What would be the appearance y fpmho3m 7e13of the Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Romant0lg7q wpq df8e wj:0+ fleet in the harbor of Syracuse by focusing the rays of the Sun with a hu8qp+0wld:g 7q0 fwjetge spherical mirror. Is this reasonable?

Although a plane mirror appears to reverse left an2qxwl-42wc) mnixj;d7q isi-d right, it doesn’t reverse up and down. qicxs2m d;n7q)i-wj 24il xw- Explain.

If a concave mirror produces a real image, is the image necessarigdlr v (5k;emxtaj2+ c6ury//ly inverted? Explku(j/2 lrr+tamcxy vg;e56d /ain.

An object is placed along the principal axis of a spherical myy)tec96u40 niocmcr7jfwg -20s -lv irror. The magnification of the object is -3.0 Is the image real or virtual, inverted or upright? Is the mirror concavejcst 6 g 0f9y)uyi mv4 cn-7ol0crwe2- or convex? On which side of the mirror is the image located?

Using the rules for the three rays discussed with reference to (Figl,m xy)( s.xl6w3cqf;bwgp7d ufm an2s9) 1g v. Below a), draw ray 2 for (Fig. d ,bw2 3s)fsl1gm6)qlam9w;u xgpvfn .x cy7( Below b).
(a)
(b)

What is the focal length of a plane mirroh96fw yanwx(3 y1ups;r? What is the magnification of a plane m61 fypswu;3x ywha(9 nirror?

When you look at the Moon’s reflection from a ripply s:cf8u9mh cy /+:+nn+lyaxvhgea, it appears elongated . Explmh ycauhynf8:9+ v/n+x g: c+lain.

What is the angle of refraction when a light ray meets the boundary between twommi1r3bexu a*.z :vi;exm.v-e,xo 1a materials perpendicularlyaxv iezx, v1m-;*1 :xeareu.o3bm. mi?

How might you determine the speed of light ihn bac0rnh uv,7 )y/4tn a solid, rectangular, transparent o7n),/0rbh htc4ynua vbject?

When you look down in7a3l h7z 2hdtito a swimming pool or a lake, are you likely to underestimate or overestimate its depth? Explain. How does the apparent depth vary lhd2t 3aiz77h with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick lfq4o dw 04 qxfao()omek 9e(w*ooks bent when part of it is under water (w f4eodq *kw4)eox af(m9q0o(Fig. Below).

Your eye looks into an aquarium and views a fish g v7 :c9a0sg1w jqs-rzvl4j;iinside. One ray of light that emerges from the tank is shown in (Fig. Below), as well a7sz;ljr- g1: w igj0sc9vqv4as the apparent position of the fish. In the drawing, indicate the approximate position of the actual fish. Briefly justify your answer.

How can you “see” a round drop of sb2r,1 ezvmf.18 g h;ot) fqrwwater on a table even though the water is transparent and co bmf8)qwf.h 1zegsr vo1rt;, 2lorless?

When you look up at an object in air from beneath the surx8 ei1us 7g5oxface in a swimming pool, does the object appear to be the same size as when you see it directly in x758o gex1sui air? Explain.

How can a spherical mirror have a negative object distanceh9mxc+)(d:mj/ a28*;hou hd nl uwk zj?

Light rays from stars (including our Sun) always bend toward the22a l99/yd8 qjpvt rii vertical direction as they pass through thev 8y99d /qt2iarp2jl i Earth’s atmosphere.
(a) Why does this make sense?
(b) What can you conclude about the apparent positions of stars as viewed from Earth?

Where must the film be placed if a camera lens kjkk:j6 q.o ll+*3ejpi93plbf 6qq y :is to make a sharp image of an object ver:.qlql +ij jq :39o klek6ppj6f*yk3b y far away?

What type of mirror is shown in (Figy it k47c(ae0 ums4pb1. Below)? Explain.

A photographer moves closer to his k4e7sl vo4-tag gr:u7subject and then refocuses. Does the camera lens move fartherk4glus 47egr 7o t:va- from or closer to the film? Explain.

Can a diverging lens form a real image under any circ*tzdd4 tr(94 rzemee )umstances? Explain.

Use ray diagrams to shoks s)mtys rfd5y 8u*bp,bk81 )1say( ww that a real image formed by a thin lens is always inverted, whereas a virtual image is always upright if the obrps k1y )b*du8)m5s kw8by(sf s,tay 1ject is real.

Light rays are said to be “reversible.” adph6hrn),9 aIs this consistent with the thin lens equati),h6dhaparn 9 on? Explain.

Can real images be projected on a screen? Can virtual images?xw:ga0) xdnaxuy/ ph, 91wnm ( Can either be photographed? Dxm/g w)ax n1xy9(0uwd:,nhpa iscuss carefully.

A thin converging lens is moved closer to a br3oq8ps4 4vy-stim :nearby object. Does the real image formed change s btqis4m8v3o4r-:yp
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of refraction n = 1.3w)ty p0ltw)in 57v2ihjyx1 jukcl+2b48qs .a0 In air, it is a converging lens. Wil+t sap2 k8 jicw4) b7txyu 2hw.1i)q l5yvjn0ll it still be a converging lens if placed in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands facing a converging lens. If tho(9yw rkdks hv-3mu* ww5jf4 su 8;d9de nose and the tail are each f;-fw8(mdoj9kvyw wdh kus us 5*34d 9rocused on a screen in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facins yfv 7be*oa*xzy/7a9g a converging lens. Under what circumstances (if any) would the image of the nose be virtual and the image of the tail be real? Where would the image of the rest of the cat be?ey* / 7baoz9 f7asy*xv

Why, in Example 13, must the conve1b1 e0 sygwka0rging lens have a shorter focal length than the diverging lens if the latter’s focal length is tebk 01 1wsy0gao be determined by combining them?

Explain how you could hi;6f)va4 9vfbl; olvdave a virtual object.

  An unsymmetrical lens (slg ,f+m./a pj3nh - )ekck*bpeay, planoconvex) forms an image of a nearby object. Does the image point changjbce/ hp+ 3fnmklp.kg e*-)a,e if the lens is turned around? ----待选择----yesno 

The thicker a double convex lens is in the center as compared to its edges, the z8rzvfi(6.na gz )ban48hy)c shorter its )iah 8gzy6.bvc) za8n(nz 4frfocal length for a given lens diameter. Explain.

Consider two converging lenses separated by some distance. An object is place8 9m2 fru-hvx6 8naq ut6 mn/zg0v8csbd so that the image from the first lens lies exactly at the focal point of the second lens. Will this combination produce an imag-a9ftg6vmun8 q 8h02x 6scr b/u8zmnve? If so, where? If not, why not?

  Suppose that you want to take a photograph of yourself ashar :4zai3umt ,xn)-b you look at your image in a flat mirror 2.5 m away. For what distance sh mz:) rtahaxu-i,3bn 4ould the camera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mirror, you sey:, scpc u4,zhw ftkzxb8nb,9a 35+ cxlzz3w/e the same amount of your body whether you are close t szlz8cfwt,bycb:93,pz +x3axu,5h4kw n /c zo the mirror or far away. (Try it and see.) Use ray diagrams to show why this should be true.

  Two mirrors meet at a 1 1.4ihbiu:o-.n,nekg1 pbcr k35$^{\circ}\,$ angle, (Fig. Below). If light rays strike one mirror at 40$^{\circ}\,$ as shown, at what angle $\phi$ do they leave the second mirror?    $^{\circ}\,$

  A person whose eyes are 1.68 m above the floor stands 2.20 m in tw*,dxw1)m u.y5cpzb front of a vertical plane mirror whose bottom edge is 43 cm above the floor, (Fig. Below). What is the hz*wwm,dyu5).pb1 ctx orizontal distance x to the base of the wall supporting the mirror of the nearest point on the floor that can be seen reflected in the mirror?    cm

  Suppose you are 90 cm from a plane mi02q-gn3ux)grjk 3 h8h cg/dbj kh wz15rror. What area of the mirror is used to reflect the rays entering one eye from a point on the tip of your nose if your pupil diameter is 5.zxk 3b)1-ghj0drkn hq8ucwh 3gj2 g/55 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrorl, 3 l)j3zlwnss meet at an angle $\phi$. a single ray reflected successively from both mirrors is deflected through an angle of $2\phi$ independent of the incident angle. Assume $\phi<90^{\circ}$ and that only two reflections, one from each mirror, take place.

  A solar cooker, really a concave mirror pointed at thr +kk1ils6b 6g-6kekge Sun, focuses the Sun’s rays 18.0 cm in front of the mirror. What is the radius of the spherica i6rk b+skk1ge66l- gkl surface from which the mirror was made?    cm

  How far from a concave mirroiymi(zo2jva q(f2la;yuz4 0* r (radius 23.0 cm) must an object be placed if its image is to be at iuyl iq0v *a((j;2zyomfza4i2 nfinity?    cm

  If you look at yourself in a shiny Christmas tree bm-1: m(mk5 vjo 4dgqshall with a diameter of 9.0 cm when your face is 30.0 cm away from it, whed4mjmh 5sg v(1qomk: -re is your image? Is it real or virtual? Is it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shows an upright image of any person who sta8 bo*m+qfy /h/hte 2kcnds 1.4 m in fqe2/c +hko bmh /f8y*tront of it. If the image is three times the person’s height, what is the radius of curvature?    cm

  A dentist wants a smalllaagzhi./r ;7x,kctvx s5- 1a mirror that, when 2.20 cm from a tooth, will produce a $\text{4.5×upright}$ image. What kind of mirror must be used and what must its radius of curvature be?
 ----待选择----convexconcave 
r =    m

  Some rearview mirrors produce images of cars behind ykf t-rn1vp 6nf u9h5jd.q-f*kou that are smaller than they would be if the mirror were flat. Are the mirrors concave or convexru1q k6f5-9fn *hjk dvnpft .-? What is a mirror’s radius of curvature if cars 20.0 m away appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm hio v;pfz k8s6a(gh is placed 20.0 cm from a convex mirror of radius of cur(s8k zaf6 ;vpovature 20.0 cm.
(a) Show by ray tracing that the image is virtual, and estimate the image distance.    cm
(b) Show that the (negative) image distance can be computed from Eq. 23–2 using a focal length of -10.0cm
(c) Compute the image size, using Eq. 23–3.    mm

  You are standing 3.0 m from a cgr1 ofh3i(-l zz o//ta mx)ni(onvex security mirror in a store. You estimate the heif/ hia3i/nolox)zz gr(m(t 1-ght of your image to be half of your actual height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object be placed i a(qo:i n9 .sua:/xeyin front of a concave mirror so that it produces an image at t: o. uq: /(iae9snaiyxhe same location as the object?
(b) Is the image real or virtual?  ----待选择----realvirtual 
(c) Is the image inverted or upright?  ----待选择----invertedupright 
(d) What is the magnification of the image?   

  The image of a distant tree is virtual and very small when viewed in a cufs r*1mwq;+n erved mirror. The image appears to b 1qfnmr* wes+;e 18.0 cm behind the mirror. What kind of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniqmz+zl k8uyh) 9ues,
(a) a ray diagram,
(b) the mirror equation, to show that the magnitude of the magnification of a concave mirror is less than 1 if the object is beyond the center of curvature $C\left(d_0>r\right),$ and is greater than 1 if the object is within $ C (d_0 < r) $.

Show, using a ray diagram, that the magnification m of a convexuov oc;-yazb-, (7ye: kvk(uv mirror is $m=-d_\mathrm{i}/d_\mathrm{o},$ just as for a concave mirror. [Hint: consider a ray from the top of the object that reflects at the center of the mirror.]

Use ray diagrams to show that the mirr qoz bl1( qrisap92so9/l09q tor equation, Eq. 23–2, is valid for a convex mirror as long qqlor09sbti/ oalps9(z q 219 as f is considered negative.

  The magnification of a a j 8n2u hht2ka/cy7-rconvex mirror is $+0.65\times$ for objects 2.2 m from the mirror. What is the focal length of this mirror? $\theta_2$ =    $^{\circ}\,$

  A 4.5-cm-tall object is placed 28 cm in front of a spherical mirror. ly/ rc;b;;4b*v h5kneh s;qipIt is desired to ph/ycp rish ;vklq ;neb;b 45*;roduce a virtual image that is upright and 3.5 cm tall.
(a) What type of mirror should be used?  ----待选择----convex mirrorconcave mirror 
(b) Where is the image located?    cm behind the surface
(c) What is the focal length of the mirror? $f$ =    cm
(d) What is the radius of curvature of the mirror? r =    cm

  A shaving/makeup mirror is designed to magnify your face by a factor of 1.35iom8 i4- eyxo3 when your face is placed 20.0 cm inoi4iy5-m o8ex front of it.
(a) What type of mirror is it?  ----待选择----convex mirrorconcave mirror 
(b) Describe the type of image that it makes of your face.
(c) Calculate the required radius of curvature for the mirror. r =    cm

  What is the speed of light in t*mpw5br-i e8g4*n yyd,mlz 7
(a) crown glass,    $ \times10^{8 }\;m/s$
(b) Lucite,    $ \times10^{8 }\;m/s$
(c) ethyl alcohol?    $ \times10^{8 }\;m/s$

  The speed of light in ice is1rrh0 7sygnz4k0dzh; $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in 3) b7oq:jsq/aa *m9 fddf lg*ta certain substance is 89% of its value in water. What is the index of refraction of this substansa:lf 3j/f 7 g mdba*do)q*9tqce? n =   

  A flashlight beam strikes the surface of a pane of glass (n = 1e* )pu-0xhs ikw m. 30z,cvte;;eanxl.58) at a 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashlight upward from beneath thel7z xv g-rv.zjd ik.9y 0dk z7pd4-wu0 water at a 42.5$^{\circ}\,$ angle to the vertical. At what angle does the light leave the water? $\theta_2$ =    $^{\circ}\,$

  A light beam coming from an underwater spotlight exits the water at+*e)gvw+mfq) 0itrn o an angle of 66.iwgm*tfq+en ov +0r))0$^{\circ}\,$ to the vertical. At what angle of incidence does it hit the air–water interface from below the surface? $\theta_1$ =    $^{\circ}\,$

  Rays of the Sun are seen to make aouc.tu 56yv,pd1x j-f 31.0$^{\circ}\,$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?    $^{\circ}\,$

  An aquarium filled with water has flat glass sides whose index of ref:bg3 n0ivy h .uhip/1iraction is 1.52. A hiv i:1 ip.bgh/30 unybeam of light from outside the aquarium strikes the glass at a 43.5° angle to the perpendicular (Fig. Below). What is the angle of this light ray when it enters
(a) the glass, $\theta_2$ =    $^{\circ}\,$
(b) the water? $\theta_3$ =    $^{\circ}\,$
(c) What would be the refracted angle if the ray entered the water directly? $\theta_3'$ =    $^{\circ}\,$

  In searching the bottom of a pool at night, a watchman s) p+pvdf)an au 9en8)ahines a narrow beam of light from his flashlight, 1.3 m above the water level, onto the surface of the water at a point 2.7 m from the edge of the pool (Fig. Below). Where does the spot of light hit the bottom of the pool, meve+9puda 8an)np f))aasured from the wall beneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an e:gg iq3 y.(pl7lh*jwbquilateral glass prism at a 45.0$^{\circ}\,$ angle to one face, (Fig. Below). Calculate the angle at which light emerges from the opposite face. Assume that n = 1.58.    $^{\circ}\,$ from the normal

  A beam of light in air strikes a slab of glass (n = 1.52) an jqsh(.noza mv,hg5; jwo,.e .dn.1 pgd is partially reflected and partially refracted. Find the angle of incidence if ta h.sgq..hwpmz 5(. en o,njg, jo1vd;he angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that fo9-v,pc2f dhvr r a light beam incident on a uniform layer of transparentvpdf 2r-ch9v, material, as in (Fig. Below), the direction of the emerging beam is parallel to the incident beam, independent of the incident angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on ayer1b zr6 u)4+8ib9 bfwz fcwb1 7juu5h w6r,a flat piece of glass with index of refraction n as in (Fig. Below). Show that if the incident rzz1 bc wuu6b5)riffj+ b4h7e 6,8au91rwybwangle $\theta$ is small, the emerging ray is displaced a distance $d=t\theta(n-1)/n$ from the incident ray, where t is the thickness of the glass and $\theta$ is in radians. [Hint: for small $\theta,\sin\theta\approx\tan\theta\approx\theta$ in radians.]

  What is the critical angle for the inter7hwbd d;w:y4zaqrse9ib s t t/;+/r(vface between water and Lucite? To be totally internally reflected,+ t4;br:w ta /d9d;(/bqvsyirse 7w hz the light must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–air surface is 4a9nt0ogb t o8w4qt -21fqw ci(7.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in a pool of water from a depth of 62.0 cm. Wher/ /xm8p(x u,rt8ejogae must it strike the air–water interface, relative to the spot directly above it, in orote8ruxxm (p/ 8ag/j,der that the light does not exit the water?    cm

  A beam of light is emitted 8.0 cm beneath the surface73mhzoiob- :dm)p l s/ of a liquid and strikes the surface 7.0 cm from the point directly above the source. If total int3p dlo:-s)7iz mm /bhoernal reflection occurs, what can you say about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face of the prism in (Fig. Below) at 45.0n6evphe z8bi 0ymo*-( $^{\circ}\,$ as shown, but is totally internally reflected at the opposite side. If the prism apex angle (at the top) is $\phi=75.0^\circ,$ what can you say about the index of refraction of the prism? $n \geq$    (retain three decimal places)

A beam of light enters the ecn; t3au- ekg:nd of an optic fiber as shown in (Fig. Below). Show that we can guarantee total internal reflection at the side surface of the material (at point a), if the index of refraction is greater than about 1.42. In other words, regardless of the angle t;: getu3k -acnhe light beam reflects back into the material at point a.

  (a) What is the minimum indbh8l ;a/krnk v.hvr 0f r(aj h90ze+a .i0y(ddex of refraction for a glass or plastic prism to be used in binoculars (Fig. Below) so that total internal refzd;rl (r.f v09.8 r/nabk dv0haji(k ayhe0 +hlection occurs at 45$^{\circ}\,$? $n_1$ $\geq$   
(b) Will binoculars work if its prisms (assume n=1.50) are immersed in water?  ----待选择----totally reflectingtotally transmitting 
(c) What minimum n is needed if the prisms are immersed in water? $n_1$ $\geq$   

  A sharp image is locai) q0z1 3q fmdphr:fy7/v xcj5ted 78.0 mm behind a 65.0-mm-focal-length converging lens. Find the x q:qcrffj0i p1/)zmy7dv53 hobject distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a f*zu 6f.lg5 rp zog6u8point 18.5 cm behind a lens.
(a) What kind of lens is it?  ----待选择----converging lensdiverging lens 
(b) What is its power in diopters? P =    D

  A certain lens focuses light from an object 2.75 m away as an image 48.3 cm r px2ajeehog10 n1w7-on the othe1w0exraj71o g2h en- pr side of the lens. What type of lens is it and what is its focal length? Is the image real or virtual?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the power of a 20.5-cm-fodqm: ve;sd8:o(soa f0cal-length lens? P =    D  ----待选择----converging diverging 
(b) What is the focal length of a lens? $f$ =    cm  ----待选择----converging diverging 
(c) Are these lenses converging or diverging?

  A stamp collector uses ee56 wh+8o18s1sg/ uuni:n0xr hh jena converging lens with focal length 24 cm to view a stamp 18 crhexuw /s8s: 0h56uoingne jh1+1ne8m in front of the lens.
(a) Where is the image located?    cm behind the lens (virtual)
(b) What is the magnification? m =   

  A -5.5-D lens is held 14.0 cm 5a-ercx dy.fjc*a8k4 ;k ey.mfrom an object 4.0 mm high. What are the position, type, and height of the ikk.ea5y cjyra-*ed4fcm 8 ;.xmage?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to focus an image on the film of a camera. lz x2dxle0nrq fkl8, r-:yy)jj m5 t:4The maximum distance allowed between the lens and the fi5,:e0tkqfxr8x 2ldj ryl)-l:4zj mnylm plane is 120 mm.
(a) How far ahead of the film should the lens be if the object to be photographed is 10.0 m away?    mm
(b) 3.0 m away?    mm
(c) 1.0 m away?    mm
(d) What is the closest object this lens could photograph sharply?    mm

  It is desired to magni(3s sbuzhr 42:fa.94 rpwhchyfy reading material by a factor of 2.5× when a book is placed 8.0 cm .afh9b c4zhyrrhs(3ws:up 24 behind a lens.
(a) Draw a ray diagram and describe the type of image this would be.  ----待选择----realvirtual 
(b) What type of lens is needed?  ----待选择----converging lensdiverging lens 
(c) What is the power of the lens in diopters? P =    D

  An object is located 1.5 m from an 8.0-D lens. By how much does the image mor2dyi, xty (o vv pjbz2hd6h-js5b 3(1u 1pfc6ve if the obj1(y2p2 hu zov3jx,jdb5 v-6ibh 6fr1c(yspdtect is moved
(a) 1.0 m closer to the lens,    cm away from the lens
(b) 1.0 m farther from the lens?    cm cm toward the lens

  How far from a converging lens with a foca p:)f6 xiiyyb-; 1ztgol length of 25 cm should an object be placed to produce a rea; y t:x6 i-p1ybzi)gofl image which is the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-lenga9n7lvz yvhh yw),f6+ ,hwpa 6th lens must an object be placed if its ima)h7va 6fp6,wylw +hh ,zyn9avge is to be magnified 2.00× and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm

  (a) How far from a 50.0-mm-focal-length lens mu0t rytc2 :yw:z(hdz6v st an object be placed if its image istd(y2yvt 6z:0ch z :wr to be magnified 2.00× and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm (formed by some other piece of optics).]

  (a) A 2.00-cm-high insect is 1.20 m from a 135-mm-focal-length lens. 8 zvz-ym1/bq qWhere is the imag v/z18y qq-zmbe, how high is it, and what type is it?
$d_i$ =    mm (real,behind the lens) $h_1$ =    cm (inverted)
(b) What if $f=-135\mathrm{~mm}$?
$d_i$ =    mm (virtual,in front of the lens)
$h_1$ =    cm (upright)

  How far apart are an object and an image formed by a 75-cm-focal-lengtqn 4pnf;,o: bjh converging lens if the image is 2.5× larger than the qj n nob:;,4fpobject and is real?    m

  A bright object and a viewing s rypba;,mb jg88;cqwgj)r/ /screen are separated by a distance of 66.0 cm. At what location(s) between the object and the scree) /jpr; y8wa/bj;g qcr8 gsb,mn should a lens of focal length 12.5 cm be placed in order to produce a crisp image on the screen? [Hint: first draw a diagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length converging lenses are ply:5flhs8 /ka4rmcr 0/p ozco ,aced 16.5 cm apart. An object is placed 36.0 cm in front of one lens. Where will the final image formed by the second lens be locasm/c /,zlr0p4k58 ch:fo a oryted? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens wit2ugvgb/5t*fikm/1 p h h $f=-31.5\mathrm{~cm}$ is placed 14.0 cm behind a converging lens with $f=20.0\mathrm{~cm.}$ Where will an object at infinity be focused?  ----待选择----realvirtual ,    cm beyond second lens.

  A 31.0-cm-focal-length converging lens is 21.0 cm behind k6n w;4:m.pr+ ge fy8bnrw 0oga diverging lens. Parallel light strikes the diverging lens. After passing through the converging lens, the light is again parallel. Wha.f:m +0rb4k8 o; pn6erwyngg wt is the focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Example 23–12 are now placed ondab jafz 90j;wg /* vv2ayl.hs5.rd9jly 20.0 cm apart. The object is still 60.0 cm5zvd wy.af .9bljvjd 9gh02rja*/s ; a in front of the first lens as in (Fig. Below). In this case, determine
(a) the position of the final image,    cm
(b) the overall magnification.    cm
(c) Sketch the ray diagram for this system.

  Two converging lenses are placed 30.0 cm apart. The focal length of the lencbgc62 jp9k av,6-q qds on the right is 20.0 cm, and the focal length of the lens on the left is 15.0 cm. An object is placed to the left of the 15.0-cm-focal-length lens. A final image from both lenses is inverted c q,acq29bp-6 dk g6vjand located halfway between the two lenses. How far to the left of the 15.0-cm-focal-length lens is the original object?    cm

  A diverging lens with a focal length of is placed 1(:e+4yg r(8 f:o5-iklvzsowh7erocb 7 bm*du2 cm to the right of a converging lens with a focal length of 18 cm. An object is placed 33 cm to the left vky7 z c-rd:e(:8ue57 bl(wbs+ o f 4hor*ogmiof the converging lens.
(a) Where will the final image be located?    cm to the left of the converging lens
(b) Where will the image be if the diverging lens is 38 cm from the converging lens?    cm to the right of the diverging lens

  Two lenses, one converging with;i)egzpd22rg4 sbw)h focal length 20.0 cm and one diverging with focal length are placed 25.0 cm apart. An object is placed 6e)4)dir 22sgpg;wz hb0.0 cm in front of the converging lens. Determine
(a) the position    cm to the right of the diverging lens
(b) the magnification of the final image formed.   
(c) Sketch a ray diagram for this system.

A diverging lens is placed next to a converg)ckek6i +etua2 5f wd)ing lens of focal length $f_C$ as in (Fig. Below). If $f_T$ represents the focal length of the combination, show that the focal length of the diverging lens, $f_D$, is given by
$\frac{1}{f_\mathrm{D}}=\frac{1}{f_\mathrm{T}}-\frac{1}{f_\mathrm{C}}.$

  A double concave lens has surface radii;rj4n1e zufy2ac1 tg s/rw4* n of 34.2 cm and 23.8 cm. What is the focal lengtj4 enrugca /s 1 y4;rw2t*znf1h if n = 1.52?    cm

  Both surfaces of a double convex lens have radii of 31.0 cm. If thez;kz6 vx3 c. lf7 t:bxeq7fpj) focal length is 28.9 cm, what is the index of refraction c7) ;z etvxjx:b3zq6f .7lfpkof the lens material?    cm

  A planoconcave lens z 0yu4nrj5nuo zfh7j11.t 6rb(n=1.50) has a focal length of -23.4cm. What is the radius of thy1nrbrf4 t160zhn u5oj .z uj7e concave surface?    cm

  A Lucite planoconcave lens (t bqa4edk3) v8yp*d6t5i7u tvsee Fig. Below) has one flat surface and the other has R = -18.4 a 7vkt ei4yp*tbq t8uv35 d)6dcm. What is the focal length?    cm

  A symmetric double convex lens with a focal length of 25.0 cm is to be mi3.m0xdgqr83d e yo1made from glass with an index of refra0qm8grxeoid 3y1m3. dction of 1.52. What should be the radius of curvature for each surface?    cm

  A prescription for a corrective lens calls for +1cxicw wl;2by :e 78i(cc5u x*11rtl ek.50D. The lensmaker grinds the lens from a “blank” with n=1.56 and a preformed convex front surface of radius ow1e2 c;xlk8 :xc1b 7wctr5* eiiyucl(f curvature of 40.0 cm. What should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fig. Below). You stand 1.5;w8 +w)cq0uw ,azcobho l3z,h m away from one of these mirrors and look into it. You will see multiple images of yourselh 0ob,z8)cuo hwlq,+cww3za; f.
(a) How far away from you are the first three images in the mirror in front of you?
$d_1$ =    m
$d_2$ =    m
$d_3$ =    m
(b) Are these first three images facing toward you or away from you?
the first image is facing  ----待选择----toward youaway from you ;
the second image is facing  ----待选择----toward youaway from you ;
the third image is facing  ----待选择----toward youaway from you .

  We wish to determine the depth of a swimming l1 b uvcl,- / ok6xozo:cjkrv*r,*kq6pool filled with water. We measure the width (x=5.50m) and then note that the bottom edge of the pool is just visible orzkx 6,o1q6 -/c,vcbkl*u v:*orlkjat an angle of 14.0$^{\circ}\,$ above the horizontal as shown in (Fig. Below). Calculate the depth of the pool.    m

  The critical angle of a certaintg2gefr qikq w e/3g 2,j01p1t piece of plastic in air is $\theta_{\mathrm{C}}=37.3^\circ.$ What is the critical angle of the same plastic if it is immersed in water?    $^{\circ}\,$

(a) A plane mirror can mjpp,c/b:9*d r0mo; ps6srhofnh ) u)be considered a limiting case of a spherical mirror. Specify what mdss,h0jhumpf: ;6/p) br r9po)co* n this limit is.
(b) Determine an equation that relates the image and object distances in this limit of a plane mirror.
(c) Determine the magnification of a plane mirror in this same limit.
(d) Are your results in parts (b) and (c) consistent with the discussion of Section 23–2 on plane mirrors?

Stand up two plane mirrors so they f,p /(fp gr x*(pns0shrorm a 90$^{\circ}\,$ angle as in (Fig. Below). When you look into this double mirror, you see yourself as others see you, instead of reversed as in a single mirror. Make a careful ray diagram to show how this occurs.

Show analytically that a diverging lens can never form a real image of a re/a /xcticl8 0m9x6biqv lrl71al object. Can you destm i/ 07cvl/ax6l ix1q9l 8rbccribe a situation in which a diverging lens can form a real image?

  Each student in a physics lab is assigned to find the l ;lmfxs *m9aogbt5l0ni( -8peocation where a bright object may be placed 09oxlia 5-np 8;gfe*blm tms(in order that a concave mirror with radius of curvature r = 40 cm will produce an image three times the size of the object. Two students complete the assignment at different times using identical equipment, but when they compare notes later, they discover that their answers for the object distance are not the same. Explain why they do not necessarily need to repeat the lab, and justify your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of a 1nj+m5b 7-uuptnvyq- prism is $\phi=72^\circ$ see (Fig. Below), what is the minimum incident angle for a ray if it is to emerge from the opposite side (i.e., not be totally internally reflected), given $\mathrm{n=1.50~?}$ $\theta_1$$\geq$    $^{\circ}\,$

The end faces of a cylindrical glal27ob0mho 3e tmn9j-g yy 5z3vss rod $(n=1.54)$ are perpendicular to the sides. Show that a light ray entering an end face at any angle will be totally internally reflected inside the rod when the ray strikes the sides. Assume the rod is in air. What if it were in water?

A lighted candle is plaq(:a cki28zt u9qs:ar ced 33 cm in front of a converging lens of focal length $f_1=15\mathrm{~cm},$ which in turn is 55 cm in front of another converging lens of focal length $f_1=15\mathrm{~cm},$ (see Fig. Below).
(a) Draw a ray diagram and estimate the location and the relative size of the final image.
(b) Calculate the position and relative size of the final image.

A bright object is placed on one sid6da. b y i:kcqi(ms92te of a converging lens of focal length f, and a white screen for viewing the im ( :ms iyd.bt96caqki2age is on the opposite side. The distance $d_T=d_i+d_o$ between the object and the screen is kept fixed, but the lens can be moved.
(a) Show that if $d_{\mathrm{T}}>4f,$ there will be two positions where the lens can be placed and a sharp image will be produced on the screen.$d_T$>4$f$
(b) If $d_{\mathrm{T}}>4f,$ show that there will be no lens position where a sharp image is formed.
(c) Determine a formula for the distance between the two lens positions in part (a), and the ratio of the image sizes.

  In a slide or movie projector, the film 2n h9ic.erd 5xpm1tf1 acts as the object whose image is projected on a screen (Fig. Below). If a 105-mm-focal-length lens is to project an image on a screen 8.00 m away, how far from the lens should the slide be? If the slide is 36 mm wide, mfcdh tpnr2i.x5191 e how wide will the picture be on the screen? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (picture size is ace mw3co* td6 sar10zl)tually 24 by 36 mm) is to be projected on a screen 1.80 m by 2.70 m placed 7.50 m from the projector. What focal-length lens should be used if the image is to cot0 )wms1a63 rzcle d*over the screen?    cm

Show analytically that the image formed by a converging lens is real and inveryoecnttx6 (z:.d /4h9) f nmzjted if the object is beyond the znm6efj/y )txc:zd (ht n .49ofocal point $(d_0>f),$ and is virtual and upright if the object is within the focal point $(d_0>f),$ Describe the image if the object is itself an image, formed by another lens, so its position is beyond the lens, for which $-d_0>f$, and for which $0$<$-d_0$<$f$.

  A movie star catches a reporter shooting picturezhkg51 a e-cxz hu(xbj+qk.8*s of her at home. She claims the reporter was trespassing. To prove her point, she gives as evidence the film she seized. Her 1.75-m height is 8.25 mm high on the film, and the focal length of the camera lens was 210 mm. How far away from thehu (xh.1ax zk qj-*bk8g5e cz+ subject was the reporter standing?    m

  How large is the image of the0erp)j r 4ai*(uyca6 e Sun on film used in a camera with
(a) a 28-mm-focal-length lens,    mm
(b) a 50-mm-focal-length lens,    mm
(c) a 135-mm-focal-length lens?    mm
(d) If the 50-mm lens is considered normal for this camera, what relative magnification does each of the other two lenses provide? The Sun has diameter $1.4\times10^6\mathrm{~km},$ and it is $1.5\times10^8\mathrm{~km}$ away.    for the 28 mm lens    for the 135 mm lens.