Does Huygens’ principle apply to sound waves? To water w hc.lwbd,dh dg j*5ib01-iu ;7t6isc haves? Explain.

What is the evidence tha*y69z- zdx p4:gu 2dakfwzze,t light is energy?

Why is light sometimes described as rays and som.y15nv;v4 -3sy ra qatoy l nmt9l0i.jetimes as waves?

We can hear sounds around corners, buttw *whszg 6d *ea8 i)qw;khe9: we cannot see around corners; yet both sound and light are iws*qw9 )e 8:wdgk*thz6;haewaves. Explain the difference.

If Young’s double-slit experiment were submerged in water, how would the frin,loz y4bhdn4t8dd7(w jw u:q(,k* swige pattern beqhbiz sdy,j4,7:8k(4t *(ow dl nwudw changed?

Monochromatic red light is incident on a dout l5ap2cnl57 dble slit, and the interference pattern is viewed on a screen some distance away. Explain how the fringe pat5pt 7l5cl2dn atern would change if the red light source is replaced by a blue light source.

Two rays of light fr-/4vnmtwfjitc a :0-jareld 4( ix-r9 om the same source destructively interfere if their path lengths differ by how much r-x r094w/fcv4iajt:jmednl t a-i- (?

Why was the observation of the double-sl;to ,v2u plm6rit interference pattern more convincing evidence for the wave theory of li;pr 6m,ut2v loght than the observation of diffraction?

Compare a double-sliqde ovw(9uc +f pg63.q/uxp 1tt experiment for sound waves to that for light waves. Discuss t uqt.cefg9p woupv+(3xd/1q6 he similarities and differences.

Why doesn’t the light from the two headlights of a dvspr kn.xq2eyd. g-0rc 7.d 4distant car produce an interference pattern?..4dr sr 7c xygd0n kqdpe.v2-

Suppose white light falls on the two slits of Fig. 24–7, but eamqe8 *e7dho dw6c95one slit is covered by a red filtdeoq8c a9weh* dm65e7er (700 nm) and the other by a blue filter (450 nm). Describe the pattern on the screen.

When white light passes through a flat p* icdb-ko;z3v*mif*.8 r 7yem h(wldfiece of window glass, it is not broken down into colors al*(kyz7ibhrmf*ce-i .8m ov*df 3wd ; s it is by a prism. Explain.

For both converging and diverging l9u-+4 slurk rtenses, discuss how the focal length for red light differs lr-kt94r us u+from that for violet light.

A ray of light is ref,;3rzv30nwio lulsuw( 2j gi*racted through three different materials (Fig. 24–55). Rank the materials according to their index of refraction, least to greatest. u3,vji;uwlz(30nlr* wo2igs

Hold one hand close to your eye and focus on a distant light sourln2/5yade 11y vkjd t6ce through a narrow slit between two fingers. (Adjust your fingers to obtain the best patternl/tk6d y eva15y1dnj 2.) Describe the pattern that you see.

What happens to the diffraction pattern of a single slit8jwn /4y mqk)p if the whole apparatus is immersed in (a) water, (b) a vacuum, insteaqn8 ypkw mj4/)d of in air.

For diffraction by a single slit, ng7,0nry curb5to67 swhat is the effect of increasing (a) the slit w70nu rb,ty7nsgo5cr 6 idth, and (b) the wavelength?

What is the difference in the interference patteg )--e9hpeio)l c q4qy- eux0yrns 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 o05nh amf mwa63f (a) many slits, (b) closely s3wa05mnham 6f paced slits?

White light strikes (a) a diff4s1;b fr oh9nm/ riws8raction grating, and (b) a prism. A rainbow appears on a wall just below the direction of the horizontal incident beam in each case. What is the color of the top of the rain 4hsb rw/;89i msnfr1obow in each case? Explain.

For light consisting of wavelengths between 400 nm and kdh7-3i 38v mc,pjv ss700 nm, incident normally on a diffraction grating, for what orders (if any) would there be overlap in the observed spectrum? Does your answer3jh,pmv-kscisvd8 7 3 depend on the slit spacing?

Why are interference fringes noticeable onlydusunsvie f*m5p, +7 be le4/2*v,uznh : :cju for a thin film like a soap bubble and not for a thick piece of glass, m :5f :elvsvcbd,ne2, su/7uue4*hj+u*pz in say?

When a compact disk (CD) is held at an angle in white light, the reflected lilx5,ad bfu. h1ght is a full spectrum (Fig. 24–56). Explain. What would you expect to see if mono.b uxlfa15,dhchromatic light was used?

Why are Newton’s rings (Fig. 24–31) closer together farther frosrc jl0bn6 i5/m the center?

Some coated lenses appear greenish yellow when seen n9 fciu-eej188c2xbgby reflected light. What wavelengths do you suppose the coating is designed to tranx-9c1j e en 2ufc8bgi8smit completely?

A drop of oil on a pond appears bright at its edges, where its thickness is m,smh n,a1bv6j uch less than the wavelengths of visible light. What can you say about the index of refraction of the m 6b ,avnsj1,hoil?

What does polarization tell us about the 3e;dhcia:tt v mh s),qmks3.se7 4 z9anature of light?

Explain the advantage of polarized sunglasses over normal tintv7louxes)md6 - 78afged sunglasses.

How can you tell if a pair ofws, v/1z4xje 3 3o6; rezdh7 byukhjh6 sunglasses is polarizing or not?

Two polarized sheets rotated at hx9tn*0 ymob -6;bh eb2j0lqlan 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 haab)f8 :bl7c/b -kc :m41i daivz8el2 +fmcpkad no atmosphere?

If the Earth’s atmosphermf9s 2:0 t/lxahn k:bx6kw1l ue were 50 times denser than it is, would sunlight still be whiteutll sxfwxb60kan:/k h:12 m9, or would it be some other color?

  Monochromatic light falling omk: 80ktc -:al+h5n elc+rfvx n two slits 0.016 mm apart produces the fifth-order fringe at ank ath+mlc en5vfc8 r0k:lx:+- 8.8$^{\circ}\,$ angle. What is the wavelength of the light used?    $ \times10^{-7 }\;m$

  The third-order fringe of 610 nm light is uv8c)., paje9yfsq/3h gc/wyobserved 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 ni2 59luf0pdycdim3 -l.6m tonarrow slits 0.048 mm apart. Successive fringes on a screen 5.00 m away are 6.5 cm apart near the center of the patte60c2p .mdtl9o-3dm5ylfnuii rn. Determine the wavelength and frequency of the light.
$\lambda\;=\;$    $m$
$f$ =    Hz

  A parallel beam of light from a)br;4l ch o0mt He-Ne laser, with a wavelength 656 nm, falls on two very narrow slits 0.0c;b0or m)lh4t60 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 slit44a yprfv :4a8;/h ea chcaba*s and produces an interference pattern in which the fourth-order fringe is 38 mm from the central fringe on a screen 2.0 m away. What is the separatio4va afch 4;b*p8y aacea4:/rhn of the two slits?    mm

  If 720-nm and 660-nm light passes through two slits 0.58 mm apart, how p9+lygwb i0 63z ej)ph(6vzdefar apart are the second-o6epw hlz(9zbye3v6djg0+ pi )rder fringes for these two wavelengths on a screen 1.0 m away?    mm

  In a double-slit experiment, it is found that blue light of wav/ v yws(-,1 ni1cuj/xp 3vtcdgelength 460 nm gives a second-order maximum at a certain location on wntjvx1 cd3-(v1,yig c u/sp/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 through two openings 5.0 cmz l bqoq3su. dg57uhel4u6r,/ apart in a board. At a point 2oeu d5l6uq /7 4bhzsgl u,qr.3.0 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 ty /7*oj q)lhlnly-.wq he lower slit in Fig. 24–7 so that the two waves enter the slits -j/ 7hyn*l qoqwll).y180$^{\circ}\,$ 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 thir4 +jmgh8+v *wp vvb9yz+kyu(zd-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 slits. Light of wavelength 650 nm is then projected through the same slits. How far from the central bri+v kz(b9u8v+pg*vyj h zw 4m+yght spot will the second-order maximum of this light be located?    mm

  Two narrow slits separated339xrm*sct ne by 1.0 mm are illuminated by 544 nm light. Find the dista3xmr 9et*s3cnnce between adjacent bright fringes on a screen 5.0 m from the slits.    mm

  Light of wavelength 43,u pfm6 x7eyoyp9ukh05a f7 e80 nm in 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) covers one slit of a double-slit apparatuzasl 4 sahj4.dcc .;0ys illuminated by 640-nm light. The cente0y4;s h zd .lsca4cja.r point on the screen, instead of being a maximum, is dark. What is the (minimum) thickness of the plastic?    nm

  By what percent, approximately, does the speed of red light (700 nm) exc;v*clr j72ovbea5u z*eed that of ;u7e **oralb5j2 zvvcviolet light (400 nm) in silicate flint glass? (See Fig. 24–14.)    %

  A light beam strikes a piece of glass at a 6uir5 h;y2rysf3 1vn6 u0.00$^{\circ}\,$ 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 wa2oog/*gjwjy g( fm d.+velengths, $\lambda_1\;=\;450\;nm$ 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 th q8 ft4lnmek(5e full angular width of tl 4(8mn keft5qhe central diffraction peak?    $^{\circ}\,$

  Monochromatic light falls on a slit tha*0v/eb)ryhzehej8 (m) h1 uyjt 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 fay *uo12;kbtoh x-z0b ulls on a slit that is $ 3.20\times10^{ -3}\;mm$ wide. Estimate how far the first brightish diffraction fringe is from the strong central maximum if the screen is 10.0 m away.    m

  A single slit 1.0 mm wide is illuminated by 450-nm light. What is the widt- 3nu v2hksmfw:gk r.*h of the central maximum (in cm) in the diffraction patt-u gr :snk .k*mh3fv2wern on a screen 5.0 m away?    cm

  Monochromatic light of wavelength 8+o l48 (y gsgaupk+dh653 nm falls on a slit. If the angle between the first bright fringes on either side of the central mg8ps8kyo h u(l+g+ d4aaximum is 32$^{\circ}\,$, estimate the slit width.    $\mu m$

  How wide is the central diffraction peak on a screen 2.30 m be0wdp;-b y s 9koswhrohad/hy)-955 pyhind a 0.0348-mm-wide slit illuminated by 58rs b oyhh5wky;0so 59ypd -9/)wdahp-9-nm light?    cm

  When blue light of wavelength 440 nm falls on a sinpx, 0vy)mj.s fgle slit, the first dark bands on either m).syp0f xj,v 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, it0obedkff 5 ig0 d*be( (hb du1th3/k2i creates a central diffraction peak that is 9.20 cm wide on a screen thate*k oe13b(b2df 0higtu/d( 5d hkf0 bi is 2.55 m away. How wide is the slit?    mm

  If a slit diffracts 650-nm light so that the diffc/*6npjr cu f qll)bt)o tr477ys,wc* raction maximum is 4.0 cm wide on a screen 1.50 m away, what will be the width of the diffraction maximum for light of *l7t6cclnjpyq rs tr4ouwf)b,c7 /*)wavelength 420 nm?    cm

For a given wavelength m *-dr 3woes8w$\lambda$, what is the maximum slit width for which there will be no diffraction minima?

  At what angle will 560-nm light prozm*)tmb/xrs ,duce a second-order maximum when falling on a grating , tmrmz)xb/*s 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 .v374e kfyedl have if the third-order occurs at an edf74v 3ylke.18.0$^{\circ}\,$ 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 ofmga:i-cpt(*4kiqf / l g:x(oh 589-nm light falling on a diffraction grating is observehiqga((:k o *mxg-i:/ ftlp4c d at 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 has b+3xdsee(da( l3x(ifj h )t5j $ 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 a y0f 1n:dy4pb z$9700-line/cm$ 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 with 6000q*;;l 9 mb0pdg3miynk lines per cm is illumin ;d my*g3pbmk0ni;lq9ated with 633-nm laser light? Assume normal incidence.   

  Two (and only two) full spectral orders can be seen on either m1*0mdgd7as yv82qrfside of the central maximum when white light is sent through a diffracti1adr* 0m f myq8dg72svon 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 nwh0ouwf.z 8kmt w5;o *i( li,lm falls on a grating withf hol(tok,wm i0.w;zuw 8l*5 i $8500\;lines/cm$ How wide is the first-order spectrum on a screen 2.30 m away?    m

  A He-Ne gas laser which produces monochromatic light;kj w6ud c.q/r 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 measure3a,k3 2 spiljq;wt1hvz)f .gsd 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 wavu ikt/v1ahsn9/g k2+uelength is most strongly reflected at the center of the outer surface when illuminated normally by white liun 9+h /autgkvs1/ik 2ght? Assume that $n\;=\;1.34$. $\lambda$ =    nm ,which is an    -  

  How far apart are the dark fringes in Example 24–8 if the glass plates are eag-xc. okh,a(g(a u r4jch 26.,jkhxg(a.rcag o-4( u5 cm long?    cm

  What is the smallest thic(in 8n8 j7prtgkness 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 yelloe t7c1iq0di :v8- djfvw ($\lambda\;=\;570\;mm$ 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*c,unrfv( zmx9. q:tc 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 thicf*u:.tn x,rv (c9qzc mker is the center than the edges?    $\mu m$

  A fine metal foil separates one end of +id+q y-in .z+ t4atzztwo pieces of optically flat glass, as in Fig. 24–33. When light of wavelength 670 nm is incident nzyz t+ +i .azn+-4qtidormally, 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 two flat glass surfaces ifb)s4pw0 zg 2yc the glass is to appeab)yc0p4 zgw 2sr 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 di,lny62gqtj)2v4t rg damond $(n=2.42)$ 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 alcohold1n 44*b elu, jfr0mk3ykz :pp $(n=1.36)$ 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 k6i(7th ljvk 6xtz+o2 apparatus (Fig. 24–31) is immersed in a liquid, the diameter ofki6( 2 +ohl7ztv6jkxt 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 the light enter (a/m+wv;nf5-9 vrxkyd jl)hfz/ oc+iing an interferometer if 644 bright fringes are counted when the movable mirror9 dix m5 nfkz;(/wrh+v+)jco/ya l fv- moves 0.225 mm?    nm

  A micrometer is connected to the movatmg)qq 2:2g3yji(d z7tnaeh(ble 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 wa:d(j a 2h7i3 gqq2(ntegz tym)velength of light used is 589 nm.    $\mu m$

  How far must the mirror l lo298kae0i r$M_1$ 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 ajs 1)n*-n8)8hkbn od(dj7l xk0fxwpn n interferometer (Fig. 24–59) passes through a small glass container containing a cavity 1.30 cm deep. When a gas is allowed to slown8)fxwd7*snn j kh8db()10knl po-jx ly 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 orq u01/vjh vc,wu9dx( eiented 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–wva juq88q (0jhfz+7l glass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s angle for a diamond submerged in water if the livgl:hsu 9ry,*7-e kxaght is hittinyek r-:7 slhv*9agx,u g the diamond $(n=2.42)$ while traveling in the water? $\theta_{p}$    $^{\circ}\,$

  Two Polaroids are aligned so th/51d4pqkztp*sd 7w na at the light passing through them is a maximum. At what angle should one of them be placed so that the intensity is subsequently * daz7kp /15n qdpwts4reduced by half?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be placed so as to h0 tefhn+9x2areduce the intensity of the incident unpolaaht 2enx+f h90rized light to
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are oriented at 4gpxv (tza91w47a , od+;w pvufxe:kl60$^{\circ}\,$ 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 oriehz m 8 xmz7lweq)m3znn4j;/ept)h ;l8nted at 38.0$^{\circ}\,$ to one another. Light polarized at a 19.0$^{\circ}\,$ angle to each polarizer passes through both. What percent reduction in intensity takes place?    %

  What would Brewster’s angle be for reflections off the surface r rb 3t(x1xl,8bm (okyof water for light coming from beneath the surface? Compare to the angle for total internal reflection, and to Brewster’s angr8b(tb3k ,mxyrl(o1 xle 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 pastrxent zdw/(:q3i7 h3ses through five successive Polaroid sheets, each of whose axis makesxd3irweznth3tq(7 :/ a 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength h.1f; g-h:c kmtdlo (8l+cqyw$ 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 re6p/;z;afn:ia e:di xeflecting from mountains or airplanes can interfere with the direct signal from the stati:ez 6d/efan;aii:;pxon.
(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 sourcesd:ax4 :wv5ytmwhb- 8h passes through a diffraction grating with hv ba4::x h5ydw-twm8$ 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 narrow slitsb:7q ok*8 xgiid/ +v1hfasl) q 0.60 mm apart. The screen is 1.70 m qiv)s/ *do+ qbgaf: 8i7xl hk1away. 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 broadcfp6hz)k3n f 8qba:o(sasts from two 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 at its midpoint as(kpa:q6bh f8z )n3ofnd 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 *ytel)6oop(k j +3wc ean outside doorway 0.88 m wide, and blows a whistle of frequy 6e*3oe+ ojlcp(t )kwency 750 Hz. Ignoring reflections, estimate at what angle(s) it is not possible to hear the whistle clearly on the playground outside the doorway.    $^{\circ}\,$ either side of the normal.

If parallel light falls on a single slit of width Dybhhz01u 9;ev 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. When bil 0imi56a5d*tb *zi a4ri9wnormally incident 460-nm light is reflected from the wing, the wingalti9 564aiw*b5i zr iib* 0dm appears bright when viewed at an angle of 51$^{\circ}\,$. How far apart are the lines?    nm

  How many lines per centimeter must a grlv:fg 2svst co+ lytm:x :v,h6sr)v) 5ating have if there is to be no second-order spec2g oss+l vy:tv:fxv t6,lrc v:)ms5 h)trum for any visible wavelength?   $ lines/cm$

Show that the second- and third-order spectraj l, -vxqyz)e5x36dsc of white light produced by a diffraction grating always overlap. What wavelengths overll, dvczsq6jx y-)x 5e3ap exactly?

  When yellow sodium lig;)wv(u fxs2lhp / nrg1ht, $\lambda\;=\;$ 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 a5 xn9gyzlg m+2 diffraction grating with and the pattern is viewed on a screen 2.5 m from the grati+5x9 g ynzm2glng. 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 mnr+/t iso y/s ;b x,j4bkaw8l-aterial if a minimum of 150 nm thickness of it, when laid on glass, is needed to reduce reflectb /a4s + j8,-oix/l rys;wknbtion to nearly zero when light of 600 nm is incident normally upon it? Do you have a choice for an answer?

  Monochromatic light of var(*mmdd 3l,pail*qpp32 x zev1iable wavelength is incident normally on a thin sheet of plastic film in air. The r (l*1,pp x3adezv3ipm*d l2mqeflected 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 aixjj0y/d: zprmb+ 2j-nti-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 between two flat glaa7 ; m apmd8165pinhg0;phsw sxu r7r1ss surfaces if the glass sangw;10rar p d1pm h7x7;58u i6hmsp is to appear dark when 640-nm light is incident normally?    nm
What if the glass is to appear bright?    nm

Suppose you viewed the light transmitted through a thin film layez :nvhk8n9v8ired 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. Con8 hnv9zi:8vn ksider 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 is the Sun when light reflbbbq i(p /6f 61jdvlw2ecting off a smooth lake is polarized most strongb d v6 jq6bfp/l12(ibwly?    $^{\circ}\,$

  At what angle should the axes ox/fjyxl,hd q im3- 4 sx*9ska:f two Polaroids be placed so as to reduce the intensity of the incidentsf ,9:x*dx-4ymx s3jh/k ilaq 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 transmissijf-1l)gkr au8w09x ic on axes are at right angles. A third polarig81 jklfwr ca0-i 9)xuzer 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 thei xxr 6mimk6yv+x2bn./r 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 width 1.0 cmve(: f+xq8sb cpq4w-p and is pointed at the Moon, which is approximately 380,000 km from the Earth. Assume the laser c4qx p8ep:q(w+-fb s vemits 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 each placs -svw(7flm-)hx tn +bed 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 n4 kt 8/(-cwp)p4b rae5fs tih$(n=1.34)$ 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 php82tb 2rhp5uo5jcln8m 4 yx .zase with each other. They 4b58oc u28j.z2 mp l5ynt rhpxare located 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 wavelengths, 420 nm and 6i 6z-aob k1vt950 nm, enters a silicate flint glass equilateral prism1a6vt bi-zok9 (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 surface and one with rz-dlt+( w ,zqb*r 0wl$R\;=\;18.4\,cm$ 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