What would be the appearance of the Moon if it qct) 0ciel+,qte 3t*3-ujzb. x legh: had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have bub:a 1 cjj5o-vxfmb)3p rned the whole Roman fleet in the harbor of Syracuse by focusing the rays of the Sun with a huge spherical mirror. Is this reasonabb f m1opxv5j3-)jbac:le?

Although a plane mirror appeaq3y)k0 /bxhgwuk: ; furs to reverse left and right, it doesn’t reverse up ufxg)by3/h;qu wk:0k and down. Explain.

If a concave mirror produces a real image, is the imyo;i *m5vrop5 vkh49w(rwz 5hage necessarily inverted? Exv 9( rmzpr*5wwhhy5oo ;ki45vplain.

An object is placed alonjmqqb k co)s9o1 lfj5z44cvp 2mh/ 8-ag the principal axis of a spherical mirror. The magnification of the object is -3.0 Is the image real or virtual, inverted or upright? Is the mirror concave or convex? On which side of the mirror is the plaz4jm vh4q2c f 51/s qbo- 9)cmj8koimage located?

Using the rules for the three rays discussedytn)hf;ur/ hux/r f20 with reference to (Fig. Below a), draw fyftu2r hr/;nh0/ x) uray 2 for (Fig. Below b).
(a)
(b)

What is the focal length of a plane mirror? What isjz4(sc4y nn4s cb9c3 x the magnification of a planec4 (n4cbjs 9sxz3ycn4 mirror?

When you look at the Mr.s(v z (vp*kfoon’s reflection from a ripply sea, it appears elongated . Er.(zsv*( kpvfxplain.

What is the angle of refraction when mg 1+khw0 w97; nn/ 5apgcyxyqa light ray meets the boundary between two materials perpendi+ a;9y1wq7wnym5n gcg /p xh0kcularly?

How might you determine thggckh6- l *5fjk5 hsu2x9x1 pqe speed of light in a solid, rectangular, transparent ox-l1xghg sq5k52h*cu f pj6k9bject?

When you look down intcceu.qxj.7 9 - jj,fjwg7: yrvj- s.xbo a swimming pool or a lake, are you likely to underestimate or overestimate its depth? Exp-ej7rcxj b jg:-j 97.xjfs.vuy,. qw clain. How does the apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks bent when part of it is * t7p7hax/wj cunder water (F hj a*/7px7wctig. Below).

Your eye looks into an aquarium and views a fish inside. One+ d(ql)gy-umv ray of light that emerges from the tank is shown in (Fig. Below), as well as the appa-(l) muy+vdq grent 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 wa.fh/z*hw mgp 7ter on a table even though the water is transm fhw.p*z/g7 hparent and colorless?

When you look up at an object ignzr9e7 7+i tgn air from beneath the surface in a swimming pool, does the object appear to be the same size as when you see it dng zr7t7gei+9 irectly in air? Explain.

How can a spherical mirror have a negative e /+y7w6o7 ll8 bufj7fvkl/zpobject distance?

Light rays from stars (including our Sun) alwayz4m)b*jsfwztku t c1)q3 n;5cs bend toward the vertical direction as they pass throughfj;m3cqnk*utc1z4 w5z ts))b the 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 is to make a shar0 6:oi5u+ee ; njxvy7b gn;qcqp image of an object vj ynegb qv;cqoe;x6ui57 :n+0 ery far away?

What type of mirror is shown in (Fig. Below)? Explailt tym, qp/118wb-mngw 9bg ./zwql5un.

A photographer moves closer to his subject:1 vyx/a7gfzl*30hmud i 1o+qku/cyh and then refocuses. Does the camera lens move farther from or closer to theou0 f7zyv1 y*kaqd:/hl3ih/mg cx1+ u film? Explain.

Can a diverging lens form aup tr;.tjh27chhukv 2)le+ n5 real image under any circumstances? Explain.

Use ray diagrams to show thu :1 ,76 r;-iyv: tic/ukj6qpigdud leat a real image formed by a thin lens is always inverted, whereas a virtual image is always upright if the object is real.kpu:6ut6e7lv: / djiy1; iudqrig c-,

Light rays are said to be “reversible.” Is this consistent with xoi.xf 4wx(z ,the thin lens equatoxzxw ix( ,.f4ion? Explain.

Can real images be projected on a screen? Can virtual images? Can either be ptz 88hx(nmn4b3xft2me h* m s(hotographed? Discuss caref nx4etnfm2bx *8h(sht( z3 8mmully.

A thin converging lens is moved closer bxrbn 68 9)ln/vve,jc/p.r ;zw x irc:to a nearby object. Does the real image formed chang ne) p,.wrvjbi c /nzrrvxl;/9:86 xbce
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a m3jxl fgc *lji k)w1bd )96hv)saterial with an index of refraction n = 1.30 In air, it is a converging lens. Will it still be a converging lens if placedk)hgw*lbx)j3 6j) 1sc9difl v in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands facing a converginvgn5 ltx0 /;lrg lens. If the nose and the tail are each fovx tng5l/r;0 lcused on a screen in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facing a converging lens. Un /oh8g 3lij1yg3gc5ke der what circumstances (if any) would the image of the nosyke1h 3g/gl5 o8cijg3e be virtual and the image of the tail be real? Where would the image of the rest of the cat be?

Why, in Example 13, must the c-o fd*)60bo kkbkdso3 iwm) a5onverging lens have a shorter focal length than the diverging lens if the lato*db )kw)m 5fod-bo06k3k s aiter’s focal length is to be determined by combining them?

Explain how you could have qnq* 5bta mgi .v8qu,oi49-msa virtual object.

  An unsymmetrical lens (say, planoconcesi7o8+w kh cya)l.3 vex) forms an image of a nearby object. Does the image point chan 8ws e+co7liy3k.)c hage if the lens is turned around? ----待选择----yesno 

The thicker a double convex lens is in the center as compar th,ebh+k -wd:ed to its edges, the shk d e,hh+twb-:orter its focal length for a given lens diameter. Explain.

Consider two converging b*s ww jzu 1t2mt2;ye-lenses separated by some distance. An object is placed so that the image from the first lens lies exactly at the focal point ofz22-su1 bettym;jw w * the second lens. Will this combination produce an image? If so, where? If not, why not?

  Suppose that you want to take a photograpl:x-a+y(z pv 1iel+v-7 d.ybbsd(wnm h of yourself as you look at your image in b:+pl. -m+wx(1l s(7devizdny -ybvaa flat mirror 2.5 m away. For what distance should the camera lens be focused?    m

When you look at youn.vv3 fif k5u0rself in a 60-cm-tall plane mirror, you see the same amount of your body whether you are close to the mirror or far away. (Try it and see.) Use ray diagrams to show why 0i fk vfnuv.53this should be true.

  Two mirrors meet at ry/gs951 2kjpvziaua ,q9ns8(s,b qha 135$^{\circ}\,$ 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 stand zk:m5 ;yr6e2drmcc(ks 2.20 m in front of a vertical pryd6z 5cke:;c(2mkmr lane mirror whose bottom edge is 43 cm above the floor, (Fig. Below). What is the horizontal 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 mirror. What area of the mirror is used to re:tz79( 4k es si5jcqpjflect the rays entering one eye from a point on the tip of your nojz it4ce ks9s:p57j(qse if your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane / gfr uyerpj.e*/ 9vzu/5n c4qmirrors 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 poin -gg*8ky.q. b +u9e/ -cs, jepcmtuh;u/mye oyted at the Sun, focuses the Sun’s rays 18.0 cm in front of the mirror. What is the radius of the spherical sure+ug/.-c/jyhp cmm8k,y;get. b 9y sqe*uou- face from which the mirror was made?    cm

  How far from a concave mir.a yncw/fk*e :(1efyy cok:q7ror (radius 23.0 cm) must an object be placed if its image is to be atkf/n:w1ycfk*o 7 qay y( .eec: infinity?    cm

  If you look at yourself in a shiny Christmas titc w2rdc,/mad(w;+q ree ball with a diameter of 9.0 cm when your face is 30rqtw+ d /,cwd(imc2a; .0 cm away from it, where 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 stands 1.kk:t-5cn 5q*h6 ybdd0g qx. qc4 m h5 cyk.:d*k0xq n5b6td cq-gq in front of it. If the image is three times the person’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror that,l*shyk4 :vg m/3uyi;c 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 you that are qab97+a n 2w achn 1arv1w7(gr pqh9k;smaller than they would be if the mirror were flat. Are the mirrors concave or convex? What is a mirror’s radiusaakaw+h b9 ap 7c1197(ng rw2nqr vhq; 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 high is placed 20.0 cm from a c ://kky mh9 f/fertp6vonvex mirror of radius of curve/htr k9k: m6vffyp//ature 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 convex security mirror in a store. 9wl40lv ;4vtsm 8 jimmYou estimate the height of your image to be half of your actual h4m9w 4m j;v 0ls8lmvtieight. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object be placed in front of a concave mirror so th l n1jesng6)+ft 2fj6 5lx8:pq vzc0uaat it produces an image at the same location as :g1c+x)tl2sqf8 vf nn j66ela5zp u0j 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 ,oad1+6gp azqis virtual and very small when viewed in a curved mirror. The image appears to be 18.0 cm behind the p 6g+daao,qz1mirror. What kind of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different tecefal:)(t y -o) 8zai o,krc;kihniques,
(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, thow)oo( gs,j8p -ijbp/at the magnification m of a convex 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 mirror equatio;t(-w5mruy 5o hvh rv-n, Eq. 23–2, is valid for a convex mirror as long ah5( wvhrvromt- ;u5 -ys f is considered negative.

  The magnification of a convex-iv 5v*umgz p, 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. It is -cjws28u r(d07ibkozx 3jk2pdesired to produce zcp7w -0r sx 8i(dk o3jukj22ba 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 1.334l(( ei ehvla3tz3cc/ when l /tvce (h(3z3ecl4ai your face is placed 20.0 cm in 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 iuj73bqm5n1v -:n m yctn
(a) crown glass,    $ \times10^{8 }\;m/s$
(b) Lucite,    $ \times10^{8 }\;m/s$
(c) ethyl alcohol?    $ \times10^{8 }\;m/s$

  The speed of light is/)/kohss4wx03 6 dhi s ,.uchxiq by9n ice is $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain substance is 89% -(-vr bm z0bmoof its value in water. What is tv-rm0mz - bb(ohe index of refraction of this substance? n =   

  A flashlight beam strikes the surface of a p(4wwna4 ,tu eyane of glass (n = 1.58) at a 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashlsbr, lg6q zzt/3:y,+gmoxq a0ight upward from beneath the 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 a186 tccte e3ocn underwater spotlight exits the water at an angle of 68oc6 ece1 3ttc6.0$^{\circ}\,$ 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 h y-j3l2gma,er,r fr,tm:plcn3 s +- omx3,zf to make a 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 s)/gbo :o p /qkibo5pc(+sw2 csides whose index of refraction is +(qoocp:bis)s 5p w2kg/bc o/ 1.52. A beam 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 shines a narrow nguu5eiug.9c.*hvsvqq2v )* 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 thu2* su)qvv .ghic5q*uvn .eg9e pool (Fig. Below). Where does the spot of light hit the bottom of the pool, measured from the wall beneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equilateral glass prism at + rzxdgg;n7v4(vs+-a*zr i uf 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 ai1f;fempviqco;1i5 tz t 8*3 qxr strikes a slab of glass (n = 1.52) and is partially reflected and partially refracted. Find the angle of incidence if i; f5tvieo z 8* 1;3x1ftpqcqmthe angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam incident on a ufjwzp;pwf-q5 - *z5d nj5sf4l niform layer of transparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the incident bfwlf4 5dfqjzs --5z;wnp5*j peam, independent of the incident angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on a flat piec pm:gskdf)f8nm:: awu87 9wak e of glass with index of refraction n as in (Fig. Below). Show that im kakd8fww:u mp fg):98as:n7f the incident angle $\theta$ 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 interface between water anqs-e 6)(iobc/fj dj;p d Lucite? To be totally internally reflected, the light must start in which m;i(p6cj)sqoe f-/ djbaterial?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–air surface i voycy5/ xgd75cykuz a7e,v; il8 1e8rs 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitteu*mcf8 8p23bmk 01ru wn)ey aad in a pool of water from a depth of 62.0 cm. Where must it strike the air–water interface, relative to the spot directly above it, in oymukerf) 2m na1pwac8 8u30b *rder that the light does not exit the water?    cm

  A beam of light is emitted 8.0 cm beneath the surface of a liquiegn: xjiu+t+ 4xe hak/h0h*/md and strikes the surface 7.0 cm from the point directly above the source. If total internal reflection occurs, what can you say about tj0+mx:hn/a4+iehth kx /*e guhe index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face i1jrzc3lj83sx1x4 vaof the prism in (Fig. Below) at 45.0$^{\circ}\,$ 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 end of an optic fiber as shohdgx: k.0yj4ewn in (Fig. Below). Show that we can guarantee total internal reflection at the side surface of the material (ahxy04d:ejg k. t point a), if the index of refraction is greater than about 1.42. In other words, regardless of the angle the light beam reflects back into the material at point a.

  (a) What is the minimum index of refraction for ahzjhryq;3*w+ qg9i :h glass or plastic prism to be used in binoculars (Fig. Below) so that total hj r+ i:;h*qwzy93qhg internal reflection 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 located 78.0 mm behind a 65.0-mm-focal-length converginzb0o- hj +smg0g lens. Find tmsgo0+-bh jz 0he object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed t4 c( r c5gsl h4.lgrvv0/2:hfnnmt9tjo focus at a point 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 b8f;n:;9jj2fui vrhcn* o( xton the other side *jr:o xfnf;(9c8;uh2jv bnit 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 2b:h cn 4ik3ps1zqd53y0.5-cm-focal-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 a converging lens with focal length 24 cm to view a stampc:a3tv; 8u las 18 cm in tc alu ;va3s:8front 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 146gd 2j p rzou1sy:53jt.0 cm from an object 4.0 mm high. What are the position, type, and height5zy2 jtju3 r:dsopg16 of the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens;w3)+e y i e1)sgi 7rnv2tydsq is used to focus an image on the film of a camera. The maximum distance allowed between the lens and the film plane is 1203 i27gqnsr idtv1+eswy ;ey)) 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 magnify reading material by a factor of 2.5× when a bo;*cq qrds38em54lm uxf j3n;wkv fx1) ok is placed 8.0 cm behind wmf1r n 3q43dm*kf5;;elxjs 8 c)vxqua 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*g3 djk 6i0*)dstgdr f from an 8.0-D lens. By how much does the image move if the objectj dfdts6* 0g3rid)gk * 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 o) vp33 hh:sxfa focal length of 25 cm should an object be placedhx):3f so3vhp to produce a real image which is the same size as the object?    cm

  (a) How far from a 50.0-mm-foca+pohzo7) ov1) *qex bbl-length lens must an object be placed if its image is to be magnified 2.00× and bx7bv )1+pob z)oqo*e he 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 must an object be placed if its z +miv*3x5 229m; 5/m 7efazadjdx wwyx-pyucimage is to be magnified 2.00× andm djym*7x+25pxz/3 - wimxuy 9 5c;wazfe2dva 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. Wp*j4h-q.c 83radoq 1x k7eee nhere is the image, how high is it, and 3r1eqnojac-xpq * d ehk7.e8 4what 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-length cn)2;ike vsjude/( e-xonverging lens if the image is 2.5× larger than the object and i;)k(esi ee-v / xud2jns real?    m

  A bright object and a viewing screen are separated by a distance of 66.0 cm. kp 7)*pgly4;ao djew6l n-a1rAt what location(s) between the object and the screen shouley41kj-an l6lo) ;7*gpra wdp d 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 arqt2j5wu8 2gix e placed 16.5 cm apart. An object is placed 36.0 cm in front of one lens. Wher5t28 2i wxgujqe will the final image formed by the second lens be located? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens witkb81 k.93mp0z w(qd bb6imaoxh $f=-31.5\mathrm{~cm}$ 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 bav8im,/ 1gig lens is 21.0 cm behind a diverging lens. Parallel light strikes the diverging lens. After passing through the converging lens, the light is again parallel. What is the focal length of the diverging lens? [Hint: first draw a v8b1/ igia,mg ray diagram.]    cm

  The two converging lenses of Example 23–12 are now pl2 bkudgz,8zyvhqo.j .k gpxd6:i7c 4 9aced only 20.0 cm apart. The object is still 62z.8g6uop kj b9gdxzq:4vh ,d i.7ykc0.0 cm 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. T+( etud h1b7nn bogl-ca;ya .,he focal length of the lens on the right i+t u-a,h; lnndyoe.c7 bg(a 1bs 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 and 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 12 cm to the 9ursij/e4t3 sright of a converging lens witi9ss/jtre 34 uh a focal length of 18 cm. An object is placed 33 cm to the left of 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 focal length 20.0 cm and one divergh j (r k:cvhi/ydp :s l2uh1s,a96xy.ding with focal length are placed 25.0 cm apart. An object is placed 60.0 cm ijsyh2 ( ax/r6.:1h9uhv, ysp:dcdk lin 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 converging lens of focal lewj6v vg2e*3x7udav- /i w(jx jngth $f_C$ 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 ruv8h )x;i o/dgo 8n fd5yv5hh3adii of 34.2 cm and 23.8 cm. What is the focal l3 nhu xdio ;y8 5vfhd)og/5vh8ength if n = 1.52?    cm

  Both surfaces of a double convex lens have x. lp )b67xd*apih zu*radii of 31.0 cm. If the focal length is 28.9 cm, what is the index of refraction of the lens materlau*dbx ipp .6x7zh) *ial?    cm

  A planoconcave lens (n=1.50) has a focar7tdtsh n94sq/7t , mcl length of -23.4cm. What is the radius of the concavt7t/st,csr dmh4n9 q7e surface?    cm

  A Lucite planoconcave lens (see Fig. Below) has one flatgp /yld ujr jt5,-g-4l surface and the other has R = t,j 45 u-glyp ljd-r/g-18.4 cm. What is the focal length?    cm

  A symmetric double convex lens with a focal length of 25.0e,6knlpn3vkkm2 s 3 ua* -fce0 cm is to be made from glass with an index of refraction of 1.52. What should be the radius of curvature for each surfacm 3naku0v,e3fc*l-2 kkenp6 s e?    cm

  A prescription for a corrective lens calls for +1.50D. The lensmaker grinds tb*v4ns 9lb7o ihe lens from a “blank” with n=1.56 and a preformed convex front surface of radius of curvature of 40.0 cm. What shl47 v9bob*isnould 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). Y*0ne0j vgde)2-sf n:b wsad*w;tws0 dou stand 1.5 m away from one of thes;0jdfw sv02gn-* s dwta)ebwds:n *0ee mirrors and look into it. You will see multiple images of yourself.
(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 pool filled with wayz37s2bs.jvp ter. We measure the width (x=5.50m) and then note that the bottom edge of the pool is just visible at an angle ob3 spy.sz jv27f 14.0$^{\circ}\,$ above the horizontal as shown in (Fig. Below). Calculate the depth of the pool.    m

  The critical angle of a y);6uvcc; a+tr,sw5vqub( rwcertain 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 be considered a limiting case f i.dm )ekd18uof a spherical mirror. Specify what this limit is. u8d)ei1mfd. k
(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 form a 90b5wpj rl4505sneo 6 be$^{\circ}\,$ 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 imagdfi3 y 8-t(kbcqwr0/9gl,yzff w: k:ce of a real object. Can you desf3 wqy:r,l: t9wkc 8d z(gkyci-f/0fb cribe a situation in which a diverging lens can form a real image?

  Each student in a physics lab is assigned to find th1kt5 oc e,2qgxe location where a bright object may be placed 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 nqx e,15k to2gceed to repeat the lab, and justify your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of a prism i2ny31b vbi pl bpl.2.hs $\phi=72^\circ$ 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 0bmg a35zxi2x glass 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 placed 33 cm in front of a -jm ch 7cqwvb bei+212converging 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 side of a convergiig,r+hx rh 8c:ng lens of focal length f, and a white screen for viewinr,hixcghr8 : +g the image 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, sf)krdjs-v px0,+ bk 9the film 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, how wide will the picture be on the scree0b kxf)vpsrjk9 - s,+dn? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (picture size iso l b,v;o*wq-w0v81lyit y :rq actually 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 f- oq8vbt 1l:ywwo lqvyi*;,r0 ocal-length lens should be used if the image is to cover the screen?    cm

Show analytically that the image formed by a converging 6wijfb6 k5vh + m tvxd14md8b-t- 6wfypmb2,wlens is real and inverted if the object is beym 4hjd66 i -1bx 2,yfw vmf58tdbt-wvkpwm6b +ond the focal 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 repfrgr5x st 4w07orter shooting pictures of her at home. She claims the reporter was trespassing. To prove her 5frt wx0 r7g4spoint, 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 the subject was the reporter standing?    m

  How large is the image of the Sun on film used in a camera with) kouv37:es+7 ldk+qi4cy jwi
(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.

  (a) An object 34.5 cm in front of a certain lens is imaged 8.20 6mbd (o+. mev-ognb;o cm in front of tv+bbod-mn(o m 6;g. oehat lens (on the same side as the object). What type of lens is this, and what is its focal length? Is the image real or virtual?    cm (diverging)  ----待选择----virtualreal 
(b) If the image were located, instead, 41.5 cm in front of the lens, what type of lens would it be and what focal length would it have?    cm (converging)