Does Huygens’ principle apply t7ro ru pri)l(,/h xur5o sound waves? To water waves? Explain.

What is the evidence that light is ener; .;l-vc.qdx(ycykr 0xt+hs:6xg zlggy?

Why is light sometimes described as rays and sometis;lbt+ 6)jic d+l5ap+n9l ooimes as waves?

We can hear sounds around corners, but we cl o3yx;fwrrme*/ xhx ;7-*obpannot see around corners; yet both sound and light are waves. Explain the p*/rhy;bl3x-r;woo* mxex7f difference.

If Young’s double-slit experiment were submerged in water,/t69smowl ud* g0p5uj how would the fringe pattern be changeg jp /dlu569um otw*s0d?

Monochromatic red light is incident on a doublev y-b y)i.j p65*b) lh .77hhfugglwct slit, and the interference pattern is viewed on a screen some distance away. Explain how the fringe pah j*p57cf7. -hg .byt) wil)gybuh6lv ttern would change if the red light source is replaced by a blue light source.

Two rays of light froul +8+ryz.(spg6assc4 s p:h zm the same source destructively interfere if their path lengths s(8rclzz: s+4 sgshy+upa6p.differ by how much?

Why was the observation of the double-slit interference pq qubilbh89e1 5id2/pattern more convincing evidence for the wave theory of light than the observation of diffeqqidlb9/u 8ph5 bi12raction?

Compare a double-slit experiment for szc pt+ lb0+j:lz9 te.bound waves to that for light waves. Discuss9+ zcztlle.b tb:p0 +j the similarities and differences.

Why doesn’t the light from tyavp5ejh m./jcr++) zhe two headlights of a distant car produce an interference pattern)5+pz. ma /+jr hevcyj?

Suppose white light falls on the two slits of Fig. 24–7, but one 7cotcp1f 3os bwgm d6w3o wv32f7m72n slit is covered by a red filter (700 nm) and the otheg bmw 7s3 d367c72wo vfnw1pfmtc32oor by a blue filter (450 nm). Describe the pattern on the screen.

When white light passes througscc1,9p*drye w 3, waw 8)djomh a flat piece of window glass, it is not broken down into colors as it is by a pripwc cd3 wea8 wms)9d,*yj r1,osm. Explain.

For both converging and diverging lez4.;i ab.ge mbnses, discuss how the focal length for red lightgba; 4bi .z.me differs from that for violet light.

A ray of light is refracted through three different mate o c4ry w ok+43j,ewylio,i(3grials (Fig. 24–55). Rank the matereg w(o3ky,4wc jo l+34yior,iials according to their index of refraction, least to greatest.

Hold one hand close to your eye and focus on a distant light source th2hhekrpc-h/-0t k 0-yq q4emk rough a narrow slit between two finger- hey/thk-p 4 qcr hk-q0ke0m2s. (Adjust your fingers to obtain the best pattern.) Describe the pattern that you see.

What happens to the diffractix4vbe,3 dvk/p 8v4 jueon pattern of a single slit if the whole apparatus is immersed in (a) water43kve xv jv /e8,bpdu4, (b) a vacuum, instead of in air.

For diffraction by a single slit, what is the effect of increa+fev,*z pee/bsing (a) the slit width, aebzv +,*eep/fnd (b) the wavelength?

What is the difference in the interference patterns formed (a) by two slitrto ,bp8lx p19z:lpm5 s $^{-4}\;cm^2$ apart, (b) by a diffraction grating containing $10^4lines/cm$?

For a diffraction grating, what i 5d yfjl -a/ * cpta28s0acon(ud9d1fos the advantage of (a) many slits, (b) closely spacet2doy-j( dna8uo/1f 9fadpa5l sc0*cd slits?

White light strikes (a) a diffraction grating, and (b) a prism. A rainbow .0*c)x: wyppc3xbk umappears 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 :3 pcxuc0km )ywx. *pbin each case? Explain.

For light consisting of wavelengteo :6toh/v0 qx0 tvimuhmhh 0 vo;/)5fhs between 400 nm and 700 nm, incident normally on a diffrmuo 6fv)h qoht emv0 / 0i/x0o:vh;5htaction grating, for what orders (if any) would there be overlap in the observed spectrum? Does your answer depend on the slit spacing?

Why are interference fringeeux1 vh6-wwpw)fj 4 x3s noticeable only for a thin film like a soap bubble and p13w ewuf w-4)6hxxvjnot for a thick piece of glass, say?

When a compact disk (CD) is hel.slxa/ sqx8+m9h4quv d at an angle in white light, the reflected light is a full spectrum (Fig. 24–56)8xlv+4xs9qumh/ saq. . Explain. What would you expect to see if monochromatic light was used?

Why are Newton’s rings (Fig. 24–31) closer together farther fr mqv6qc*9u1:7yzy 7f:fo6;pc gqxvlpom the center?

Some coated lenses appear greenish yellow whe; jbbhlac7 cwa6: -szq:p*oh)n seen by reflected light. What wavelengths do you suppose the coating is designed to transmit completelbl : j7-s caw*hoa;:6zbq)pchy?

A drop of oil on a pond appeaimj3nl45b 0crwq 0p.crs bright at its edges, where its thickness is much less than the wavelengths of visible l rwqb c 0j5nl.p3mi40cight. What can you say about the index of refraction of the oil?

What does polarization tell us ab;dosv38j(-kz bx zrn,out the nature of light?

Explain the advantage of polarized sunglasses over normal tinf5v* z*jfwc )lted sunglasses.

How can you tell if a pair *lif ,l i*g jf9cedv44of sunglasses is polarizing or not?

Two polarized sheets wagdxt/ 2 n*;erotated 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 hadg7(yddp /hl+uu9 oz +s no atmosphere?

If the Earth’s atmosq)o v)u tj i-nlj;p9,xphere were 50 times denser than it is, would sunlight still be white, or would it be nox;) ltuvq,p-9j j)i some other color?

  Monochromatic light +nflq8oxa n38falling on two slits 0.016 mm apart produces the fifth-order fringe at an88qan+xof nl 3 8.8$^{\circ}\,$ angle. What is the wavelength of the light used?    $ \times10^{-7 }\;m$

  The third-order fringe of 610 nm light is obserg r //fn,mn/ ezui5av0ved 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 apart. Successive fr65qfsr +l *q-u(bgvb )c;c uecinges on a screen 5.00 m away are 6.5 cm apart near the center of the pattern. Determine the wavelength and u ;b*uqcq-6 s(f lvc)c+ebr 5gfrequency of the light.
$\lambda\;=\;$    $m$
$f$ =    Hz

  A parallel beam of light from a He-Ne laser, with a wavelength 6 eg ;pbdr dogt949,r.r56 nm, falls on two very narrow slits 0.060 mm apart. How far apart are the fringes 9.drrg; t4ge9rpbod, 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 int7xiegtkp,igt j97k ), erference pattern in)eitg,7gi t9jxk7p ,k which the fourth-order fringe 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 mm apart, how far apart l08s2ubn0c6w,ob rvl are the second-order fringes for these two wavelengths on a screen 1bu,lws0 c2r60 lvbo 8n.0 m away?    mm

  In a double-slit experiment, it iswg 7q7 t plhl4x;(1nnf found that blue light of wavelength 460 nm gives a second-order maximum at a certain location on the screen. Whllh;pw g n7 nxtq14f(7at wavelength of visible light would have a minimum at the same location?    nm

Water waves having parallel crests 2.5 cm apart p2 o: 7 pgzb/bfuqq.a-vass 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” d-qg vaufpb/b z7 q2:.oirection would there be little or no wave action?

Suppose a thin piece of glass is placed in front of the lower smkl*s ;5b( ppplit in Fig. 24–7 so that the ;msklp(p* bp5two 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 wavelezi:ucy;rzz:( ngth 500 nm is located 12 mm from the central bright spot on a screen 1.6 m from the slits. Light of wavelength 650 nm is then projected through the same slits. How far from the central bright spot will the second-order maximum o:: ;zz(yrziu cf this light be located?    mm

  Two narrow slits separated by 1.0 mmr z1ct rezx170 are illuminated by 544 nm light. Find the distance between adjarz 01zexc7rt 1cent bright fringes on a screen 5.0 m from the slits.    mm

  Light of wavelength 480 nm in air n:9 x 2ktcj;kgowx/ :efalls 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)y zzt:s zq6p/0 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 (minimum) thickness of thes zzp: 6/0tyqz plastic?    nm

  By what percent, approximately, does the speed of red lightuh b :q./h;tgg (700 nm) exceed that of violet light (400 nm) in silicate flint glas;:bgghhqt./ us? (See Fig. 24–14.)    %

  A light beam strikes a piece of glass at asd8;bzyn7wcd;jxi38, s,sh w 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 contai7 fbx7 lio,f*nning 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 ftl tad-m l:+s0 k2:gc g+yvco7ull angular width of the central diffracticcl2tg +my:tkv g0o7d -:+slaon peak?    $^{\circ}\,$

  Monochromatic light falls on a sg qu z0czua)/1lit that is $ 2.60\times10^{ -3}\;mm$ wide. If the angle between the first dark fringes on either side of the central maximum is 35.0$^{\circ}\,$ (dark fringe to dark fringe), what is the wavelength of the light used?    nm

  Light of wavelength 520 nm falls owa;u3/ 6poa0j wzm p:un 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 by 450-nm light. What is the wibd4mtu+8 t+bvdth of the central maximum (in cm) in the diffraction pattern out+vbb4 tm8 +dn a screen 5.0 m away?    cm

  Monochromatic light of wavelength 653 nm falls on a slit. Ivenx-.gg ..qe f the angle between the first bright fringes on either side of the ce.g x..ege q-vnntral maximum is 32$^{\circ}\,$, estimate the slit width.    $\mu m$

  How wide is the central diffraction pead; zb4*fpj. fr)lo1, ossug+bk on a screen 2.30 m behind a 0.0348-mm-wide slit illuminated by 589-nm light? 1 , fo;bj+ *g.)zpbls ufd4sor   cm

  When blue light of wavelength 440 nm fallryoo9zpr 3vdf, i.d 1,s on a single slit, the first dark bands on ei f yp,odz3 o.vr9id1r,ther 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 singlk( zuu /gl0/8xsqutz+ e slit, it creates a central diffraction peak that is 9.20 cm xz/k+z0gutlq(/ su u8 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 maximum is 4.0 cm widdpt*c34 jr00v4 v kqtye on a screen 1.50 m aw0dk3 pq *vtyr4v40 cjtay, what will be the width of the diffraction maximum for light of wavelength 420 nm?    cm

For a given wavelength 8(gqv5b( zwok ,v jh6g$\lambda$, 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 m ts81;5r ls1x6hx4 upkjyv *l6wge d:caximum when falling on a grhcwek *x6 1y4j p8u;sl6rgv sld1xt:5ating 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 the thir yxe6pbtk* arz8h6 9e9d-order occurs at an a8z r* kbp9yxt9eeh6618.0$^{\circ}\,$ 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 diffraction gratin:pd *c9iri kz;g is observed a pz:i9d ;cikr*t 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 hao,wx (bqdz*b v4*/ kals $ 6.0\times10^{ 5}\;lines/m$. Find the angular spread in the second-order spectrum between red light of wavelength $ 7.0\times10^{-7 }\;m$ and blue light of wavelength $ 4.5\times10^{-7 }\;m$.    $^{\circ}\,$

  Light falling normally on zv 7/k)y:f5rf *plh v; bcdte9pji5v0a $9700-line/cm$ 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 be32sxg /b) dnzx seen if a grating with 6000 lines per cm is illuminated with 633-nm 3 ) 2nz/dxbsgxlaser light? Assume normal incidence.   

  Two (and only two) full spectaawll q5b ;(qv9x .zjm-rly (tg5bh /;ral orders can be seen on either side of the central maximum when white light is sent through a dibqv;5y9wt5( qbxmra/jl; . -gah (llz ffraction grating. What is the maximum number of lines per cm for the grating?    $ \times10^{ 3}\;lines/cm$

  White light containing wavelengths from 410 nm to 750 nm falls on a gratin1xlpsl3: h(k uxzy*m1 g with 31: lyshzlupk( x1*mx $8500\;lines/cm$ How wide is the first-order spectrum on a screen 2.30 m away?    m

  A He-Ne gas laser which produces monochrom5ydx1v0cmhn3 /xs tf(atic 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 spectrum lines are measuree/g v- k5pdpekrv64t1 d 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 wave n/f-; c ejpbdk*4r9ir/goh-r length is most strongly reflected at the center of the outer surface when illuminated norbf ri*ro-njg/p hk e94;c/-rdmally by white light? Assume that $n\;=\;1.34$. $\lambda$ =    nm ,which is an    -  

  How far apart are the dark fringes -kw3 db/ns 04 gskzho+3w p3ig*2saa iin Example 24–8 if the glass plates are each 26.5 cm lo0wb a gi/ +z2* 3d-shsk 3napowi4s3gkng?    cm

  What is the smallest thio crty c;3jmsl hp4 205y8odg-ckness 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 (4jf(. avy.ko p$\lambda\;=\;570\;mm$ 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 (nb,o,l 1fwz*4lnu s 9rnot counting the dark spot at tr1nl,, 4bl9w o ufnsz*he 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 edges?    $\mu m$

  A fine metal foil separates one end of two pieces of optically fl *nhxe04sswwp-p)7fyw q3 6t lat 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 thickwft3wlq- p6s*p s0 ne x7w)4yh is the foil?    $\mu m$

  How thick (minimum) should the air layer be bet5ty a.ul9i2 c*r tf:2gppk7k eween two flat glass surfaces if the glass is to apk2u9a5:tg ip7 le*y 2.kr ftpcpear bright when 450-nm light is incident normally?    nm
What if the glass is to appear dark?    nm

  vA piece of material, suspected of being a stolen 6) ;dkuf3kan ebesk8( 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 alcohomxb i09kd w)(ag+b:d ))zows 9s ds3gjl $(n=1.36)$ 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 liqvu 4yrfl0mk2 vp qgp2/-v: yw.uid, the diameter om0 wf2kyp2ylv r-v.p:4 uvq/ gf the eighth dark ring decreases from 2.92 cm to 2.48 cm. What is the refractive index of the liquid?   

  What is the wavelength of tdx* amjo3gs .u;w:;lx he light entering an interferometer if 644 bright fringes are counted when the movabl;u*xa. gs 3 o;wjxml:de mirror moves 0.225 mm?    nm

  A micrometer is connectedf m404fmybb-+vw6,xsjno9 uh m+ew: k to the 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 micrometer, is 272. What is the thickness of the foil? The wavelybuj94,-+mm 0 evbf :wk wms+nof6h x4ength of light used is 589 nm.    $\mu m$

  How far must the mirw6fobhdf yzoe6nn*4 ptq -2(x9/ re0bror $M_1$ 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 througcoe8*v, .e tw53mh:g och tr/th a small glass t.85* cteog,r :/e tvchh3 owmcontainer 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 omfe3 de7ez*29 x mukl:riented at 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 air–gland;2r+bytr de( yw a1w 7nhd:;ss $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s angle for a diamond submerged in water if the 1g/e c2 edd;dtlight is hitting the didd1;/2te cedg amond $(n=2.42)$ while traveling in the water? $\theta_{p}$    $^{\circ}\,$

  Two Polaroids are aligned so that the light pass wf:tv;oh ;z3j g/fo(jguh80ring through them is a maximum. At what angle should one of them be placed so that the ir;j/3:zofw8 vg jhgfh; otu (0ntensity is subsequently reduced by half?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be placed so asitv/k0uvaeg;j ;8yqqd ).z x +r+kgu5 to reduce the intensity of the incident unpolajvg+0uxg uq8d/y r);+i.e;vt5 a kzkq rized light to
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are oriented at 4ohokja z ,:o-.8zjr6b 0$^{\circ}\,$ 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 oriented25rzknppe/) i 1kx crrz;2*pr 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 fowjdfwk/i)x.d khn0 4tj ; lv6n9 0zg1gr reflections 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 fromlj0xng0 nigw. j1 v/kfz 9kh6dd4wt; ) 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, each of w aeyz,dp:0u 9 1jrjy+whose axisp z9j+e :, wdyaurj01y makes a 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength g7vrt c0sd5t)$ 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 interfe hjfdwv dky)4;23 d*zk v,jf.ire with the direct signal from the stationhz v4d*k2j ;,fifvydw)j3k.d .
(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 diffydky4wnvv 7jddbr a00f4 1:;r raction grating with y:a y j04db 0nvrwdvf47;1k rd$ 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 narhk3 xr gsl9eo:9rw y7.t03- m iudvde(row slits 0.60 mm apart. The screen is 1.70 m away. A second source of unknown waveluv0h xeey ( ddl.mro3r7k93 :gsi-9w tength 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 qbc) kn3jxuu.y - 2um+j1rdq2from two identical antennae at the same elevation but nm2uc 1j3yx bq -u+drq2j ).ukseparated 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 r7/l. fiey/ugoutside doorway 0.88 m wide, and blows a whistle of frequency 750 Hz. Ignoring reflections, estimate at what angle(s) it is not poss.7e/uf/yilr gible to hear the whistle clearly on the playground outside the doorway.    $^{\circ}\,$ either side of the normal.

If parallel light falls on a 9ja 4/bu g:z)yfy6rlr single slit of width D at a 30$^{\circ}\,$ angle to the normal, describe the diffraction pattern.

  The wings of a certain beetle have a series of parallel lines across them. Wheli 9 8ho c l-dygx;,7tthpb6; *x)bqjwn normally incideng7p-t6 cb;t)b9d 8 *yh,olw;jq lxxiht 460-nm light is reflected from 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 mu ,/ u6r,tvdcdj6n2nxnst a grating have if there is to be no second-order spectrum for any visible wave/2,6 uc 6jdrnvdn,ntxlength?   $ lines/cm$

Show that the second- and third-order spectra of white light produced by a difdy7vy/ h:e c;i7j; trdm(,b ozfraction grating always overla(z;r c: jdt yh io,7;eym/7dbvp. What wavelengths overlap exactly?

  When yellow sodium lid))xp9 :sg ibcght, $\lambda\;=\;$ 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 .i-kv b y dn.2,yb4pma9c adp( and the pattern is viewed on a screen 2.5 m from the grating. The incident light bea- mdyb9(.vd.yp ac4pak2,bnim 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 a minimum of ); lqd3r3 lh2uj7soqz150 nm thickness of it, when laid on glass, is needed to reduce reflection to nearly zero when light ou3 )qrlqz 7s32 djlho;f 600 nm is incident normally upon it? Do you have a choice for an answer?

  Monochromatic light of variapa a sev:v,)oa/.kx;x ble wavelength is incident normally on a thin sheet of plastic film i ,a)xa xpv sevk/.o;a:n air. The reflected 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-reflectivedt b wec9e);6l1.a6i3/0 m lzmdfqkbn 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-zxq4 gb*fi 2cgjrr+, r42pw( ydw0p6gr ero) thickness for the air layer between two flat glass surfaces if the glass is to appear dark when 640-nm light is incident no4i w+pfc y2bgrrg6q 4rjx g 2,*0rpw(drmally?    nm
What if the glass is to appear bright?    nm

Suppose you viewed the l/q 9v .x-oq h32ngv;o( popojeight 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 th(v- qo/3x;goe2ojp.9vqpno he relative size of the minima compared to the maxima and to zero.
24-30
24-36

  At what angle above the horizon is the Sun when light reflectim w3(5vbqms/qt -o1 fhng off a smooth lake is po- sq mfqh/b1o3mv(tw5larized most strongly?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be placed so as to redu i ,*:gjye6bgrce the intensity of the incident unpolarized g:i rye*,gj6blight 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 transmission adoz ;24e yta8qxes are at righ4ayd;zo8 tq e2t angles. A third 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 th4lbceg sr .dxs0yk/h u95;p3 deir axes 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 widb eq b/1v t 4.i s0 zuxeyv;k-nax/v0dhso*6e8th 1.0 cm and 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 t .th/oq1e0 i beyv8zk nudes46xv*x0;/ bvs a-he beam when it reaches the Moon.    km

  A series of polarizers are evx m*gccm2: .vach 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 q uc*.6b eh xd*urzdtw1,6c 7b$(n=1.34)$ 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 other.q+ 0grrac/ tt-, lvh(v They are located -,hv +a/t gr(rlc0 vtqat points $S_1$ and $S_2$, separated by a distance $d\;=\;175m$, Fig. 24–61. What are the first three points on the y axis where there will be destructive interference? (Destructive interference in this case means that a radio receiver placed at that point would pick up no signal).    m    m    m

  A parallel beam of light containing two wavelengths, 420 nm an:)l+(ccfq m )xo t*dobd 650 nm, enters a silicate flint glass equi*o)q m l(ccdx+t :bo)flateral 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 hx z vri6fz1ml). nc6b;as 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