Does Huygens’ principle apply to snm75gxq6m q;ia +ae59afr( mb 7pzb(qound waves? To water waves? Explain.

What is the evidence that light isjm 3, xpx+(te*wre.( l7c8mbpk ; cbvx energy?

Why is light sometimes descria-lx dg36j* dsbed as rays and sometimes as waves?

We can hear sounds around corners, but we cannot sev;q;te,v n,68 wyqbuhs+j( hle around corners; yet both sound and light are waves. Explain the differenc6+n wus h 8;;, lhvvyj,tqeb(qe.

If Young’s double-slit experiment were submez;kde 1oj)dsx 9 yfda) uxwd:0s/in+9rged in water, how would the fringe pattern bd9s s )d9fod+;xyunx)aie kj10wdz/:e changed?

Monochromatic red light is incident on a double slit, and the intes at3./ztb9wg rference pattern is viewed on a screen some distance away. Explain how the fringe pattern would chang9/w t 3atszg.be if the red light source is replaced by a blue light source.

Two rays of light from the same source destructively ilo63h 47ok jwnnterfere if their path lengths differ 7k6olh43 jnow by how much?

Why was the observation of the double-slit interference pattern more conu3m6jhd+q s qp,lq+c- vincing evidence for th3mjq 6+,sc-p+duqlhqe wave theory of light than the observation of diffraction?

Compare a double-slit)uuy0j( i s 43yy5j yobe6m +e.xqkaa. experiment for sound waves to that for light waves. Discuss the simila6 (.jaa 5.ex ye)sum0yuykjb q+ i3y4orities and differences.

Why doesn’t the light from the two headlights of a distant car produce an interl05ohog;st s3 q eps8,fet l e5oo gq0p3hs,;s8srence pattern?

Suppose white light falls on the two slits of Fig. 24–7, but one svad.o,a lo02s/mw e3wt4 vc7vlit is covered by a rde0 ,lsotoc 4a23a7vwv/w.v med filter (700 nm) and the other by a blue filter (450 nm). Describe the pattern on the screen.

When white light passes0 ;v2uhv r5knh through a flat piece of window glass, it is not broken down into colors as it is by a h2vknv0h r5 ;uprism. Explain.

For both converging and diverqvp9) jqs ea/sys 72 dm73hvx*ging lenses, discuss how the focal length for red light diff*h7sve7 2/ jqqssv) d3mxyp9aers from that for violet light.

A ray of light is refracted through tfqs86*lr- tgd2 v janp 9jd7s;hree different materials (Fig. 24–55). Rank the materials according to their index of refraction, least to greatestt;ndg 9jla pj62vs8sr7d *qf- .

Hold one hand close to your eye and focus on a distf+d5jebmxr y;onq66dy6c .m0ant light source through a narrow slit between two fingers. (Adjust your fingers to obtain the best pattern.).eod m 6dm05c6 j+bryfyx q;6n Describe the pattern that you see.

What happens to the diffraction pattern of a single slit if the whole apparatus nj4k 6t8*gqwob; j:ivh)ac5x is nci8*g qv) ;6t4 kwoxajjb:5himmersed in (a) water, (b) a vacuum, instead of in air.

For diffraction by a single slit, what is the effect of increj13p1zc3 cbdq( czlj *asing (a) the slit width, and (b) c1jdl1 3z (zjb*cqp3cthe wavelength?

What is the difference in the interferencex 42db7fk zjb/kr(ks8 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, (sm9i kc qi0ompe7-z+ /b) closely spaced slitsm eiok0c 9zq-+i7ms/p?

White light strikes (a) a diffraction grating, and (gf8atpru gk + e+(r2n5b) 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 o+ (28 5gfptnregkrau+f the rainbow in each case? Explain.

For light consisting ofyt) 9n5b 3mfz(jdsvh* wavelengths 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 yy 3z95vj(bnsd) *mhft our answer depend on the slit spacing?

Why are interference fringes noticeable only for a thin film like a soapwc-s8y xo hid0:z; x6c bubble and not for a thick piece of glao yh0 -xc8 6:zsixc;wdss, say?

When a compact disk (CD) is held at an angle in white lighqem.3np *p8eu hkp0 r.zb+wx.qrd5i 7t, the reflected light is a full spectrum (Fig. 24–56). Explain. What would you expect to see if monochrkw*x8mnhp. .q3.b pqi 0+u 5epr erd7zomatic light was used?

Why are Newton’s rings (Fig. 24–31) closer togethe-5 c nao4r//qk, uxvq.(mwmeur farther from the center?

Some coated lenses appear greenish yelld w1ko,g+u4a+)j qjhoow when seen by reflected light. What wavelengths do you suppose the coating is designed to tran1quwg+ k,oad 4+hojj)smit completely?

A drop of oil on a pond appears brigh h2jnfn *5e/ryt at its edges, where its thickness is much less than the wavelengths of visible light. What can you say about the indeennj*/ hyf 2r5x of refraction of the oil?

What does polarization tell us about the nature of pq98b2on4.va hcaq4slight?

Explain the advantage of polarized sunglasses over normal mp: oqwf5 16jx3o n,qjtinted sunglasses.

How can you tell if a pair of sunglasp khv t,/buhf cmo y6p()7dk,1ses is polarizing or not?

Two polarized sheets rotatewchomapyf - +eiy/+.iq*a .uj9/-dufd 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 ha ctf6./wdawo-aymz7 * d no atmosphere?

If the Earth’s atmosphere were 50 timud ;5g+s 2:keqg +qsgoes denser than it is, would sunlight still be white, or would it be+gk;5:eqqgd s2og s+ u some other color?

  Monochromatic light falling on two slits 0.0);+w;j hlx dmb16 mm apart produces the fifth-order fringe+lhb);d;wm xj at an 8.8$^{\circ}\,$ angle. What is the wavelength of the light used?    $ \times10^{-7 }\;m$

  The third-order fringe of 610 nm ligh 31 b0quagy 5(epq7e; sip7jyvt 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 (l/ ;p0ico3r*vbnqgq two very narrow slits 0.048 mm apart. Successive fringes on a screen 5.00 m agl( q*rp;/ i 3bqncvo0way 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 ;s al.:ucdfokt4t lk6/ap/* z laser, with a wavelength 656 nm, falls on two very narrow slits 0.060 mm apart. How fd .s /ot*4 aa/6 llut;kpfz:kcar 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 projqw e99 v/gl8z8j9e:uokg -f+3 shqrbduces an interference pattern in which the fourth-order fringe is 38 mm from the central fringe on we+s-h jg8 oe:v/uf99jb9l r3q8qgkza 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 09i q*0bhjrgia 8 8f,6akutm5 b.58 mm apart, how far apart are the second-order fringes for these two wavel9k* 0g,raajh5mi6btbf8 qi u8engths on a screen 1.0 m away?    mm

  In a double-slit experiment, it is found that blu)5 lfbesi0; kpe light of wavelength 460 nm gives a second-order maximum a bp5fse;lk)i 0t 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 ps7l zg4m6)i/+16md*1t mydffmddaz2.5 cm apart pass through two openings 5.0 cm apart in a boards6 mz m +1zf *ydt fdp14)m/7mldag6id. At a point 2.0 m beyond the board, at what angle relative to the “straight-through” direction would there be little or no wave action?

Suppose a thin piece of glass is placed in front of the lower slit in Fig. 244p*( m6 mft)f,hbyap n–7 so 4a mf(ht pp6ym),nb*fthat 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 tx+ibjz ,ql,i- t1dnt( - ju-cphird-order maximum for light of wavelength 500 nm is located 12 mm from the central bright spot on a screen 1.6 m from the slbtic z j+t-n(q,x j-1p,u i-dlits. 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 h 2xec/b l-;ytby 1.0 mm are illuminated by 544 nm light. Find the distance between adjacent2be/ c;ytlx-h bright fringes on a screen 5.0 m from the slits.    mm

  Light of wavelength 480 nm in air falls on ykw7olh( sr)0/gn s+p9u ewr+ 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) coverr* g yiewlnz4ufx xx2d99,p++7fist/ s one slit of a double-slit apparatus illuminated by 640-nm light. The center point on the screen, instead of being a maximum, is dark. What is the (minimum) thickness of tfg9 +xei t9z*72 lrxwpdy4+s xuf/,nihe plastic?    nm

  By what percent, approximately, does the spee- .a;rozvplbc;z f 9i6d of red light (700 nm) exceed that o vz;pzf o6cl;r b-.a9if violet light (400 nm) in silicate flint glass? (See Fig. 24–14.)    %

  A light beam strikes a pilj7bia q z;v86ece 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 lic- v2lf .zyb2kvs/vd-b.xaaa1i s myw*1s4x;ght 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 tefh 7 8y9, 6k/sevrik4mxh,jat is the full angular width of the centrxmheierfy,h j 8/769 t k,s4vkal diffraction peak?    $^{\circ}\,$

  Monochromatic light falls on a ;b0l5n tt;kexa e56h/h zc jy8slit 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 nmuy z ugpis3fk7fy ));gxu;,. x falls 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 illgd;(,tg: bu q2n3+g0xe td zmvuminated by 450-nm light. What is the width of the central maximum (in cm) in the diffracti2d;utg eg(:mg , b 0xvd+3zqtnon pattern on a screen 5.0 m away?    cm

  Monochromatic light of wavelength 653 nm falls on a slit. If the angle betwe g/xi/2536vsb x) sntmlo 8lhken the h s g3l k5/nvbli)6oxm/2xs8t first bright fringes on either side of the central maximum is 32$^{\circ}\,$, estimate the slit width.    $\mu m$

  How wide is the central diffraction peak on a screen 2.30) x)5lsoda7ke m behind a 0.0348-mm-wide slit illum skd57ao) )exlinated by 589-nm light?    cm

  When blue light of wavelpj*jo(*ksk e6h s80c 8ro4un dength 440 nm falls on a single slit, the first dark bands onr*pjo8h(0*d6k j 4uknssc 8oe either 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 falls on a single slit, it creates a ce *k/kmc n5*jngntral diffraction peak that is 9.20 cm wide on a screen that is 2.55 m away. How wide is the slit** gkmnk ncj5/?    mm

  If a slit diffracts 650-nm light s;5 xr8ny jv(uno that the diffraction maximum is 4.0 cm wide on a screen 1.50 m away, what wil;8vyn5u(nr jxl be the width of the diffraction maximum for light of wavelength 420 nm?    cm

For a given wavelengm s .s;m0hdv kba-mal .9r)w(hth $\lambda$, 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 maximuhs,qf vrw q9 v j(b *61bjukh85u9g8jzm when falling on a grating whose s*85vb buj kq,g1jrhwq6h9(zuv8sj f9 lits 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 grati8w*5/kfbd9u dsd n3l wng have if the third-order occurs at an dw*/ku5l8w b9ndd 3s f18.0$^{\circ}\,$ 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 dif: 7ote )+ozob p+xq1j 8f1iczzfraction grating is observed atz z)t+7b cq1ioo+z8fox:1pej 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 has1,htu/nmwi8.gh+hd4j2+ m .v dqjd w z $ 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 onkvny-799ttw9v( ke l:qo b:we 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 ao: 1q(effs f4v grating with 6000 lines per cm is illuminatedfq(sv4 ofe1 f: with 633-nm laser light? Assume normal incidence.   

  Two (and only two) full spectral ori vxy:4ycerl /fbs d7sl9-r1: ders 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 per cm for the grating? l s l ridf94: 7vbce-y:rxs1/y   $ \times10^{ 3}\;lines/cm$

  White light containing .uqxecbx/4q5ad1 qr* wavelengths from 410 nm to 750 nm falls on a grating with *qbracdxeu qx/.5q14$8500\;lines/cm$ How wide is the first-order spectrum on a screen 2.30 m away?    m

  A He-Ne gas laser which produces monochromatic lez; p11o/nx e-z tuoi.ight 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 specpy5jihyp1 * l rt-p8v(trum 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 reflected at r4c d-cyh2v2gw-h 5opthe center of the outer surfac- c5r d4vh2cyp-2 hogwe when illuminated normally by white light? Assume that $n\;=\;1.34$. $\lambda$ =    nm ,which is an    -  

  How far apart are the dark 51swgl m v:b;0mdnvu0 fringes in Example 24–8 if the glass plates are each 26.5 cm lon;mvw0u m bg0 1d5slv:ng?    cm

  What is the smallest thickve-/ p6krtim2 .y9es lness 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 yellow wty8c 24p,ypp ($\lambda\;=\;570\;mm$ is strongest) when white light reflects from it. What minimum thickness of coating $(n=1.25)$ do you think is used on such a glass $(n=1.52)$ lens, and why? $t_{min}$    nm

  A total of 31 bright and 31 dark Newton’s rings (not counting the 2.thay1zk8eu3 s pec j -jizp)rr7.j.dark spot at the center) are observed when 550-nm light falls normally on a planoconvex lens resting on a flat glass surfacec .hejp kr3sa72 )puiejr8t jz. 1z-.y (Fig. 24–31). How much thicker is the center than the edges?    $\mu m$

  A fine metal foil separate *:g-n mc2 ui1l6+peie nfn3vhs 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). How thick is the foil? ni6fum13:c2e+ niegh- p l*vn    $\mu m$

  How thick (minimum) should the air layer be between two flat gz 1bgk,lpy:95v1fg/o e*vhml lass surfaces if th:9z/opghm b * 11y,l5 kfvgevle glass is to 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 beingr2 38nflkc 3eg qvt2.g 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 99r1hsu p j:eq;b8 gnuj -r5g,ycnnj8$(n=1.36)$ 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, theeiz 5ld; lip0ttk9w3n1io1 3ye(cte - diameter of the eighth dar913it d1 e3wp5( - teliyiknzotlec 0;k 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 brig no 2rpn m8lslrev4(;q8g,dc7uz.ae pf- 1b0vht fringes are counted when the movablec r1epfq; sv8 d ll4zbme2-.70,8oguvanrnp( mirror moves 0.225 mm?    nm

  A micrometer is connected to the movable mirror of an iny9q7un 54o jhzterferometer. 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 thicknesjn7yq9u4h5zo s of the foil? The wavelength of light used is 589 nm.    $\mu m$

  How far must the mirror12 08 xmj7bzk t7u8 zgii8ahcd $M_1$ 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 interferometj7( vo (cyo5zger (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 wavelength of 610 nm. Calculate the index of refraction of the gas, assuminy5ocv( z7ogj (g that the interferometer is in vacuum. $n_{gas}$

  

  Two polarizers are oriented at 6ov5i6u zi(h5e5$^{\circ}\,$ to one another. Unpolarized light falls on them. What fraction of the light intensity is transmitted?   

  What is Brewster’s angle for an aig+ v*nw.gq i8hr–glass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s angle for a diamond submht24tp 63s9bely;lsx q q)q)8stln+ y erged in water if the light is hittinst yythsnpll eq8 x6;3+)l)t9 s2qbq4g the diamond $(n=2.42)$ while traveling in the water? $\theta_{p}$    $^{\circ}\,$

  Two Polaroids are aligned so that the li1ap:1 uv3fjghght passing through them is a maximum. At what angle should one of them be placed so that the intensity is subsequentvgfh 1:aju31 ply reduced by half?    $^{\circ}\,$

  At what angle should the axes of tw.c ed6 .or(u4jqzcfm, o Polaroids be placed so as to reduce the intensity of the incident unpolarized lightec zcq(.6 u,f jro.dm4 to
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are orientedqsvt)48v7gh r 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 or(kt i4aqego 82iented 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 refdz4u zps241 wolections off the surface of water for light coming from beneath the surface? Compare to the angle for total internal reflection, and to Brewster’s angle frousdw44z1z 2o pm 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 Polaroid sheets, e,bkfl5vwohl +8*v; flach of whose axis make v58* llwv l;h,+offbks a 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength c0b5/t5put. tbn z7 aa$ 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 reflrm+opz7 /hobm rv /m3*kxq+/35nqwr becting from mountains or airplanes can interfere with the direc/m3bowkbz5rq7mnm*xp+h v qr+o 3//rt signal from the station.
(a) What kind of interference will occur when 75-MHz television signals arrive at a receiver directly from a distant station, and are reflected from a nearby airplane 118 m directly above the receiver? Assume $\frac{1}{2}\;\lambda$ change in phase of the signal upon reflection.  ----待选择----constructivedestructive 
(b) What kind of interference will occur if the plane is 22 m closer to the receiver?  ----待选择----constructivedestructive 

  Red light from three separate sources passes through a diffraction gratinqs *ed0 vz4k5cg with q sk504de*zv c$ 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 nagrnm ea,z u9uz(t(j1 (rrow slits 0.60 mm apart. The scre1ta umu((gn,9zrze (j en is 1.70 m away. A second source of unknown wavelength produces its second-order fringe 1.33 mm closer to the central maximum than the 590-nm light. What is the wavelength of the unknown light? $\lambda_2$    nm

A radio station operating at 102.1 MHz broadcasts from two identical antennae at*de 32ncdgl6 v the v n6e2cl 3ddg*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 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 blnr 0z, f;po .sru/1zan outside doorway 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 outsn , .pobus1rl ;0z/frzide the doorway.    $^{\circ}\,$ either side of the normal.

If parallel light falls on a single slit of width D at a 305 3yfv7q 2ovqo$^{\circ}\,$ angle to the normal, describe the diffraction pattern.

  The wings of a certain beetle have a series of parallel lines acrolte n7nyga+u2 lz2v*; ss them. When normally incident 460-nm light is reflected from the wi nv7 z;ty2ln gua2+el*ng, 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 ndl dy9+ks 89osecond-order spectrum for any visible wasnddlk 9yo89+velength?   $ lines/cm$

Show that the second- and third-order spectra of white lpb qv+4kei: pl(-vmk7ight produced by a diffraction grating always overlap. What wavelengths overlap e7+iqkvpl4mvbke-p :( xactly?

  When yellow sodium light, / ov;f k85+ m7aj1lj pjs3hyiz$\lambda\;=\;$ 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 paz;gnoat s.7a9q/s+c uttern is viewed on a screen 2.5 qz9. ganu+ast;so / c7m from the grating. 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 bqonws 4vxm - 5;fir-dx 5+vr-a minimum of 150 nm thickness of it, when laid on glass, is needed to reduce reflection to nearly zero whe5d o5xfr-w;v min rx--qsb4 v+n light of 600 nm is incident normally upon it? Do you have a choice for an answer?

  Monochromatic light of vas 8p bzs.8.mazriable wavelength is incident normally on a thin sheet of plastic film in air. The reflected light is a minimum onzp88s bs. a.mzly 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 ant yy6h db+l3 8kx6jyb.wi-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 thq 8h8)qnkfr.1ymmv+w lllwk 6h+8 :l ve air layer between two flat glass surfaces if the glass is to appear dark when 6mq n 1 w8 8m+.6llh:vfrqlv8yw khlk+)40-nm light is incident normally?    nm
What if the glass is to appear bright?    nm

Suppose you viewed the light transmitted through a thin film layered on a fla 8pfhw7est+b +t 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 the maxima ands+ p7f8+btweh to zero.
24-30
24-36

  At what angle above the horizon is t00 :n l*de.uca3k2e-as+xz/dcb jg.: efargrhe Sun when light reflecting off a smooth lake is polarized most stronglyjd - n graea0*:.l.xz:bgf3+rc/c2kuead s 0e?    $^{\circ}\,$

  At what angle should the at d.w mzy50uu;o2: jwu.1bktz xes of two Polaroids be placed so as to reduce the intensit1k tbu dj5:zu.20 .omwywtu; zy of the incident unpolarized light by an additional factor (after the first Polaroid cuts it in half) of
(a) 4,    $^{\circ}\,$
(b) 10,    $^{\circ}\,$
(c) 100?    $^{\circ}\,$

  Unpolarized light falls on two polarizer sheets who0rgbm7r8/ ii fse transmission axes are at right angles. A third polarizer is pb ifgi8rr m70/laced 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 axesd*3l (ikp1f b2hase 6px,ly 3m vertical, at 30$^{\circ}\,$ to the vertical, at 60$^{\circ}\,$ to the vertical, and at 90° to the vertical.
(a) Calculate what fraction of the incident unpolarized light is transmitted by the four polarizers.
(b) Can the transmitted light be decreased by removing one of the polarizers? If so, which one?
(c) Can the transmitted light intensity be extinguished by removing polarizers? If so, which one(s)?

  A laser beam passes through a slit of width 1.0 cm and is pozqv9-(in.o gointed 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).qgo-o n9v(zi . Estimate the width of the beam when it reaches the Moon.    km

  A series of polarizers are each placed at a k*k4; vov 7g.c+ryffpu -)jrt10$^{\circ}\,$ 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 letvn.bb .6i+danfx,9c, 9 fs $(n=1.34)$ 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 radiatih,l gt1 ft3md/f x ,2w5 1ujmr7y9tr70mrmdepng 6.0-MHz radio waves in phase with each other. They are located at pointgxf 9t,remtm/fd 7 m170yjrrpth1u2lw3,d 5ms $S_1$ 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 wavelengthseib*88ls)r k aw9 crq;vnbc2xl12ye8 , 420 nm and 650 nm, enters a)8c;ab81qr2cw b9e xk lsi2nvey* lr8 silicate 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 flat s s.ojnmz,*d2ilxti3. urface 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