Does Huygens’ principle apply to sound waves? To water waves? Expgje- e/:ec.u;o pplgx4t1vcd*5 2xnplain.

What is the evidence that ligh, *c,eh kjhrpv+l,g;4a hz ;bzt is energy?

Why is light sometimedu0n:xhkdy k+1ic 8e / bkn6./sb.aszs described as rays and sometimes as waves?

We can hear sounds around corners, but we cannot see arounargzp 1ou ub +0:0c) 8abljkxhu ,pb:;d corners; yet both sound and light are waves.0a;0p gluu:1+h8r cxbbk j a,p:z)bou Explain the difference.

If Young’s double-slit experiment were submerged in water, howil8ongng(o-ocz :q7 . would the fringe pattern be chqgn8i .(z gl:oc7no o-anged?

Monochromatic red lighde 1t0hgi70ke *bvqu/ q e-hm:t is incident on a double slit, and the interference pattern is viewed on a screen some distance away. Explain how the fringe pattern would change if the red light source is replaced by a blue light sot:01/ikq*q0b m7e h-dev eu hgurce.

Two rays of light from the same source destructively incyw0mg8se r 24terfere if their path lengths differ by how 248r ew ycgm0smuch?

Why was the observation of the doubleq hg(; 59ps2cphvrl1e -slit interference pattern more convincing evidence for the wave theory of light thep(1cgsp hq9v 2;h5lran the observation of diffraction?

Compare a double-slit experiment for sound waves to that for light w.jpok3*hn mb-xgr rw52u8 - hoaves. Discuss.bokmj-o*g uw 3h8 5-2h xrnrp the similarities and differences.

Why doesn’t the lighqvs9a z6t64t ht from the two headlights of a distant car produce an interfere 64tqzth6av9snce pattern?

Suppose white light falls on the two slits of Fi:dk6gxj z6go-/hgbe5: p .xo-b0npsxg. 24–7, but one slit is covered by a red filter (700 nm) and the other by a blue filter (450 nm). Describe the pattern on the sk :xgxxb . 6/pb0o5 g hsoje-:6pndgz-creen.

When white light passes through a flat piece of window glass, it is not brokw hcq xc16d5(vc0kf- cen down into colors as it0c q6c-v5(1fd x cckhw is by a prism. Explain.

For both converging and diverging lenses, discuss how the f vakl1z*cs9fx96don7;; xdr rocal length for red light differs from tfa x6dkrc91;x znvol*r9; d7 shat for violet light.

A ray of light is refracted through three diff cto9/q5k7sucerent materials (Fig. 24–55). Rank the materials according to their index of refrc/ kq9c7 t5ousaction, least to greatest.

Hold one hand close ,y.vy3u2 ykin:p1 yyzto your eye and focus on a distant light source through a narrow slit between two fingers. (Adjust your fi zk12yyyni. yp:3yvu ,ngers to obtain the best pattern.) Describe the pattern that you see.

What happens to the diffra/pmrul o3iyak 92bf)8 ction pattern of a single slit if the whole apparatus is immersed in (a) water, (b) a vacu3b)8oakuyfip /2r9lmum, instead of in air.

For diffraction by a single slit, what is the effect of increasing (a) the sli mr3i1 3r/izi;pm;gfyt width, and (b) the wavelength?1mr yz/i3f;i ;p m3gri

What is the difference in the interference patterns formed (a) by two slitsjn)p,i or;bjmibop3l 85,hla0l0* iv $^{-4}\;cm^2$ apart, (b) by a diffraction grating containing $10^4lines/cm$?

For a diffraction grating, what is the advantage of (a) many slbx4st t-87ug2w wrkl24 xd/dqits, (b) closely spaced sliqdx7d2/k -4xlrbtt4wu s w2g 8ts?

White light strikes (a) a diffraction grating, and (b) a90 yd rq.wkmd) 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 each case? Explainwk0dyq drm 9)..

For light consisting of wavelengths between 400 nm and 700 nm, incident normal,wlt*/f(nl8ctu. tv vsf79uo ly on a diffraction grating, for whatvll/ ts(c9u f.t*wf8vtu7o, n orders (if any) would there be overlap in the observed spectrum? Does your answer depend on the slit spacing?

Why are interference fringes noticeable only . aa1g op1eotit)c*:y for a thin film like a soap bubble and not for a th ga*y1oecpt1 ao):i.tick piece of glass, say?

When a compact disk (CD) is held at an angle in white lk79hn 7:o hzdeight, the reflected light is a full spectrum (Fig. 24–56). Explain. What would you expect to see if monochromatic ligod7e h:7h 9nkzht was used?

Why are Newton’s rings (o9* sjvu)r xyxyf:0g3l9z/o cFig. 24–31) closer together farther from the center?

Some coated lenses appear greenish yellow when seen by reflected93luj6i /z cc58qal xo:fjzp * light. What wavel9xaj8cpzoll u :z*q3/5c6ji fengths do you suppose the coating is designed to transmit completely?

A drop of oil on a pond- c(p a ehy4nll; tbki5l7+fja.0:nhl0fba3d appears bright at its edges, where its thickness is much less than the wavelengths of visible light. What can you say aboynl(eh bfal50:ha nll jp;3cb4 . k-dtif+0a7ut the index of refraction of the oil?

What does polarization tell us about the n3,kh(f jbpz0iature of light?

Explain the advantage of polarized sunglasses over normal tinted sunglaj t, m9u5py.ame(yrqsr mj1.3sses.

How can you tell if a pair of sunglasses is polarizing or nsln;evp d/f,5i;d b o/ot?

Two polarized sheets rotated at an angle of ft*p/ zx: yucso6td/; ec1 v3 jrft1d)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 had no qu,if ;f,i7ggatmosphere?

If the Earth’s atmosphere were 50 times denser than it is, would gw+ 2c l5ko7i.u ;nofcsunlight still be white, or7io+.;fng5ckcuw2ol would it be some other color?

  Monochromatic light falling on two slits 0.016 mm apobp *ki7 ht 0ml.ig3+fart produces the fifth-order fringelmko3i7i g+tb 0p f.*h at an 8.8$^{\circ}\,$ angle. What is the wavelength of the light used?    $ \times10^{-7 }\;m$

  The third-order fringe of 610 nm light is observed at an angle odxow etjfr9. k 9xfah7 ,9*vz(f 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 0.0l2s-c qh +rq+f48 mm apart. Successive fringes on a screen 5.00 m away are 6.5 cmrhc q+-l +2fqs 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 thg.i q/ 5tv*zfpea)1 laser, with a wavelength 656 nm, falls on two 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 a1ta )e5hqvt*z i./fgpway?    cm

  Light of wavelength 680 nm falls on two slits and produces an interference pattei /.*be tce0f6i,kgnu ru9 gc1,s a:kdrn in which the fds gre1ebf96ua i g:, 0,*c.uki/k tncourth-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 p+ 86b a il x*qx5myw.skapje(6asses through two slits 0.58 mm apart, how far apart are the second-order fringes for these two wavelengths on a screen 1.0 m away? a 66wap+jl yx5iqs(kb8x* .em    mm

  In a double-slit experiment, it is found that blue light of wave-:eyge .7 gpmtlength 460 nm gives a second-order maximum at a certain location on the screen. What wavelength of visible light would have a minimum at the same locatio7 tg: gem.pey-n?    nm

Water waves having parallel cres2yuw(rgdc099q hj;kure ;u o9tazch)5y y.3 vts 2.5 cm apart pass through two openings 5.0 cm apart in a board. At a point 2.0 m 9rkt9 vuh)5(zdyqr.e3 y;;h02ucoagj c 9w yubeyond 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 frontmx or hsowt.5yl ,29u+ of the lower slit in Fig. 24–7 so that the twm. yox ,5h9o2l+rtwsuo 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 wavelenc0ury)x*(6tvq : oglvynvg 9; gth 500 gtn : cv vqy6;9g*0 xu)o(ylvrnm 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 of this light be located?    mm

  Two narrow slits separated by nqur/y/-yg(x 1.0 mm are illuminated by 544 nm light. Find the distance between adjacent bright fringes on a screen 5.0 m from the slits/uynyr/ q-gx(.    mm

  Light of wavelength 480 nm in air falls on t9*2fho0a(e;l 7 astz o;fbora wo 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 srb8p+ +jv 7qeplit of a double-slit apparatus illuminated by 640-nm light. The center point on the screen, instead of being a maximum, is dark. What p++8qpjber7v is the (minimum) thickness of the plastic?    nm

  By what percent, approximately, does the speed of red vie sg3y(9m qeg4js)1light (700 nm) exceed that of violet light (4 1 3mjesvq)gyei4(g 9s00 nm) in silicate flint glass? (See Fig. 24–14.)    %

  A light beam strikes a piech(d9 rwd fun53e 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 light*nw jl3z-t9p 91l u09ybal aob 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 slit8vz* ey+ fi2evmow,x- 0.0440 mm wide, what is the full angular width of the central diffractw,eif-v8*ove2z+m x yion peak?    $^{\circ}\,$

  Monochromatic light falls on a s;+ziaz*yrdu0gbd/e3i 7ev4 glit 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 on a slit that wv3uqf +42ye3/gf ujais $ 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+:h 4l5kw 5 hsqu8pnaeh of the central maximum (in cm) in the diffraction pah4sne5 :hq5 pak+lwu 8ttern on a screen 5.0 m away?    cm

  Monochromatic light of waveleng.h.obnfflp;3b l (f2 dth 653 nm falls on a slit. If the angle between the first bright fringes on either sob23( ;l.bpd .fhflfn ide of the central maximum is 32$^{\circ}\,$, estimate the slit width.    $\mu m$

  How wide is the central diffraction peak on a scr*qw*ixk+7p/ d4y z0az1jyru23jc slp /wti6 ceen 2.30 m behind a 0.0348-mm-wide slit ils/ dp1r6 7/auzkw z* 20xyijp4wcyi+qj l3*tcluminated by 589-nm light?    cm

  When blue light of wavelength 440 nm falls on a single slit, the first dark8 ::rp q+;*l-id dcdjix(gbiw bands on either side of center :w dilp8+ddi b:xi; g- jr*qc(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 chjxfd5*efj5 + entral diffraction peak that is 9.20 cm widejxff*5dje + h5 on a screen that is 2.55 m away. How wide is the slit?    mm

  If a slit diffracts 650-nmnlc .e/ 4w*ilh*ie-w j light so that the diffraction maximum is 4.0 cm wide on a screen 1.50 m away, what will be the widthle * / h*wwc.ejil4in- of the diffraction maximum for light of wavelength 420 nm?    cm

For a given wavelength3tkwxpk/ x*9p (-d1 kvicovp, $\lambda$, what is the maximum slit width for which there will be no diffraction minima?

  At what angle will 560-nm light produce a second-orderx4t jl7hop2:pvib0 *a maximum when falling on a grating whose sli0avxbt:*l j p i4o27hpts 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 g xsev c:4v7 z;u)n. ny3iv0gvprating have if the third-order occurs at an ngxv :.3z7v ycs4;v uv0pn)ie18.0$^{\circ}\,$ 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 fardxj c+:).vnv (bxhb-lling on a diffraction grating is observed at a 1bvv +jc.hrdn xb(: x)-5.5$^{\circ}\,$ angle. How far apart are the slits?    $\mu m$
At what angle will the third order be observed?

  A diffraction grating ha, z;1cytf7 ;r :c7rfsqo5a rhls $ 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 nji+/qoeg33.dfr +um on a $9700-line/cm$ grating is revealed to contain three lines in the first-order spectrum at angles of 31.2$^{\circ}\,$, 36.4$^{\circ}\,$, and 47.5$^{\circ}\,$. What wavelengths are these?
$\lambda_{31.2}$    nm
$\lambda_{36.4}$    nm
$\lambda_{47.5}$    nm

  What is the highest spectral order that can be seen if a grating with 6 67qe2 kqh6mog000 lines per cm gq76e q 62mokhis illuminated with 633-nm laser light? Assume normal incidence.   

  Two (and only two) full spectral orders can be seen 5u,g u dqu. ,(oabr(eeon either side of the central maximum when white light i ubrde(,u g5ae,o (q.us sent through a diffraction grating. What is the maximum number of lines per cm for the grating?    $ \times10^{ 3}\;lines/cm$

  White light containing wavelengtimjey p/ fkb-6j -)tik+gn a;*hs from 410 nm to 750 nm falls on a grating witht *ny-fp6iig k/eb- +)a; kmjj $8500\;lines/cm$ 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 knyws90xbjpi4 p2v jl +le (,-cqown 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 m;bsu eq:-d xsc ,8afmfb7hs94ju / v)ceasured 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 wm8gj5k und: -xavelength is most strongly reflected at the xd-n mgu:5j8k center of the outer surface when illuminated normally by white light? Assume that $n\;=\;1.34$. $\lambda$ =    nm ,which is an    -  

  How far apart are the dark fringes in Exampl cp*cuw pmi/ 9p,5gqo2s7i2tm e 24–8 if the glass plates are each 26.5 cm long? cpq t59*wsiu2m7o2 m,g /icpp    cm

  What is the smallest thtml ) ;swv (gx,4-hkxhickness 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 greeng+:cdc1 3gk3f w5v fqyish 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 an qh/jit 2x34nkd 31 dark Newton’s rings (not counting the dark spot at the center) are observed when 550-nm light falls normally on a planoconvex lens resting on a flat glass surface (Fig. 24–31). How much thicker is the cextnk3 /q2h j4inter than the edges?    $\mu m$

  A fine metal foil separates one end of two pieces of opticalln:d *j971f4waew)vs.giw wyiy 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 thick9i*jai vy1wdns w :w.w4e )gf7 is the foil?    $\mu m$

  How thick (minimum) should the air layer be between two flat glass surfaces if t.ry 2 oiqgx0.the glass is to appear bright when 450-nm light is incident normagy2oix.0. rtq lly?    nm
What if the glass is to appear dark?    nm

  vA piece of material, suspected ofwu uteq) .zj90ui .ejwmy 8k;+ sovk-3 being 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 alcohofcenx9-o n+ q,ltmv**wbc3v 6l $(n=1.36)$ 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, 2p/iqpuus :6o the diameter of the eighthqspi o:puu2 6/ 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 entering an in y8n0bdk9uh0l+ie1 +4eiem hdterferometer if 644 bright fringes are counted when tey +n 4ii hd0el0 1bu8md+he9khe movable mirror moves 0.225 mm?    nm

  A micrometer is connevxj3pxz3q)*ykw0a o: cted to the movable mirror of an interferometer. When the micrometer is tightened down on a thin metal foil, thv3j*x3x0 owzyaq:p k)e net number of bright fringes that move, compared to the 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 mirr*4c0 mhfqga4qor $M_1$ 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 b .q7,jwvg3it interferometer (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 7iqg.w ,3b tjvcontainer, 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 aetcg,5cvu6q v6 /c6mjt 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 d vq*sbvt3.k ;air–glass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s angle for a diamond submerged in water if the light is )+ imfbp h,v (cm16gw):oqntlhitting th+p ,o bctviw1h)m: f6l(gmqn)e diamond $(n=2.42)$ while traveling in the water? $\theta_{p}$    $^{\circ}\,$

  Two Polaroids are aligned so that the light passing through :5)i5 z lj4pb ar (r fbm5o,kmpdux;0xthem is a maximum. At what angle should one of them be placed so that the intenslb:a m5r(zpb5i 0f 5m4),;purkxojdxity is subsequently reduced by half?    $^{\circ}\,$

  At what angle should th7,+w eqdr 6lbxtej9 6ee axes of two Polaroids be placed so as to reduce the intensity of76+l 6xd b,jrt9eewq e the incident unpolarized light to
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are oriente0ep r:2adhdp6vahe ; hu 4)*zqd 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 ori h0+lwj-o 3 ak-ezv4 *aj y*ou(o1qzmfented 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 surf n83*y v/wicpj ao7h:aace of water for light coming from beneath the surface? Compare to the angle for total internal reflection, and to Brewster’s angle from above the surface. a7c3w8a:iy*/j nvpo h
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, h jl.u.6d0o m- wh(gtjeach of whose axis makesmw6gj0.hu .thjo d (l- a 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength /(j0x wf mi2 ;v,gc6r adoqx5l$ 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 re+sb .8fx*9:r5a b gg misrt.qsflecting from mountains or airplanes can interfere with t.issbrs.*g : 5bqxma+9 f8r gthe direct signal from the station.
(a) What kind of interference will occur when 75-MHz television signals arrive at a receiver directly from a distant station, and are reflected from a nearby airplane 118 m directly above the receiver? Assume $\frac{1}{2}\;\lambda$ change in phase of the signal upon reflection.  ----待选择----constructivedestructive 
(b) What kind of interference will occur if the plane is 22 m closer to the receiver?  ----待选择----constructivedestructive 

  Red light from three separate sourcsu4hhb1u*/sw es passes through a diffraction grating with b1hwu4 ss* /hu$ 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 niq+9 z,7xgd2 ,vk,fxp oulp;yarrow slits 0.60 mm apart. The screen is 1.70 m away. A second source of unknown wavelength produces its second-order fringe 1.3+,pk 7p,ygdx lxq29u;o,v ifz3 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 operaj1qi8wz2p.yu m 7oz4w ting at 102.1 MHz broadcasts 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 and extending horizontally in both directions. If the midline is takenmoz u28pyw 7iwq4zj1 . 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 dsfbo1j*t-q -poorway 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 whp *sot--q fb1jistle clearly on the playground outside the doorway.    $^{\circ}\,$ either side of the normal.

If parallel light falls on a sx15sy xl ;y7bmx1 i,zuingle 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 acro( qkk-1q3v hwcss them. When normally incident 460-nm lighq1w k-h3q(kvc t 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 maad:. mlw jb ye:wxx80 sa5i(3ust a grating have if there is to be no second-order spectrum for any vis daa s amwlj80i:ewxbx.: y3(5ible wavelength?   $ lines/cm$

Show that the second- and third-order spectra of white light produced by a d(7ch/ vf+-q cxm boh qre7k.e5iffraction grating always overlap. What waveleng/q7(h-f.vok7xc h+rbeqce5m ths overlap exactly?

  When yellow sodium l6jhb6jq,1mp awktk6;ight, $\lambda\;=\;$ 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 pattxn bxx 7rm vv83t:l/ j7dn,oor 5((rrlern is viewed on a screen 2.5 m from the grating. The incident lightox tr8m5jr,r 3r7vb7dvo:nlx (/lx( n 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 of22 pw 1;edytrxi8mvh u v)0i;l13 oeljer8xy5 a clear material if a minimum of 150 nm thickness of it, when laid on glass, is needed to reduce reflection to nearly zero when light of 600 nm is incident normally upon it? Do you have a choice for an an l)etxhy 08rxe; io iumvlr52pd 38 wj2v11ye;swer?

  Monochromatic light of variable wavels+j4stp(jgx1+ +/xz a 1 kwmclength is incident normally on a thin sheet of 1j++ tzp4j /glk(ma1+s xwcxsplastic film in 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-reflective c i,r.rue+ yybps2om15qvqf 3g2 h-7dxoating $(n=1.38)$ 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 fyb5j6 oapqc1 e8r4vj* m* xccg4t1 -npor the air layer between two flat glass surfaces if the glass is to appect*r-1qagvc* b54n8p ycep61m o4xjjar 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 layeryd.fn;: o r4lged 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 vfod rln4:g ;.yalues 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 92xc*j1+;nm nv(uuntyuwq o . horizon is the Sun when light reflecting off a smooth lake is polarized most stronglynyun2;owt m u+n (x9uj.*c v1q?    $^{\circ}\,$

  At what angle should the axes of t/oaqx1..so)kl xpy /rwo Polaroids be placed so as to reduce the intensity of the incident unpolarized light by an additional factor (after k)lpo /.y sxq.ax1o/r the first Polaroid cuts it in half) of
(a) 4,    $^{\circ}\,$
(b) 10,    $^{\circ}\,$
(c) 100?    $^{\circ}\,$

  Unpolarized light fal a8cb xkn202m n;an7fay)h8 xpls on two polarizer sheets whose transmission axes are at right angles. A third polarizer is placed between the first two so that itan 82k8xfy n) n hap2ca70mb;xs 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 su5x+ 7ao5f p6npdw 8vbjwukb (8ccession with their 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 )f uu:okjp s4i.r 8/kj1.0 cm and is pointed at the Moon, which is aok/).r48 kuf j upis:jpproximately 380,000 km from the Earth. Assume the laser emits waves of wavelength 630 nm (the red light of a He-Ne laser). Estimate the width of the beam when it reaches the Moon.    km

  A series of polarizers are each plapq ns6,xf.nuxk/b .sjdi ((4 aced 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 dfd8e olrj0s /k6wc 0i 58yni*$(n=1.34)$ 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 a:7vnlp j*02ifx as.x 6.0-MHz radio waves in phase with each other. They are loca.lvia*n: s2pa f0x7jxted 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 650 nm, enter-77v m(l k q-su;tvyqhs a silicate flint glass equilatkhtqvs muy7(q-;-v 7 leral 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 surfacv ,tot i w qdnz-79:prnrh1b5*e 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