d) *i    cm

  Monochromatic light of wavelength 653 nm falls on a slit. If the j*eg*) / k yb-,vtzx5adsy9d langle between the first bright fringesdl/z g-j9b ,)d*a 5tsvxy* yke on either side of the central maximum is 32$^{\circ}\,$, estimate the slit width.    $\mu m$

  How wide is the central diffraction pe;0nzsu v*k/ dd; ;rug d:pdg1gak on a screen 2.30 m behind a 0.0348-mm-wide slit illuminated by 589-n u;g*n/01rszdp u;:d ggd; kdvm light?    cm

  When blue light of wavelength 440 nm falls on a single i6g6:xlmli2. om (zv w7ot.grslit, the first dark bands on either sideotlzmm2o6 i6:(l .vggw.ixr7 of center are separated by 55.0$^{\circ}\,$. Determine the width of the slit.    $ \times10^{-7 }\;m$

  When violet light of wavelength 415 nm falls on a single slit, it createsm n-hs(* byut2ap(0f x a central diffraction peak that x u (hna(02 ymb-fp*stis 9.20 cm wide on a screen that is 2.55 m away. How wide is the slit?    mm

  If a slit diffracts 650-nm light so that the diffraction ma1 ;t0mbtmgg 4kximum is 4.0 cm wide on a screen 1.50 m t gtb;1mm04 gkaway, what will be the width of the diffraction maximum for light of wavelength 420 nm?    cm

For a given wavelengthjum /iovt1 uj;i2;x(k $\lambda$, 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 whenu9rmw+sm tycg *;rn 5 laz.0s7 falling on a gratw0y.cla5ur+7g; *s9 rztmmsn ing 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 gratin cfj swlg-1t 5hs)x9,mg have if the third-order occurs at an 18.01jf wx5)tsg -lhs9m c,$^{\circ}\,$ 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(ah 2ov0(4 l opge,oojion grating is observed at a 15oj(a h0oog v(4plo2,e.5$^{\circ}\,$ angle. How far apart are the slits?    $\mu m$
At what angle will the third order be observed?

  A diffraction grating haxl;t c2hcz7/m1xf w 7vs $ 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 normalg-eap+9q c z xou.b-m86i bh5gly 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 l bqn3qxn 2j4,/ty4 kdteb (c4bat5 m02oho :jwith 6000 lines per cm is illuminated with 634tq bk, 4bt02t5o:l/x2 (hjyq n d43amcobejn3-nm laser light? Assume normal incidence.   

  Two (and only two) full36nbkmkl+4.j(x uwpi spectral orders can be seen on either side of the central maximum when white light is sent through a diffraction grating. What is the +k w.ulmxp4(i6kb j3n maximum number of lines per cm for the grating?    $ \times10^{ 3}\;lines/cm$

  White light containing waveleng-z xy ifohlb;.w zp3u ) 2rcr1dbbpm(30: kx9gths from 410 nm to 750 nm falls on a grating withrb 1pkldbi y g ()xc90zf23;rwp z3o-:muhxb. $8500\;lines/cm$ How wide is the first-order spectrum on a screen 2.30 m away?    m

  A He-Ne gas laser which produces.z246v6nurf q q 2qtfc monochromatic light 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 specty69vb)g 77q-t ; vkotx1lcudsrum 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 most strongly reflectbi4s6bu(8vm b ed at the center of the outer surface when illuminated normally by whit 4bism8bvb(6 ue light? Assume that $n\;=\;1.34$. $\lambda$ =    nm ,which is an    -  

  How far apart are the dark fringes in Example 24–8 if tss0 gq)m-1un xhe glass plates are each 26.5 cm s sxg1q)0 num-long?    cm

  What is the smallest thicknesr wu8d/vjlybc 9z,wt25 x45fw s 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 yelloiuh6,bn7s ds3w ($\lambda\;=\;570\;mm$ 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 3hd+8g0b 2 gg:i2nfje*omk5 cu1 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 glass surface (Fig. 24–31). How much thicker is the center than the edgei8g2*bh0+ nof:5decgj 2ugkm s?    $\mu m$

  A fine metal foil separates one end of two pieces of optical0w1 su19 n+qo8 7e0bzxv lxvwzly flat glass, as in Fig. 24–33. When light of wavelength 670 nm is incident normally, 28 dark lines are observqws1 z n9oze01uv 8x0vwxb+l7ed (with one at each end). How thick is the foil?    $\mu m$

  How thick (minimum) should the air layer *y ,qr qpg-err 3e-hx:be between two flat glass surfaces if the glass is to appear bright when 450-nm lier-* g- p:qxrh,e3 yqrght is incident normally?    nm
What if the glass is to appear dark?    nm

  vA piece of material, suspected of being a stolen dmlc 4 tj bn6ps)i6q99qiamond $(n=2.42)$ 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 alcohox s506s2j7qx4; q:ebw8:f g ykuntns wl $(n=1.36)$ 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 voxix +(xs ,zc)3wu9n(Fig. 24–31) is immersed in a liquid, the diameter of the eighth dz(u c,xo39v)+x xnsi wark 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 c5avq((:c) vyvz3 fpjx gbi78if 644 bright fringes are counted when the movable miry:p g((i bj8aq37zvf5cxv) vcror moves 0.225 mm?    nm

  A micrometer is connected to twr ;sxd3fy-)f+xsh g:he movable mirror of an interferometer. When the micrometer is tightened down on a thin metal foil, the net number of bright fringes that move, compared to the empty microg:s)yff -x ;d3x+wrs hmeter, is 272. What is the thickness of the foil? The wavelength of light used is 589 nm.    $\mu m$

  How far must the mirrfv aub.cf,)8 vor $M_1$ 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) pab290lpn dd +dj 3ypga5sses through a small glass container containing a cavity 1.30 cm deep. When a gas is allowed to slowly ygp3alndd0p5 29 b +jdfill 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 w4m-fy 8iwqgcj0 a+f3 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 ggt/p5u- uy; ,im scz3j 4vl)iair–glass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s angle for a diamond submerg vnbv)v/ e.a9ked in water if the light is hittinga en)v9/v kbv. the diamond $(n=2.42)$ while traveling in the water? $\theta_{p}$    $^{\circ}\,$

  Two Polaroids are aligned so that the light passing through them is a maximumm)j*tnixjg)8u no (/9dynjust 8u3 7d. At what angle should one of them be placed so thamyuju )go sij8td nu93t xd7/n (8j*n)t the intensity is subsequently reduced by half?    $^{\circ}\,$

  At what angle should the axes of two Polaroids x+w4 v(sewlp4ow,8c jbe placed so as to reduce the intensity of the incident unpolarelp,+w(j wwsco 44v8xized light to
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are o0azjr a2)m.n ,jipq*r riented 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 ataz)4ija.m/2 e p7pjtn 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 forb0jz:y mno9 1y reflections off the surface of water for light coming from beneath the surface? Compare to the angle for total internal reflectzo1 yj:m9y b0nion, 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 s8arak +bts(88mdv:e9woct, cuccessive Polaroid sheets, each of whose axis, 98ma:ct(ecd baokw8 +8 srvt makes a 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength lwm0 hy 3:b;oe$ 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 inteeoklyeqogt19 (pry c/e-0 ,:t6 eh)zdrfere with the:elyz0(toe16he c kqd-p9rgeoyt) ,/ 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 passes through a diffract bipra m.k :9c75p+awyion grating with pybw7m5akir.p+ac9 :$ 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 m+k2e, i1rh(jgbf6h ft1ei)j nm 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 than the 590-nm light. What is the wavelength of rt,efk e hm2hij)j 1i(bg61f+ the unknown light? $\lambda_2$    nm

A radio station operating at 102.1 MHz broadcasts from o pmtdq32 *x/etwo 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*dxp2t q3e/mo 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 0.88c++ z,t mj :s,i+j ux/vdk9bkq m wide, and blows a whistle of frequency 750 Hz. Ignoring reflections, estimate at what angle(s) it is not vkb +itjsdk z9,q+m,jxc/ u:+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 width D at a z)i 4f p-,tqewbvrk1 0q waxx1*0q1zt 30$^{\circ}\,$ angle to the normal, describe the diffraction pattern.

  The wings of a certain beetle have a se+;olrwpcgq+*l5ri l ,b9 (fud ries of parallel lines across them. When normally incident 460-nm light is reflected from the wing, the wing appearri 5lguwdq+; lc(rpb 9o*l+f, s bright when viewed at an angle of 51$^{\circ}\,$. How far apart are the lines?    nm

  How many lines per centimk5 d./pt- m jd/;unhxheter must a grating have if there is to be no second-order spectrum for any visible wavelength? d-hju xh/nk;pd.5m/ t  $ lines/cm$

Show that the second- and third-gmz6d0t 4xc; 8t q-ezxorder spectra of white light produced by a diffraction grating always overlap. What wavel q4gt-xtdc;m60xz e z8engths overlap exactly?

  When yellow sodium ligh ojnvx; sz*o* )x29jact, $\lambda\;=\;$ 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 pz okx 88tob4 5neeg aj9tyi2upg+r.mfv 6j/9; attern is viewed on a screen 2.5 m from the gratinrxzfjo/e9 k 4m8v ;g5e2b9pg.nj8i ut t +yao6g. 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 clearstzf t+ :e jm1p/u40tt material if a minimum of 150 nm thickness of it, when laid on glass, is needed to reduce reflection t/:j tpts1 e f+zt0utm4o nearly zero when light of 600 nm is incident normally upon it? Do you have a choice for an answer?

  Monochromatic light of variable wavelengtyka kx3zi0c+k 10 be /5otqg6uh is incident normally on a thin sheet of plastic film in air. The reflected0uc3keibzkk 0ay g t6o5 +1qx/ 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 annohb a6s,c (qc+:h (v6hw2a*qbtr8dbti-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 betweenndz:itm00f rw1e8.wm0pk2 n2j8ljf a two flat glass surfaces if the glass is to appear dark when 640-nm light is incident normally? tir1f82wm npl.d aj0 8e:njm20z w0fk   nm
What if the glass is to appear bright?    nm

Suppose you viewed thpo v-h qe)r85ye 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 describe the conditions requir5 e)v-r8 qoyhped 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 isc( n mk7x+,rjht9:bap the Sun when light reflecting off a smooth lakec7+mta9(bhpnkj,x : r is polarized most strongly?    $^{\circ}\,$

  At what angle should th.gt1f7f ;n7gii 0wqbve axes of two Polaroids be placed so as to reduce the intensity i t0iv7 . nq;g1gwf7fbof 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 transmi d lugj5us2,5up kg;h.* 8jigession axes are at right angles. A third pola,ugj g js;d gle5k285puu.h *irizer 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 axey5 tlcce+2xu+/m lv3q s 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 ap1s ikoep+, /yng he()tq*u*m slit of width 1.0 cm and is pointed at the Moon, which is apyn sgtu1(ph, q**)eio+pk me /proximately 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 Moon.    km

  A series of polarizers are each8gy ta.2 7oz/ j5d4nr)5vtbp /jzyx4wqy. j ok 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 0am/oxd j b/tm36:hr hy 5wssx,/o,nl$(n=1.34)$ 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 each othe i(za;fc/d1 9v3 o8ev5wi eohly48vmdr. They are located adimvoeoavy3e(f/89 d w5418v chi l;zt 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 contaa/6s +lm+oj ko 7i7ljow daa(,ining two wavelengths, 420 nm and 650 nm, enters a silicate flino(a loow++6ikm d,lj77 ajas/t 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 :xxhwx u) zr35;n1 byrsurface 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