Does Huygens’ principle apply twcwiior- iw+ 0 i; rmw/6b.sbf4,wv f4o sound waves? To water waves? Explain.

What is the evidence that light ir;z,0o1h 1b8vtu f6 k/mg0hgthj x0nns energy?

Why is light sometimes described as rayso d3bu(d*-j5q(c)low3fiv mt and sometimes as waves?

We can hear sounds around corners, bsc(,axue/ :s- al ivw*ut we cannot see around corners; yet both sound and light are waves. Explain the difference( *cisx/w,vu: -ls aae.

If Young’s double-slit experiment were submerged vxbzfl9:i48l in water, how would the fringe patt4 llx:9f8vb ziern be changed?

Monochromatic red light is incident on a double slit, and td :/kg85lypohvz (s p-he interference pattern is viewed on a screen some distance away. Explain how the fringe pattern would change if y:(v d5h - so/pzk8glpthe red light source is replaced by a blue light source.

Two rays of light from v7q mo7bmv0f 9the same source destructively interfere if their path lengthvvqfo7m0 9m 7bs differ by how much?

Why was the observation of the double-slit interferh850: o(qgn*;erobn snei bw +ence pattern more convincing evidence for the wave theory of light than the observatehgrwnqn8s :in5bbo;+*0(oeion of diffraction?

Compare a double-slit experiment for s+c,5u008h)g uvjh ) jvqxs zyyound waves to that for light waves. Discuss the siy0uvu)x8jjs vhchz) +,50y gqmilarities and differences.

Why doesn’t the light from the two headlights of a distant car produce2zn lzc4imc5,6)d ote an interference patn265m ie zl4dc ),zocttern?

Suppose white light falls on the two slits of Fig. 242vwy-s h s*xz)–7, but one slit is covered by a red filter (700 nm) and tx2yss * )wv-hzhe other by a blue filter (450 nm). Describe the pattern on the screen.

When white light passes yp-(dj-,6h tejxvu *sthrough a flat piece of window glass, it is not broken dowesyh6*,v(upx-d j-jtn into colors as it is by a prism. Explain.

For both converging and diverging lenses, discuss how the fo ub ):t0ojo9jmcal length for red light differs fro j jobu:)0tmo9m that for violet light.

A ray of light is refracted through three different materials (Fig. 24–55). Ra:e:p+udrsr4 ,z8-qfdq t qh( f .uko/enk the materials according to their index of refraus .rdz:(huke+d/ :pq- fqtr84feq,oction, least to greatest.

Hold one hand close to your eye and focus on a distant light source tvatf4 ;83,ayxvhrz 2shrough a narrow slit between two fingers. (Adjust your fingers to obtain the best vv4yth;32fasz8ax,rpattern.) Describe the pattern that you see.

What happens to the dg rb fhhi/ +8c0j0k,ddiffraction pattern of a single slit if the whole apparatus is irh/jgd h 0bf+dc8,ik0 mmersed in (a) water, (b) a vacuum, instead of in air.

For diffraction by a single slit, what is the effect of increasinguyiw2pw lrcj+:p y+xm50: 4tgo n g8g8 (a) the slit width, g+mn428r5wcuyg lx:pp j o:it80+w gyand (b) the wavelength?

What is the difference in the interference pat 7hal6tdk i-f(k;hsb 67/+g3azmlf dqterns formed (a) by two slits $^{-4}\;cm^2$ apart, (b) by a diffraction grating containing $10^4lines/cm$?

For a diffraction graxcz bc; jx-y9/ting, what is the advantage of (a) many slits, (b) closely /jyc-zxcb; 9xspaced slits?

White light strikes (a) a diffrairb / -5ur9f2;3y kqoz otx3nfction grating, and (b) a prism. A rainbow appears on a wall just below the direction of the horizontal incident y33 i5f 2r trbz/kq9;-no fxoubeam in each case. What is the color of the top of the rainbow in each case? Explain.

For light consisting of wavelengths between 400 nm and 700 nm, incident normalxsztm owcg8r;h4x6pc7/2+z h*u-jal ly on a diffraction grating, for what orders (if any) would there becxs 2hml4o7ztr;g8*az-chp w/ ju6x+ overlap in the observed spectrum? Does your answer depend on the slit spacing?

Why are interference fringes noticeable only for a t7qy:i ;wp( rqn2tch (chin film like a soap bubble and not for a thickc7cy(:iqpn(r h;2 wtq piece of glass, say?

When a compact disk (CD) is held at an angle in white l r m0p7fop4u9fr( g6oish 4l(gight, the reflected light is a full spectrum (Fig. 24–56). Explgm u f7g44s0(96fr p priloo(hain. What would you expect to see if monochromatic light was used?

Why are Newton’s rings (Fig. 24–31) closer t-qw d8 s1tn6vkogether farther from the center?

Some coated lenses appear greenish yellow when seen by )nxyo/l))sjd reflected light. What wavelengths do you suppose the coating is designel/y)o)jn xds) d to transmit completely?

A drop of oil on a pond az.jrf 5sx+ y w95cvpmet0+8gappears bright at its edges, where its thickness is much less s5cpj8e. wtg +v5r+f yz09x mathan the wavelengths of visible light. What can you say about the index of refraction of the oil?

What does polarization tell us about5sc- y:senfs ( the nature of light?

Explain the advantage of polari9tn fvi87km53 el3raczed sunglasses over normal tinted sunglasses.

How can you tell if a pair of r)aikuorm78rx(k48cw5 nqu: sunglasses is polarizing or not?

Two polarized sheets x8(sc.7 bb +wukoi7bgrotated 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 sh jx-6m1qsdap e m1v7.ky if the Earth had no atmosphere?

If the Earth’s atmosphere were 50 times denser than it is, would8xz qcauh+8gvu dl.d+ aw, t+5 2oqj0s sunlight still be white, or woul uzsgjlv++wx80c,+5haqd dqoa8. u 2td it be some other color?

  Monochromatic light b9w).pq vl0kut,oiexc:ou + ;falling on two slits 0.016 mm apart produces the fifth-order fringe at a0.,wq+io9ktxcl:u o; pbe)u vn 8.8$^{\circ}\,$ angle. What is the wavelength of the light used?    $ \times10^{-7 }\;m$

  The third-order fringe of 610deq0 kq9mm-8 wbj(v*u nm light is observed at an angle of 18$^{\circ}\,$ when the light falls on two narrow slits. How far apart are the slits?    $\mu m$

  Monochromatic light falls on two very nayhu6f2lid4 5l(ww j 9errow slits 0.048 mm apart. Successive fringes on a screen 5.00 m away are 6.5 cm apart near the center of the pattern. Determine4 u(2j9i6heydl lww5f the wavelength and frequency of the light.
$\lambda\;=\;$    $m$
$f$ =    Hz

  A parallel beam of light from a He-Ne laser, j0dlspz2,ju;pl:. okeme -c) with a wavelength 656 nm, falls on two very narrow slits 0.060 mm apart. How far apart are the fringes in. spc-j o0kee:2zldup;l), mj 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 interferemvkr 9 tg 59gj4t)t(nq,+usjsnce pattern in which the fourth-order fringe is 38 mm from the central fringe on a screen 2.0 m away. What is the separation of n9+)(gvgj9q k,4 5 utsmstj trthe two slits?    mm

  If 720-nm and 660-nm4 w4pxbdxp5)r light passes through two slits 0.58 mm apart, how far apart are the secon)xwrbd 4x4pp 5d-order fringes for these two wavelengths on a screen 1.0 m away?    mm

  In a double-slit experimee l olm 5pla.*w*rt*0hn)bj6xnt, it is found that blue light of wavelength 460 nm gives a second-order maximum at a certain *l0mbjlo.l*5nr x*w)a6 t phe location on the screen. What wavelength of visible light would have a minimum at the same location?    nm

Water waves having paralleldz5;8illq f h1 crests 2.5 cm apart pass through two openings 5.0 cm apart in a board. At a point 2.0 m beyond the board, at what angle 5 i18zq hfd;llrelative to the “straight-through” direction would there be little or no wave action?

Suppose a thin piece of glass is plav4 karxjn o bm*k3 pa60jp9;q0ced in front of the lower slit in Fig. 24–7 so that the two waves enter the slits 180mq 4rap k6o k;*xjv00 jp39nab$^{\circ}\,$ out of phase (Fig. 24–57). Describe in detail the interference pattern on the screen.
24-7
24-57

  In a double-slit experiment,4k,.zc2hs*q)-sbd ,) o l fcy/axsuth the third-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 throughzq4oyuk.chfa2ss-sd h /)t * xlbc),, 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 2bd,:wg 7xfys mm are illuminated by 544 nm light. Find the distance b2 xfd sb:ywg,7etween adjacent bright fringes on a screen 5.0 m from the slits.    mm

  Light of wavelength 480 nm in air faljb48/tgaz*af eg 5dxupsl2) ;ls 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*b2b. aw5nujk1f k5nj=1.60) covers one slit of a double-slit apparatusjbw kj5n2.nbu1 f k*5a illuminated by 640-nm light. The center point on the screen, instead of being a maximum, is dark. What is the (minimum) thickness of the plastic?    nm

  By what percent, approximatelyt(,y)kq:p y xcycgx, (, does the speed of red light (700 nm) exceed that of violet light (400 nm) yx(qcc:kyg, x py)t(, in silicate flint glass? (See Fig. 24–14.)    %

  A light beam strikes a pie, 7)ilv2:nej.evk9v 8yhqjb yce 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 containing two w s1z3jd4uiidt b2ijok4 qi)4)avelengths, $\lambda_1\;=\;450\;nm$ 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 full anggden0 . 2yy(rrular width of the central diffraction pd( y 0r2g.eryneak?    $^{\circ}\,$

  Monochromatic light f tiyn0t*sxb0m 3/c r(xalls on a slit 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 52 qyo :+b3rhih /2e jijj9zfu620 nm falls on a slit that is $ 3.20\times10^{ -3}\;mm$ wide. Estimate how far the first brightish diffraction fringe is from the strong central maximum if the screen is 10.0 m away.    m

  A single slit 1.0 mm wide is illuminated by 41wjpu1 h8z;rn-7in: aogref, 50-nm light. What is the width of the central maximum (in cm) in the diffraction pattern on a screen 5.0 m awag;p8:1ez1wr 7nhfuj ro- ai n,y?    cm

  Monochromatic light of wavelength 653 cyb(g6x-r 46 sk ggad.nm falls on a slit. If the angle between the first bright fringes on either side of the central mk ( dsg argc6x6yb.g4-aximum is 32$^{\circ}\,$, estimate the slit width.    $\mu m$

  How wide is the central diffraction peak o99s-,kscw nkmn a screen 2.30 m behind a 0.0348-mm-wid-nmsskw9c k 9,e slit illuminated by 589-nm light?    cm

  When blue light of wavelength 440 nm falls oq v:v+(omw4 mun a single slit, the first dark bands on either side of center are separated by 5 vm(v:mq w+4uo5.0$^{\circ}\,$. Determine the width of the slit.    $ \times10^{-7 }\;m$

  When violet light of wavelength 7cr-r1vc()x7mabqqv ,(q e)ya g4*ofedh ,o f415 nm falls on a single slit, it creates a central diffraction peak that is 9.20 cm wide on(farq -o bv,c*7y47m(1,)q)hfgcvq rdoe ax e a screen that is 2.55 m away. How wide is the slit?    mm

  If a slit diffracts 650-nm li7pj pcnge5/j/ft)0 a;kx(ha zght so that the diffraction maximum is 4.0 cm wide on a screen 1.50 m away, what will be )tkeajnh cp5 x0/ /jg;(afp 7zthe width of the diffraction maximum for light of wavelength 420 nm?    cm

For a given wavelengttm)abp8 +h8hl y:b0y bh $\lambda$, 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 when falj5 konf;.0z xlling on a grating whose slits are .o05;lnkxfj z $1.45 \times10^{-3 }\;cm$ 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 centi vho5k631qj wt2 crl,qq cz+n(meter does a grating have if the third-order occurs at an 18.1 ,qo c(vjl6t3qnk+hq5 czw2 r0$^{\circ}\,$ 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 ligh.4csd5tnmgicxx 1u 2l0k+ s/bt falling on a diffraction grating is observed/gc5kcxlud0it x. +bs14n ms2 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 ha5b*rh+fn0a+lt h e.yms $ 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 normallydr ;0 b.d+mtn;zjooc-d,f mpsac)n- g,wr-v. 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 sppsu ;6zek d34xectral order that can be seen if a grating with 6000 lines per cm is illuminated wspez;xu6d4 k3 ith 633-nm laser light? Assume normal incidence.   

  Two (and only two) full spectral orders can be ),gw i+:a le qs7gzee,seen on either side of the central maximum when white light is sent through a diffraction grating. What is the maximum number of lines per )gz:s+q weai7 ge, ,lecm for the grating?    $ \times10^{ 3}\;lines/cm$

  White light containing wavelengths from 410 nm to 750 nm falls o4*q6 6w +5sykejzvxlvn a grating with +5l6wj6 4se v*vzk xyq$8500\;lines/cm$ How wide is the first-order spectrum on a screen 2.30 m away?    m

  A He-Ne gas laser which produ, dm43 on6; qz/skpj9pbu 6kuqces monochromatic 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 hqk/l2 gv 3mykfj s0*4are measured by a $9500-line/cm$ spectroscope at angles, on each side of center, of +26$^{\circ}\,$ 38$^\prime$,+41$^{\circ}\,$ 08$^\prime$ and -26$^{\circ}\,$48$^\prime$,-41$^{\circ}\,$ 19$^\prime$. What are the wavelengths?
$\lambda_{26.72^{\circ}}\;=\;$    nm
$\lambda_{41.23^{\circ}}\;=\;$    nm

  If a soap bubble is 120 nm thick, what waveleng a1dl3::av gb w1d*gpcth is most strongly reflected at the center of the outer surface when illuminated normally by whi3g ld1wc1v g:b*:dp aate light? Assume that $n\;=\;1.34$. $\lambda$ =    nm ,which is an    -  

  How far apart are the dark frijt h 25gw*x mugg 7aau/x*4m2xnges in Example 24–8 if the glass plates are each 26.5 cm long?x7u*2u4gxg/5t w*a hmxma 2jg    cm

  What is the smallest thickness of 57f6 )b kyfin8c.jfyka 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 p;9 0 nfttx)mfv*shp+ ($\lambda\;=\;570\;mm$ 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 countifu;tub,,z) cdvk7 l/-rf;xtl ng the dark spot at the center) are observed when 55 /b)zc f;dv-;lurl,tf 7u,xtk 0-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 opticg2n z*2jg zn.oally flat glass, as in Fig. 24–33. When light of wavelength 670 nm is incident normally, 28 dark lines are observed nz*zg g.on22j(with one at each end). How thick is the foil?    $\mu m$

  How thick (minimum) should the air layer be between two flat glass sur/ bd-xt8f ocw+faces if the glass is to appear bright when 450-nm light is incident no wdfo+/tc- xb8rmally?    nm
What if the glass is to appear dark?    nm

  vA piece of material, suspected of dvnu y5j2t3f15flc *zbeing 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 alcohol9r 3h)9zc6c; mw l4vcl/5e+gi mf nzpz $(n=1.36)$ 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 immersedli t2ie9j2hh 5(( czx,)ihh4yb.auzm in a liquid, the diameter of the eighth dark ring decreases from 2.92 cm to 2.48 cm. What is the refractive indexjhtih chy9.xm4,uz i)ezlh(2i 25a(b of the liquid?   

  What is the wavelength of the lightzyot9o q:ac 9wvj tc/r,s8-4 h entering an interferometer if 644 bright fringes are counted when the movable mirror moves 0. q-4o 9 z9,h/wtcoac8 tv:rsjy225 mm?    nm

  A micrometer is connected to the movable mirror of an interferomete62l(i 8cbhsvjp w2l *etkp:/f r. 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 wavelengt2*lb hp/v8s ik(cwl62t:f jeph of light used is 589 nm.    $\mu m$

  How far must the mir 6neb81khomdywm t,ym0s 6.o*ror $M_1$ 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) pabqb)8/f*5c w8 u c)qcfw abzp9sses through a small glass container containing a cavity 1.30 cm deep. When a gas is allowed to slowly fill the container, a total of 236 dark fringes are counted to move past a reference line. The light used has a wavelength of 610 nm. Calculate the index of refraction of the gas, assuming that the interferometer is b) f98c *cwb)wc5bqa8p /qufz in vacuum. $n_{gas}$

  

  Two polarizers are ori qqp7fj,j9e-pllrz 9( ented at 65$^{\circ}\,$ to one another. Unpolarized light falls on them. What fraction of the light intensity is transmitted?   

  What is Brewster’s angle fo dn6v5a8xex:u*shh2 kr an air–glass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s angle for a diamond submerged in water if thsfks*l cjdqf,.3-u9b e light is hitting ,k3ub q-f lf*.cdjss9 the diamond $(n=2.42)$ while traveling in the water? $\theta_{p}$    $^{\circ}\,$

  Two Polaroids are aligned so that the lig3t1vpng- q1a *t5jhopg g4g 1kht passing through them is a maximum. At what angle should one of them be -v t4g o113naj k1pg*tq5ph ggplaced so that the intensity is subsequently reduced by half?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be placedi4 hruf;eo(4 1hj1j cd so as to reduce the intensity of(4urhjjc h 4io1f1 d;e the incident unpolarized light to
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are or/c r,u7r ;ubd9o*zl n8xzz i31ukn: eriented 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 orientem6t2xysna:n 4mik7n 5rz c55td 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 reflectiou1/3voidtp a7h rou h/. nl- e/-z;gvvns 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 from above the su/ue1rh .3 zgt/;/iva dpv vh-u -o7nlorface.
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 thrckex f 6k ,cnlp8p4z58ough five successive Polaroid sheets, each of whose axis makes apzf xe6 8nc48kkpl ,c5 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength : ; sb-izk e;fkw7yqa+$ 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 orwmp4n) layk9k(-o5 e f airplanes can interfere with the direct signal fr(na-w fe k4 5m)py9olkom the station.
(a) What kind of interference will occur when 75-MHz television signals arrive at a receiver directly from a distant station, and are reflected from a nearby airplane 118 m directly above the receiver? Assume $\frac{1}{2}\;\lambda$ change in phase of the signal upon reflection.  ----待选择----constructivedestructive 
(b) What kind of interference will occur if the plane is 22 m closer to the receiver?  ----待选择----constructivedestructive 

  Red light from three separate sources passes through 2dk,ii(y9 fh da diffraction grating with i hdyf9k,id2($ 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 slits 0.60 mm apnq4 1r7 pkdk+eart. The screen is 1.70 m away. A second source of unknown wavelength produces its second-order fringrn ek7 +1qdp4ke 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*i4*i,n hxsdn zx l3(l from two identical antennae at the same elevation but separated by an 83 l*d4ls(x,*zix ihnn .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+ cklm ;iq /c0rcxu6u0.88 m wide, and blows a whistle of frequency0 rk+u ;cim6l0 ccxqu/ 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 shb:l-wiv q3 fn9 0ato0lit 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 ppbsjktdj;5*a9d e zvb8qax1zo* m,w)9n-vv1 arallel lines across them. When norma98 *e-vs*znb11t x)k;qpwvd5d jzabvo 9j ,mally incident 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 cen c;y4:ztypi t-v5v1u ntimeter must a grating have if there is to be no second-order spect1z4 5tvtyp: -;i cnvuyrum for any visible wavelength?   $ lines/cm$

Show that the second- and third-ord9 uo; mrnk0s2veyr )ji:1h7r fer spectra of white light produced by a diffraction grating always overlap. What wavelengtho r)urfjv2ne y 0 s91rm:hi;7ks overlap exactly?

  When yellow sodium light,c g9o3u3ir.7j7 o47f,sbp lrha/ qeiz $\lambda\;=\;$ 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 o(v)*z m rzq2bhn a screen 22q*hrzv z(m)b.5 m from the grating. The incident light beam consists of two wavelengths, $\lambda_1\;=\; 4.6\times10^{ -7}\;m$ and $\lambda_2\;=\; 6.5\times10^{ -7}\;m$. Calculate the linear distance between the first-order bright fringes of these two wavelengths on the screen.    m

What is the index of refraction of a clear material if a minioe21ixfs*.w po9: sxamum 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? D 9x:sa2 f1p*w.xei osoo you have a choice for an answer?

  Monochromatic light of variablera2cj;- ,oalg+j uk3k wavelength is incident normally on a thin sheet of plastic film in air. The reflecteda3auc;,2jkk- g or+jl 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-rf )eo v3)sedct(g t4k9 g:r2gjjc0i( s+yagb7 eflective 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 a-wj 42j+j)lyf msse ym5h7m2uir layer between two flat glass surfaces ihf4-mj5m2)umy slj2syj+e w7 f the glass 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 layered on a dg;w5 :4da6 aw um:beuflat piece of glass. Draw a diagram, similar to Fig. 24–30 or 24–36, and describe the conditions required for maxideb uwgw46 : u:5aadm;ma and minima. Consider 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 wtw n/uxa:ag(ua7e 5/phen light reflecting off a smooth lake tn:/uxaa /pue57( gawis polarized most strongly?    $^{\circ}\,$

  At what angle should the axes of two Polaroids bv/;0x, hwjq vme placed so as to reduce the intensity of the incident unpolarized light by an additional factor (after the first Pol;v/wm 0j,xhvq aroid cuts it in half) of
(a) 4,    $^{\circ}\,$
(b) 10,    $^{\circ}\,$
(c) 100?    $^{\circ}\,$

  Unpolarized light falls on two polarizer sheets whose 1 zvnk 8:on pd;7pp+lltransmission axes are at right angles. A third polarizer is placed between the first two so that its axis makes a +pko ndl ;8:l nzvp17p62$^{\circ}\,$ 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 injq0 i2jz,p v;i succession 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 widr-+hju c7wp: qth 1.0 cm and is pointed at the Moon, which is approx7-p: r +cwqhjuimately 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 pl3r jo89v8vkqvaced 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 iq,// jbrv;vk$(n=1.34)$ 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 pha7e ac7h2* lvpw3am2 yhse with each other. They avael mh2237a7py*chw re 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 /0as qutkzi4) nm and 650 nm, enters a silicate flint glass/0)qza sk u4ti equilateral prism (Fig. 24–58).
(a) What is the angle between the two beams leaving the prism?    $^{\circ}\,$
(b) Repeat part (a) for a diffraction grating with    $^{\circ}\,$

  A Lucite planoconvex lens has one flabegdc+ ho 6-:rt 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