Does Huygens’ principle apply to sound waves? To water waves? Exp;. cs /x9pey h6yng,dalain.

What is the evidence that s hap5mq +1aijfz.k +*light is energy?

Why is light sometimes described as rays and sz;ou a4x )+xpcrni*d1 ometimes as waves?

We can hear sounds around corners, but we cannot senp 3as3p:g h+he around corners; yet both sound and light are waves. Explain the differenn+gp:ashp3 h3 ce.

If Young’s double-slit experiment were submerged in wa( bz9jj,wl/. gtdofl1ter, how would the fringe pattern tljjf /zgl1.o, (bdw9 be changed?

Monochromatic red light is inciden4i) bmeb*p/ wp);gc s7it/edv t on a double slit, and the interference pattern is viewed on a screen some distance away. Explain how the fringe patterbebiip /pt d;* )w7 4g/cvesm)n would change if the red light source is replaced by a blue light source.

Two rays of light from the same source destructively interfere ifewr j/ +c h1nqbirxv dp(ooe(3; 8l3hz)fo,s, their path lenrqb o1l(rpfi 3wh/ v)o x hcdn8j+;s,o e,e(z3gths differ by how much?

Why was the observation of the doup,1 33aajic x cop4;14jnpeoqs97ooj ble-slit interference pattern more convincing evidence for the wave theory 7 qcpa ;ox4psa,j oec4 313on1po9ijj of light than the observation of diffraction?

Compare a double-slit experiment for sound wavzzie(6 wpej;gkze/yum57 7 p (es to that for light waves. Discuss the similarities ane/p6j7m egki;((pwzzu57 ey z d differences.

Why doesn’t the light from the two headlights of a dyu jcw 723o/;r/iocay istant car produce an interference jir3 u oc/w;2o7/cyyapattern?

Suppose white light falls on the two slits of Fig. 24–7, buttv0 q8:zc(p woiab000etyqpki4u 07 m one slit is covered by a red filter (700 nm) and the other by a blue filter (450 nm). Describe the pattern on the screen.yqa:t 00ptck0ew4q 080 u7mzo(iv pib

When white light passes through a flat piece of window glass, it is notxydgx ik3u:zs5( b3g) broken down into colors as it is by a prism. Explainz xi33y)xsdgbuk: (5g.

For both converging and diverging lenses, discuss how t pag;,+oxd+ns r2mytkf ti943he focal length for red light differs from that for violet ligm9,frigxk +p4 t a+3t2s dony;ht.

A ray of light is refracted through three different materials (Fig. 24–55). j0hjb;l f.sfafo3 4lhxsev6ok/ 5:u4Rank the materials according to their index of refraction, least to greatest. a5ubf /xff; hle64h0jvsjk4o3s: o .l

Hold one hand close to your eye and focus on a distant light sourcnd0h;w+;t sh pe through a narrow slit betweenn h+spthd ;;0w two fingers. (Adjust your fingers to obtain the best pattern.) Describe the pattern that you see.

What happens to the diffraction dgsh . 5qw23e)aiba3e pattern of a single slit if the whole apparatus is immersed in (a)a q ah23e5de).3bs giw water, (b) a vacuum, instead of in air.

For diffraction by a single slit, what is the effect of increasing (a) thej;nsk 09 oe3yoag8 j(j slit width, and (b) the wavel(j jo8gj93syoa0kn e;ength?

What is the difference in the interference patterns formed (a) by twon( ks+gm nt,r6 slits $^{-4}\;cm^2$ apart, (b) by a diffraction grating containing $10^4lines/cm$?

For a diffraction grating, what is the advantab9fe;zi7ox.u t 9va5b ge of (a) many slits, (b) closely si .bf;57vz9 eouatbx9 paced slits?

White light strikes (a) a diffraction grating, a9l;d (ig.rcqk nd (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 the rainbow in eac.cdrk q;gl 9(ih case? Explain.

For light consisting of wavelengths between 400 nm a vhji 0gw dqtdx55xp/ww 9oq*)eg.*5lnd 700 nm, incident normally on a diffraction grating, for what orders (if any) would there be overlap in the observed spectrum? Does your answer depend on th)twvjl 0 5*5qqdg.x h/epiwo5w 9dg x*e slit spacing?

Why are interference fringes noticeable only for a thx:-gr ozy w:f8in film like a soap bubble anzx::-8fyowrg d not for a thick piece of glass, say?

When a compact disk (CD) is held at a +*qamuu 8kwb6n angle in white light, the reflected light is a full spectrum (Fig. 24–56). Explain. What would you expect to see if monocbu*6q uk a+8mwhromatic light was used?

Why are Newton’s rings (Fig. 24–31) closer togeth:is+;:4 pip;n vm :o ioycdjs3er farther from the center?

Some coated lenses appewos-+ s4mez-v ar greenish yellow when seen by reflected light. What wavelengths do you suppose the coating is designed to transmit c mov4ze +-w-ssompletely?

A drop of oil on a pvcss5pecp f1 ,mwe(1f5v+ s-vond appears bright at its edges, where its thickness is much less than the wavelengths of visible light. What can you say about the index of refraction of the ovc+se e5s wmv-11p scpvff( 5,il?

What does polarization tell us about the naturr(3ii 4z8kn oje of light?

Explain the advantageetxsqut9.11( af*mf q of polarized sunglasses over normal tinted sunglasses.

How can you tell if a pair of sunglasses is polarizing or nnqozjtt+n r9y,zqcp7 l20/v7ot?

Two polarized sheets rotated at an a tdh6 d9;p3ajod,-wn:(ow.a mng t e6lngle 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 had3oalm0 1o,t rl5d(m rv no atmosphere?

If the Earth’s atmosphere were 50 times denser than it is, wouldzy:2+qo7 hro c sunlight still be white, or would it be some other oor7hc+yz:q2color?

  Monochromatic light falling on two slits 0.016 mm apart produc aqllw83 axvaapr2 boy-( 9,z*es the fifth-orderwyrvpl(-3 2xaz a8*ba9aq ,ol 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 obser/q(hiz5(gh us ved at an angle of 18$^{\circ}\,$ when the light falls on two narrow slits. How far apart are the slits?    $\mu m$

  Monochromatic light falls on two very narrow slits 0.048 mm ap rj9k vmr+ka+. hji05iart. Successive fringes on a screen 5.00 m away are 6.5 cm apart near the center of the pattern. Determinea 5ii0j9+jkmrhvrk +. the wavelength and frequency of the light.
$\lambda\;=\;$    $m$
$f$ =    Hz

  A parallel beam of light from a He-Ne laser, with a wavelength 656 nm ;ov 2xlna .pny6)c8w h9 ets+tcwi-v6, falls on twoy ;2hnie8-tc6.v)x ln+tpo69aw cswv very narrow slits 0.060 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 slitai;p8 fz b3gri4+ xt;fs and produces an interference pattern in which the fourth-order ff;z fa rtgx4;3p+iib8 ringe is 38 mm from the central fringe on a screen 2.0 m away. What is the separation of the two slits?    mm

  If 720-nm and 660-nm light passes through two slits 0.58 mm8wkp1n m9u k*(9j.ewj qjdjn0 apart, how far apart are the second-order fringes for these twp(nqk wj. nku01wjj em8*99jdo wavelengths on a screen 1.0 m away?    mm

  In a double-slit experiment, (vi 0yp np0hcimf76qn9 6y 5gzit is found that blue light of wavelength 460 nm gives a second-order maximum at a certain location on the screen. What wavelength of visible cv76yzy6(p h95fmgq pin00nilight would have a minimum at the same location?    nm

Water waves having parallel crests 2.5 cm apart pass throughup( t+mcb rkpyk8q,1 n -x4r3k 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 thtcru - 8qrpnk,3 xkk(mbyp41+ere be little or no wave action?

Suppose a thin piece of glass is placed in front -zn69za w r9h, h2sv9 rizn*ccof the lower slit in Fig. 24–7 s2 99 c *zhz9vairs6ncw,nzhr -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 lighnugr/w 7o4-*m u- fsglt of wavelength 500 nm is located 12 mm from the centfnu7 g -lousw*4m -rg/ral bright spot on a screen 1.6 m from the slits. Light of wavelength 650 nm is then projected through the same slits. How far from the central bright spot will the second-order maximum of this light be located?    mm

  Two narrow slits separated by 1.0 mm are illuminated by 544 nm light. Find the g.5veu-p y 5ywdistance between adjacent bright fringes on vy.p-e g55ywu a screen 5.0 m from the slits.    mm

  Light of wavelength 480 nm inr/ 3h3rwnom4h) m7 trv 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) xj-ppd).yg zg.3zl- 0cqdizsu )zs+pv7n l2 +covers 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 (minimumsygid-x-qcp g + 0znj7 z+.ld)zv3pz.l2) ups) thickness of the plastic?    nm

  By what percent, appro;eazco- 6 x6g:5 htzmhximately, does the speed of red light (700 nm) exceed that g6o h6:-ahczm;ztx5e of violet light (400 nm) in silicate flint glass? (See Fig. 24–14.)    %

  A light beam strikes a piece of glassirkwh, y3/feg3;l;of ,ly sx2 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 containing two wavelengths, ib / k7b6szg6s$\lambda_1\;=\;450\;nm$ 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 my: )g+rko/k*d t xlhm2m wide, what is the full angular width of the/hydk*)t: mg rx lo2k+ central diffraction peak?    $^{\circ}\,$

  Monochromatic light falls on a slit t: hr 1ptr58de z;ljtck9+a1hb hat 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 osm-prs,eyx ji10 ./t4nfqv r, n 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 mma):5b )b0jrlkb od /vq wide is illuminated by 450-nm light. What is the width of the central maximum (in cm) in qkr a l0/5o)bb bj)v:dthe diffraction pattern on a screen 5.0 m away?    cm

  Monochromatic light of wavelength 653 nm falls on a slit. If the ah 4oohw52 0go6pwbyq/ ngle between the first bright q/gohbp64oho 5 ww02yfringes 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-mlzrh:m-0 1 ctic6kz 1xm-wide slit czch01t izkl6:x -mr1illuminated by 589-nm light?    cm

  When blue light of wavelength 440 nm falls on a single slit, the first dark /(qkgac.ow a,9x damhge + pyt9rz80-bands on either a hyz9 ed+m(.kp9orxqc /gat- w,80ag 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 p )zkspvz9 (nt +i +awy,i0cw*central diffraction peak that is 9.20 cm wi iin9a,(pc wk psw)t++ 0yv*zzde on a screen that is 2.55 m away. How wide is the slit?    mm

  If a slit diffracts 650-nm light so that v pbij/- j1n:xyaj *m5the diffraction maximum is 4.0 cm wide on a screen 1.50 m away, what will be the width of the d /xj*:jiy nmp5bvj1 a-iffraction maximum for light of wavelength 420 nm?    cm

For a given wavelengm5f9hi8/ vh0sn iac (sth $\lambda$, 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 whv,gh q)e i/6p/t2gr9c cpac .r1glnb* en falling on a grating whosecg ,chrir 2gv1pe c/) p9/g t.*qba6nl 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 the third-order occurs at.exx11(bv fahsox(2b an sh .2v bxb(1 x(ex1fao18.0$^{\circ}\,$ 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 fall ry2jf-db91mc7ycki0 ing on a diffraction grating is observed at a 15.ybjr071-mc d 29ifcky5$^{\circ}\,$ angle. How far apart are the slits?    $\mu m$
At what angle will the third order be observed?

  A diffraction grating ha.8iy d:eg4 /z 8tu2vbkb3kfcls $ 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 normallybfvwo* qp9k35 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 )mw3()f9 nks;cwku rmthat can be seen if a grating with 6000 lines per cm is illuminated )m);m3(fwnwkcs9ru kwith 633-nm laser light? Assume normal incidence.   

  Two (and only two) full specg1h.xtn g/q v)tral 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 lv1/txgnhgq). ines per cm for the grating?    $ \times10^{ 3}\;lines/cm$

  White light containing wavelengths from 410 nm to 750 nm falls on a grating wexd98ep b7x+withxe+7dx9 e8 bpw $8500\;lines/cm$ 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 knia zj*j;n5u:vown 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 mea0-9w zzu+tsms*cb yfu/v l l:x 8ki6d0sured 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 thic6e,l)z qzxb o.k, what wavelength is most strongly reflected at the center of the outer surface when illuminatzxq6ozl b,) e.ed 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 gc jw8a e1+kx1mbu gg)is)3xxu 2r0sl 5lass plates are each 26.5a1 i1+e)suxg urx 2lmcg38s wk)b0jx5 cm long?    cm

  What is the smallest thickness of a soap filqe,bz4yi-*y6 z0rxmrm $(n\;=\;1.42)$ 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 greenr8 nk ,q ds49e i83e+kdfei(bey 7:ynlish yellow ($\lambda\;=\;570\;mm$ is strongest) when white light reflects from it. What minimum thickness of coating $(n=1.25)$ do you think is used on such a glass $(n=1.52)$ lens, and why? $t_{min}$    nm

  A total of 31 bright and 31 dark Newton’s rings (nv rg7db h.of0:ot 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 cent:.7dvhr bogf 0er than the edges?    $\mu m$

  A fine metal foil sep /+: ocrndhf9zarates one end of two pieces of optically flat glass, as in Fig. 24–33. When light of wavelength 670 nm is inzrnh9o/c:f d+ cident normally, 28 dark lines are observed (with one at each end). How thick is the foil?    $\mu m$

  How thick (minimum) should the air layer be between tw1h j5,ffmce a,jn 1 vsic 97jj(df87tpo flat glass surfaces if the glass is to appear bright when 450-nm light is incident normally?vai j sm785cdjn cj7e1ff(jt,,hf19p    nm
What if the glass is to appear dark?    nm

  vA piece of material, suspected of being a stolen diamfie (( 66kw*q 2qevurlond $(n=2.42)$ 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 h06 uh7/aopmq $(n=1.36)$ 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 e 8as-,6jge0sxmq7wqfsx; u0 in a liquid, the diameter of the eighth darse mq7- ;sg6 xea800,wqsf jxuk 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 enterh09n 4ltns abb6sj,s(p;quo ;ing an interferometer if 644 bright fringes are counted when the movable mirror moa ;l6 bst0js( s po94uqn;hbn,ves 0.225 mm?    nm

  A micrometer is connected to the movable mirror of an interferl m;ste8 95gc6vzzz f.ometer. When the micrometer is tightened down on a thin metal foil, the net number of bright fringes that move, compared to tetlg z8czs m.;96zfv5he 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 mirrg+zccbt4 u m,1qd (uz*s iy:h,or $M_1$ in a Michelson interferometer be moved if 850 fringes of 589-nm light are to pass by a reference line?    mm

  One of the beams of an interferometer (Fig. 24–59) passes throug /o8hglqn4grwf3)3hch a small glass container containing a cavity 1.30 cm deep. When a gas is allowed to slowly fill th nf )h3qlgc8r3h4w /oge 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 6hp frx149 orozeikm5-d -j()n0bq1w w5$^{\circ}\,$ to one another. Unpolarized light falls on them. What fraction of the light intensity is transmitted?   

  What is Brewster’s an;fnx xa:7vg 9mpmbmp6pz n4 .*gle for an air–glass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s angle for a diamond submb6p:mrl kfrh 8tg,+p7erged in water if the light is hitting the dirgl8h ,:7km 6+tbpfpr amond $(n=2.42)$ while traveling in the water? $\theta_{p}$    $^{\circ}\,$

  Two Polaroids are aligned so that the light passing through them is a maximum.. a htgf ft-9.gq0/xph At what angle should one of them be placed so that the intensity is subsequent f.x/h pf-0a9tg.gthqly reduced by half?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be pla74 zt7oph+jjz nc(unkg1e)pyq (, ,:hc xf4ncced so as to reduce the intensity of theo n c7hf(ucpnep,c z47+x hn,jt:g( jzkyq 14) incident unpolarized light to
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are oriented at 455fit u e6rr2e0$^{\circ}\,$ 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 oriencg2h1xjvjn+;ks ;m 2yii6e ;urok2c7 ted 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 31 sxdv+smh 5yfor reflections off the surface of water for light coming from beneath the surface?v+h3sxd s y51m 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 Polaroid sh6arl aw xk6z g329yx(g 4tp4uj nr-yb:eets, each of whose 6aygja4 g (w34rbnxl-xuyzt6kr92:paxis makes a 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength u/;0wxoycx s mr6d 5h9$ 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 inter/xfjdm5r cg/2n4a lg.q9lk :k fere with the direct signal from the s/5qfak .gjc kd mg/:4lxln2r9tation.
(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 diffcx (2mg ngnsv. -6c)lzraction grating with l ncczg.) m gsvn(62x-$ 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 narrol 4c wxo8w2-v qr0eh2uw 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 centu02w28-4r ovq h wcxelral 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 fr)hj5 c- day8g1q/9haz7 kngf yom two identical antennae at the same gd- )y fg7kny/5ah8j a9cq1hzelevation but separated by an 8.0-m horizontal distance d, Fig. 24–60. A maximum signal is found along the midline, perpendicular to d at its midpoint and extending horizontally in both directions. If the midline is taken as 0$^{\circ}\,$, at what other angle(s) $\theta$ is a maximum signal detected? A minimum signal? Assume all measurements are made much farther than 8.0 m from the antenna towers.

  A teacher stands well back from an outside doorway 0.88 w8vuc6 *t0x2h2*t6r klhrhwsm wide, and blows a whistle of frequency 750 Hz. Ignoring reflections, estimate at what angle(s) ikh 0 lh2 x6rr*2ctshvww8t*6ut 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 width D at a 3,usi f 60hjssvcc 5*0r0$^{\circ}\,$ angle to the normal, describe the diffraction pattern.

  The wings of a certain beetle have a series of pab.5r1e9 viyzuh b 4al5rallel lines across them. When normally incident 460-nm light is reflected froi y9azvu.541r lehbb5m the wing, the wing appears bright when viewed at an angle of 51$^{\circ}\,$. How far apart are the lines?    nm

  How many lines per centimeter must a grating kbowg: : .z/twhave if there is to be no second-order spectrum for aw/zkgw: to:b.ny visible wavelength?   $ lines/cm$

Show that the second- and third-order spectra o;lp3 vobu3h 1/.p)z h7rrskwif white light produced by a diffraction gra/vh w)p1rszlprh;bo73i 3uk.ting always overlap. What wavelengths overlap exactly?

  When yellow sodium light,/yd,w(z,, kn1 rfawtz $\lambda\;=\;$ 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 pattern is viewed on ; 7utz;.kcky j+llm/ na screen 2.5 m from the grating. The incident light beam consists of tw+ku c; yjnl7;ml .zk/to 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 min 5it5f 05nypqlimum of 150 nm thickness of it, when laid on glass, is needed to reduce nlyt 55q0pf 5ireflection to nearly zero when light of 600 nm is incident normally upon it? Do you have a choice for an answer?

  Monochromatic light of variable wavelength is ot94yt)wxqsrin 4c)2-mmy7p incident normally on a thin sheet of plastic film in air. The re4m 2) yps7cy9wim)q4tx-ortnflected light is a minimum only for $\lambda\;=\;512nm$ and $\lambda\;=\;640nm$ in the visible spectrum. What is the thickness of the film $(n=1.58)$? [Hint: Assume successive values of m.]    nm

  Compare the minimum thickness needed for an anti-refl qwhu9t-v*j:qh4 md n, 17bzdnective 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 between two flatrw9mhedso,yz5,k 2axpez- 4s ;9w j3 e glass surfaces if the glass is to appear dark why9re swj-z m,he5zpks42 ,dew3a;x 9oen 640-nm light is incident normally?    nm
What if the glass is to appear bright?    nm

Suppose you viewed the light transmitted through a thin film layeriglt-. vw -wp(ed 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 refr- tg- w.viwp(laction. Discuss the relative size of the minima compared to the maxima and to zero.
24-30
24-36

  At what angle above thoip z9o)t.obmb)z; 2vrjy,+y e horizon is the Sun when light reflecting off a smooth lake i zo2jp),;yo.+)mz y9trbivobs polarized most strongly?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be placed so as to reduce tm zn-pph /e6c/he intensity of the incident unpolarized light by an additional factor (afterpcn z/-/ep6hm the first Polaroid cuts it in half) of
(a) 4,    $^{\circ}\,$
(b) 10,    $^{\circ}\,$
(c) 100?    $^{\circ}\,$

  Unpolarized light falls8m0f b ycw*:so9uz5a x on two polarizer sheets whose transmission axes are at right angles. A third polari9cyf0u o58* :wasxz mbzer 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 ve7bq(.qac3 8wzll 5s pyrtical, 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 an0peqk y11+r f ee8bkb5d 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 widthfe+e8k51q1 bkeyr0 bp of the beam when it reaches the Moon.    km

  A series of polarizers are each placed atm yhh87nwm, z jr-w;sp+; wxk. 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 (boca 1r.a-m f$(n=1.34)$ 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-MHamvzh1.1+d c(wt y( gvlr*m(az radio waves in phase with each other. They are locat wh*grzayva d1c( lm.t1(m v+(ed 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 ta;1yu/ blohbtvl.r m77-6qpwavelengths, 420 nm and 650 nm, enters a silicate flint glass equilateralrl/o pt 6;17h.l7-bv ubmatqy 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 lep*6 l17 t0sxbhzqq7hz ns has one flat 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