Does Huygens’ principle apply to sound waves? To water waves? Ex: f gg+iczkn5b2mk c(:plain.

What is the evidence that light is e6s zt1k+kkk 1onergy?

Why is light sometimes described as rays and sometimes awhhs:.3he4fs hz az92 2wvq6wt/r m a*s waves?

We can hear sounds around corners, bwp,rimjzu k y/597 cd+ut we cannot see around corners; yet both sound and light ri7u+zdj 5 /mkwyp,c 9are waves. Explain the difference.

If Young’s double-slit experiment were submerged in water, how would l t0.pb3m,,b ct3 jawrthe fringe patterb3 t,tc.3wba lj,0prmn be changed?

Monochromatic red light is incident on a do6fv)o c(zqh *:zogpvba2 8 hytbt-+4a uble slit, and the interference pattern is viewed on a screen some distance awa ovq )oz8(-fthy24:tv6+ b*p cazgbah y. Explain how the fringe pattern would change if the red light source is replaced by a blue light source.

Two rays of light from the same source destructively interf ppel ujq w)spl9y0vn1)4m0+27lrql fere if their path lengtvpq j0y p0ln4u)rell q 1s7wlf+ p)92mhs differ by how much?

Why was the observation of the double-slit integj4)df/ui d.la c4 bo.y)l9no rference pattern more convincing evidence for the wave theory of light than the observationlo ngdf 4)dj/c..)9obli4 uay of diffraction?

Compare a double-slit experiment for sound waves to that for light warp)uwnew5 . 2wqemq29 ves. Discuss the similarities and dien.uwqm)p 5wr 92e2wq fferences.

Why doesn’t the light from the t 05rcd4 0dhafnwo headlights of a distant car produce an interference adfh5c00 dn 4rpattern?

Suppose white light falls on the two sfpkda6-2 j69e0uisakr ) .it flits of Fig. 24–7, but one slit is covered by a red filter (700 nm) and the other by a blue filter (450 nm). Describe the )6r0k.p9f adsk iejuf6t-2ia pattern on the screen.

When white light passes through a flat piece of window glass, it is1+7*r aio:qe/5vcojymhe /u sgc p 61q not broken down into colors asje17:ihya sro 1*m/uqpc+eov q 56cg/ it is by a prism. Explain.

For both converging and diverqzz5 l8 2u*pt( qg+hrrging lenses, discuss how the focal length for red light differs from that forz gh 5l+r qzqr(8*upt2 violet light.

A ray of light is refracted through three different materials (Fig. 24–55). Rad;7a. pyxstm0 vlh6+y nk the materials according to their index of ref.t+ld y;py0 xhmva s67raction, least to greatest.

Hold one hand close to your eye and focus on a distant lighkz(i o+bkn(a oy)ed0330l h m)kvs g-qt source through a narrow slit between two fingers. (Adjust your fingers to obtain h+0z k-3i( b)g)asdlno o qk(vy3kme0 the best pattern.) Describe the pattern that you see.

What happens to the dif/otr m60sorpa6 i.j)gn0md6 zfraction pattern of a single slit if the whole apparatus is immersed in (a) water, (b) a vacuum, instead r6 )/anrojzs6m6.toi0m pgd0 of in air.

For diffraction by a single slit, what is the effect of increasing (a) the pgsox:g 4tgu ome) +oti5zh)y 0)( yg:slit widot ggy yugg(ipxm+4)tos:)0 e)z :5oh th, and (b) the wavelength?

What is the difference in the interferenc0f9wf1istcovu j;m xs8;)s1cw+ 3k;zx; vksre patterns 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 advantagep2/gjkk zfmf);r/k y 2 of (a) many slits, (b) closely sjmf;y2 )kzgkf k/2pr/paced slits?

White light strikes (a) a da *koo/c: o:. tccmx0kiffraction grating, and (b) a prism. A rainbow appears on a wall just below the direction of the hori:/.mo: 0ac*ckc toox kzontal incident beam 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 norma7jngm , ix4mf/ p;6l2odne6 m/:hrxe tlly on a diffraction grating, for what orders (if any) would ther mft x;i7d/e egn2mhnpo/4xm,j6:l6re be overlap in the observed spectrum? Does your answer depend on the slit spacing?

Why are interference frie*lu16cndf)y 4mo 4dynges noticeable only for a thin film like a soap bubble and not for a thick pieo1l4)6dycmu fe y nd*4ce of glass, say?

When a compact disk (CD) is held at an angle in white light,.oagqjxz (;2g,x6pw f the reflected light is a full spectrum (Fig. 24–56). Explain. What would you expect t x( fq.x;,6 2gpzojgwao see if monochromatic light was used?

Why are Newton’s rings (Fig. 24–31) closer together f )dvi )-k8iuqharther from the center?

Some coated lenses appear greenish yellow when seen by reflected li8:1tnq 9az pq1olwh09 1clb oight. What wavelengths do you suppose the coating is designed to transmzic p9nq wtq81l1h9:aoo0l b 1it completely?

A drop of oil on a pond appears bright at its edges, where its thickness if- tf rtvtty:a * 0nki,x926wds much less th6xnw 9ti tvdta -0ff,*t 2r:ykan the wavelengths of visible light. What can you say about the index of refraction of the oil?

What does polarization tell us about the n5bfj7h- z)a vyature of light?

Explain the advantage of polarized sunglasses over normal tinted sungla( ag0zb.1 c:elanxl8j+bz-m x sses.

How can you tell if a pair of sunglasses is pol m)o 2penn3 6h*;chmzlarizing or not?

Two polarized sheets rotated at an angle ofolzpkh7nfwj c2pk4b* f568)q 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. a(3qmcj(du p1ygm,.f bcf0 *cz 3ipa if the Earth had no atmosphere?

If the Earth’s atmosphere weiq)/ nq 9 tdl52qyuk60bt* dxdre 50 times denser than it is, would sunlight still be white, or would it be some other color?b09qd d)t 2ikyt/qxnqd *65 lu

  Monochromatic light falling on two slits 0.016 mm apm gssy7zn,5 +yart produces the fifth-order fm+yy5z7nss ,g ringe 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 obseapv0nqmumjhhi78ts4qyxiw* :5f iu,7v;r 1( rved 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. (0rpdyf7tf z two very narrow 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. Determin(.t0p7 frzfdy e the wavelength and frequency of the light.
$\lambda\;=\;$    $m$
$f$ =    Hz

  A parallel beam of light from a He-Ne laser, with a wavelengr3 nkw cj0v,(bth 656 nm, falls on two very narrow slits 0.060 mm apart. Hovj3r,cnb kw 0(w 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 slits and produces an in ahyfny*y(t /:terference pattern in which the fourth-order fringe is 38 mm from the central fringe on a screen 2.0 m away. What is the separationhy (af /:*nyyt of the two slits?    mm

  If 720-nm and 660-nm n-j )qr8 ay/+k ltvmfoi3r37vlight passes through two slits 0.58 mm apart, how far apart are the second-order fringes for these two wavelt/)qno+vvya f j l73r8mkr-i3engths on a screen 1.0 m away?    mm

  In a double-slit experiment, it is fol gepsgred30- hz0pb8m 5)4 cxund that blue light of wavelength 460 nm gives a second-order maximum at a certh8g45 zlc-epgb3s)exm 0rdp 0ain location on 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 cwkrpkxtj7 hs+l8)l qj. :d:-sm apart in a board. At a point 2.0 m beyond the board, at what al)7 x.d8:jt:p kl s r-wk+qjshngle 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 the lower sl 6 t,dv6x,xdwhit in Fig. 24–7 so that the two waves enter the slits ,, xhd 6vd6wxt180$^{\circ}\,$ 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 wave 0/gc0 b)njlk r:wbl,nlength 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. Hg, n0clbnbwj:k /rl0) ow far from the central bright spot will the second-order maximum of this light be located?    mm

  Two narrow slits separated by 1.0 mm are illuminated by 544 nm light. Find twqneuhga63k g73(2 8lo.w e xk7phwp(he distance between ad( e3(p7q2k 3e khwognxhl. u8gw6 ap7wjacent bright fringes on a screen 5.0 m from the slits.    mm

  Light of wavelength ;yp1-v4t f.x;pafksj//qv g x480 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 s*6lli vj,/dqglit 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 l,i/ j6dq*lvg of the plastic?    nm

  By what percent, approximately, does th-wed gx gp/vu4xir -+8e speed of red light (700 nm) exceed that of violet light (400 nm) in silicate flint xg8/-pdw ier4-g +vxu glass? (See Fig. 24–14.)    %

  A light beam strikes a piece of glass at ar/gr5wq q cb ov66i)w6 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 ny ee/74 nvhd*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 slit 0.0440 mm wide4z n1uo+eimm6 , what is the full angular width of the centzi 61nemo+ m4ural diffraction peak?    $^{\circ}\,$

  Monochromatic light fallkk(2glo3s8nk 8 rhyr4 s 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 5 dvh07u7dgro /20 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 illumina/pnk02+u9 tmu cf9hlla1d o0kted by 450-nm light. What is the width of the central maximum (in cm) in the diffraction pla 2u9c90/ ku + kot1l0nmhfpdattern on a screen 5.0 m away?    cm

  Monochromatic light of wavel-g syt9jv7+ se,) yshtength 653 nm falls on a slit. If the angle between the first bright fringes on either side of the centr)ts+,9te 7hjgysv s-yal maximum is 32$^{\circ}\,$, estimate the slit width.    $\mu m$

  How wide is the central diffraction peak on a screen 2. sovk3 g512bje30 m behind a 0.0348-mm-wide slit illuminated by 589-nm l s voek25b1g3jight?    cm

  When blue light of wavelength rvs2e1 /6vsr3pgsmm. mhm6: i 440 nm falls on a single slit, the first dark bands on eith6s .ehp3gm vs/v:mr2 mrm16 sier side of center are separated by 55.0$^{\circ}\,$. Determine the width of the slit.    $ \times10^{-7 }\;m$

  When violet light of wavel4+nxv5 9g vxbeength 415 nm falls on a single slit, it creates a central diffra 4+gb xxv59venction peak that is 9.20 cm 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 i+mek -d.fj)uq/a/f nvs 4.0 cm wide on a screen 1.50 m away, what will be the widthknj- e/.)dmf/+qa uf v of the diffraction maximum for light of wavelength 420 nm?    cm

For a given wavelengthv,0z4r)6c j7rebsm 1wlz x,j y $\lambda$, what is the maximum slit width for which there will be no diffraction minima?

  At what angle will 560-nm light prodj- t( i7l+i,mzg1lth4jy3m tr uce a second-order maximum when falling on a 3lttt74jh1y(j+ m i rz,mi lg-grating 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 ia hvl8yj ((3zw5pr,sa grating have if the third-order occurs at an 3(sj,hir5al8vp(y z w 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 o0 zt;7lrg5crc 23t ioma:m j1of 589-nm light falling on a diffraction grating is observed agrr7o0l;tztia co3m :21c 5jmt 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 bp*0r b1wi4:.rrk mra+0t9yhw qr1dd$ 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 normalo9vo jtp x8)2g3lp 5;uvo e/slly 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 6000 linqfel)clnow+ e:(u m-rncs8q5zo +k38 es per cm is illuminated with 633-nm laser light?l:kf zl3+8w+r suoeem 8-qc)no5qcn ( Assume normal incidence.   

  Two (and only two) full sp:/1gno8ii zafectral orders can be seen on either side of the central maximum when white light is sent through a diffraction grating. What is the maximum number of lines per cm oaii/8zng : 1ffor the grating?    $ \times10^{ 3}\;lines/cm$

  White light containing y2u-2rhmoxm; wavelengths from 410 nm to 750 nm falls on a grating withur2 ;h-ym 2oxm $8500\;lines/cm$ 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 known wavelengt iu(cuc8ep0e0 h $\lambda\;=\;6.328\times10^{-7 }\;m$ 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 liq:d wcwa6b-.l cg7;0m e q+updnes are 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 w5rp*9p *lusq9v r*y lqavelength is most strongly reflected at the center of the outer surface when illuminated normally by white light? Assume tpl5lv* p* u9q9ysrq r*hat $n\;=\;1.34$. $\lambda$ =    nm ,which is an    -  

  How far apart are the dark fringes in Example 2mktl0w fb vm6zk hm48a/*u )y44–8 if the glass plates are each 26k ym z* f8tu)vma04kw6 4bh/lm.5 cm long?    cm

  What is the smallest thickness of a so mrar d93t5bl - id++dmh5e)oeap 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 yello z-e 4j9if33bdmc1 1 k4foyptkw ($\lambda\;=\;570\;mm$ 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 3t*/7k t 7je4comyk-kf1 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 center*c 7k4yte of7- mjtk/k than the edges?    $\mu m$

  A fine metal foil separates one end of two pieces of opftsoakh(aqrz,o,: t2yzlh5 o .k,2 v8tically flat glass, as in Fig. 24–33. When light of wavelength 670 nm is incident normally, o5otkv.(q 82l a, y ,rs2oh,aft:zzhk28 dark lines are observed (with one at each end). How thick is the foil?    $\mu m$

  How thick (minimum) should ther*; g2fzfsp . urca. der8v/(x air layer be between two flat glass surfaces if the glass is to appear bright (p f ;rdcfzrvuea/*gr8x2.s. when 450-nm light is incident normally?    nm
What if the glass is to appear dark?    nm

  vA piece of material, ol5 z4no/xk-u suspected of 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 alcohol oy7n8db 0+l zf3qx0lr$(n=1.36)$ 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, the diamet:/t/vq u*h pzx4v4m 4soky) aeer of the eighth dark ring decr/z xtv4a4q:o pv/)ymes* uk4heases from 2.92 cm to 2.48 cm. What is the refractive index of the liquid?   

  What is the wavelength of the ligsmiz1 q8)p8p4nns ovsl76 x+dht entering an interferometer if 644 bright fringes8ps )dl s 17nmxop6svqi+z 84n are counted when the movable mirror moves 0.225 mm?    nm

  A micrometer is connected to the movable mirror of an interferometer. Wh.gt4u k . nga,l7on9ssen 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? T no,ggn.9. 4sut lsk7ahe wavelength of light used is 589 nm.    $\mu m$

  How far must the mir5d x(8x.wvs27nmsh/(jvhf i(ik 2( f8cknccy 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 in;yganawqb qa/- .0li:terferometer (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 container, a total of 236 dark fringes are countedi -yqng a w;/:alq0a.b to move past a reference line. The light used has a wavelength of 610 nm. Calculate the index of refraction of the gas, assuming that the interferometer is in vacuum. $n_{gas}$

  

  Two polarizers are oriented at 8)vtyjmq79dog )xg;l*hh n )m65$^{\circ}\,$ to one another. Unpolarized light falls on them. What fraction of the light intensity is transmitted?   

  What is Brewster’s angh8)o, 5je h3wuf kfvgjp6r27ble for an air–glass $(n=1.52)$ surface? $\theta_{p}$    $^{\circ}\,$

  What is Brewster’s avde8fwz*48yej 9/ ttr ngle for a diamond submerged in water if the light is hitting the diw89z/*84rdyjete ft v amond $(n=2.42)$ while traveling in the water? $\theta_{p}$    $^{\circ}\,$

  Two Polaroids are aligned so that the light passing through the0 d qn)sro8hy6m is a maximum. At what aoq yr6nh8)d0s ngle should one of them be placed so that the intensity is subsequently reduced by half?    $^{\circ}\,$

  At what angle should the axes of two Polaroids be pmk58i2ry fvb;laced so as to reduce the intensity of the incident unpolarized lirbkv; 2fim 8y5ght to
(a) $\frac{1}{3}$ ,    $^{\circ}\,$
(b) $\frac{1}{10}$ ?    $^{\circ}\,$

  Two polarizers are orientb 7gpt+ 0xpe,u joy,m/ed 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 o5z)m .a4y pozariented 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)z1izrki 4, tup iw88m off the surface of water for light coming from beneath the surface? Compare to the angle for total internal reflection, and to Brewster’s ani1zzi rp4tk8 im)8wu, gle from above the surface.
If the light is coming from water to air, $\theta_{p}$    $^{\circ}\,$For the refraction at the critical angle from water to air $\theta_c$   $^{\circ}$ If the light is coming from air to water $\theta_p'$   $^{\circ}$

  Unpolarized light passes through five successive Polaroid sheets, each of who /9v+ zotrfh7n3vl ymisn732 ygy nm59se axis3mnyv3ny f7y ght95 n9mo7lv+s/ zi2 r makes a 45$^{\circ}\,$ angle with the previous one. What is the intensity of the transmitted beam?    $I_0$

  Light of wavelength ,oejzns+:.- i w i+qdo:0 icaz$ 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 airplb2tcb :+hntm3 3yu(a qanes can interfere with the dirmy+3u(cq2n 3batthb :ect 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 sources passes through a diffraction gratiaq eeq( f5:m1zl)u7bq,k 5gqd ng with :ad kbuqm)eqqz(15 qgl5e, 7 f$ 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 narn,e9 /t zrp.fbrow slits 0.60 mm apart. The screen is 1.70 m away. A second source of unknown wavelength produces its second-order,nz9tr/ e p.bf 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.erm*u l(adh4dk(ak* -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 signa e4(d*( ldakakrhu-*m l is found along the midline, perpendicular to d at its midpoint and extending horizontally in both directions. If the midline is taken as 0$^{\circ}\,$, at what other angle(s) $\theta$ is a maximum signal detected? A minimum signal? Assume all measurements are made much farther than 8.0 m from the antenna towers.

  A teacher stands well back from an outside doorway 0.88 m wide, and blows aixhykp v,82).g oy.xavfo.u 9 whistle of frequency 750 Hz. Ignoring reflections, estimate at what angle(s) it is not possible to hear the whistle clearly on the playground o.yx89uo. hof)vvi gx2y. ap ,kutside the doorway.    $^{\circ}\,$ either side of the normal.

If parallel light falls on 1851bp tqytvl a single slit of width D at a 30$^{\circ}\,$ angle to the normal, describe the diffraction pattern.

  The wings of a certain beetle ha8ob*k/s eit q:zn6-)v x6yg iuve a series of parallel lines across them. When normally incident 460-nm light is reflected from the wing, the wing appears bright when viewed ati k q68 ne-bgi)o/x*syuv6:zt an angle of 51$^{\circ}\,$. How far apart are the lines?    nm

  How many lines per centimeter must a grating have ef tldac+ z8 xf :4o2f-v-y3arif there is to be no second-order spr8 a :c 2fvfty-+a d-xe4floz3ectrum for any visible wavelength?   $ lines/cm$

Show that the second- and third-order spectra of white ligh tiju.v9u/,j st produced by a diffraction grating always overju9/tsj,. ui vlap. What wavelengths overlap exactly?

  When yellow sodium l 9iq:u)vzm /y7 eoftq9ight, $\lambda\;=\;$ 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 viewedq6njp)cq6 z lbdcs27 5 on a screen 2.5 m from the grating. The incident lightc6psq5n c7 db2j6 q)zl 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 materucu:insu9zii kq f yc - zvj88ky7,/4+ial if a minimum of 150 nm thickness of it, when laid on glass, is needed to reduce reflection to nearly zero when l/k7i y, vju cku8zc+y9n4-uiz8i f:sqight of 600 nm is incident normally upon it? Do you have a choice for an answer?

  Monochromatic light of variable wavelength is incident n mls;(c+a w siix.m)q.ormally on a thin sheet of plastic film()wm;+clisi x. sma q. 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 thick9fqszig 6 n1.iu* yb)fness needed for an anti-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 agxc) h-3szg 0air layer between two flat glass surc-gz0ax sh3)gfaces if 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 layjem 2 8agtq)5fered 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 the relative size of the minima compared to2 tq)fem5g8aj the maxima and to zero.
24-30
24-36

  At what angle above the horizon is the Sun when light reflecting ofh 13gl ptvubn4d6:i:g f a smooth lake is polarized pht:glbi6g1 v43dun:most strongly?    $^{\circ}\,$

  At what angle should the axes of two Polaroids bttb rh9vk,w*s28j ze9k)eo-d e placed so as to reduce the intensity of the incident unpolarized light by an additional factor (after the first Polaroid cuts it in halwhz*jtet k) o-v 9dk 8r9e,2bsf) of
(a) 4,    $^{\circ}\,$
(b) 10,    $^{\circ}\,$
(c) 100?    $^{\circ}\,$

  Unpolarized light falls on two polarizer sheets wkt ql a6zmj3 )ht3eo:ax: 4e1uhose transmission axes are at right angles. A third pola3xoqej:hm4a t) : lua t3k1ez6rizer 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 sucm7sf61f et6 lbl6e9zf cession 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 sli 4c.oxxpt0yeslseqs5,j8.u 0 t of width 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 thexp0tus5cj,.4 s e8 s. eyxol0q width of the beam when it reaches the Moon.    km

  A series of polarizers are each plazeqx/*81/dvka z w yqvtf) ,6xced 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 e7qgi* i,vkcb0l 0n4c$(n=1.34)$ 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-Mr,hu *b-qe,mzr f-;gd Hz radio waves in phase with each other. They are locau,reg hf;*--d ,bm rqzted 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 twf6 (:x2e)1c lrl h0ueebap+lfo wavelengths, 420 nm and 650 nm, enters a silicate fl6fpe l :2alh 1l(ef+xcrbue0)int glass 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 flatfxyh6n.een1o+7e p ln+j: k,. mfw (cu 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