What would be the appearance of tt deg0 bup:)2xhe Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fleet in tnm ounsm)5cgi-hr ; 02he harbor of Syracuse by focusing the rays of the Sun withh- s)n0uno ;m rgm2c5i a huge spherical mirror. Is this reasonable?

Although a plane mirror appears to reverse left and right/ns*jl v; rhao+ agr55, it doesn’t reverse up and downrj 55+/lhsrnaavgo; *. Explain.

If a concave mirror produces a real imageee .st3y/gnrse s z:n*63n6 re, is the image necessarily inverted? Expla/rs6y e n rngs*n33e6e. tsz:ein.

An object is placed along the principal axis of t2i ) usj3:toza spherical mirror. The magnification of the object is -3.0 Is the image real or virtual, inv:z )uo 2ts3jiterted or upright? Is the mirror concave or convex? On which side of the mirror is the image located?

Using the rules for the three rays discussed with reference to (Fi+ .b,wgeo9pz ;t ecpq:g. Below a), drawpb,q;.cpw9gozee :+ t ray 2 for (Fig. Below b).
(a)
(b)

What is the focal length of a plane mirror? Wton3klqigm4 24 e*g: dhat is the magnification of a plane m3kl g4e gi:n4q2m d*otirror?

When you look at the Moon’s reflection from a ripply sea, it appql(oag 5vrz+j)mvn + 4ears elongated . l+z gar 5v 4(o)nqjvm+Explain.

What is the angle of refractirii 3,xo-f-br on when a light ray meets the boundary between two materials perpendb-f3ox-ii ,rricularly?

How might you determine the speed of light in a solid, rectangular, trgnz4 4 zqhxng627p z5oansparent objectz5og2z6n4 gxh zp7qn4 ?

When you look down into a swimming pool or a lake, are you likely to oqwr5l0ef d9 (underestimate or overestimate its deprl09 fwdqeo5(th? Explain. How does the apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stickmzmv*n1 uz.+sg9o dg8 looks bent when part of it is under water (Fig. Below).mvg n9.1 *mdzuo8g+sz

Your eye looks into an aquarium and views a fisht3; tl:ufpk :m inside. One ray of light that emerges from the tank is shown in (Fig. Below), as well as the apparent position of the tpl :m3;kuft:fish. In the drawing, indicate the approximate position of the actual fish. Briefly justify your answer.

How can you “see” a round drop of water on a table even though the watecufak4-:hn s zdb*g*sq+r+/ gr is transparent and sr gd a+4-cf zub:k*qn +sg*/hcolorless?

When you look up at an88m3dvcdv -in /il 6gx2rz)k n object in air from beneath the surface in a swimming pool, does the 8vkdmni6g 2x/)l38cz i r-ndv object appear to be the same size as when you see it directly in air? Explain.

How can a spherical mirror have a negaty8rq ba) r0+fkive object distance?

Light rays from stars (including our(sr,nhn . gd6g Sun) always bend toward the vertical direction as they pass through the Earth’.g s,gn6hn(drs 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 s6kqgbx9bs28 1 fiwa,rharp image of an object bkg1b q w68s xf29ria,very far away?

What type of mirror is shown in hbc kfwpcbg 3,gz ;841gp2l*h(Fig. Below)? Explain.

A photographer moves closer to his subject and then refocuses. Does the camerjks)q3w19 luno+zw 5pa lens move farther from or closer to the filslwn +1jpkoqzw 9) u35m? Explain.

Can a diverging lens form a real image under any circumss3 o:mmqin q1-+:nbcrn kbo; :tances? Explain.

Use ray diagrams to show that a real image formed bf+s;yevqq) c ;e*euhq1f .h:f afwz-dg ,wq48y a thin lens is always inverted, whereas uy4: evwq,q)q +hfh1.es- gwzce*f;d;fq 8fa a virtual image is always upright if the object is real.

Light rays are said to be “reversible.” Is this consistent with the thin lens een5f.ni nsum33l 8u* dqnnfel 3d3 .5su8i num*uation? Explain.

Can real images be projec)gid jy5a: lgp 9ta :),qmyz-zted on a screen? Can virtual images? Can either be photographed? zy,lp: gtmy5zagjq a)-9d i: )Discuss carefully.

A thin converging lens is moved close 54vqom1blem 0x +wh2qr to a nearby object. Does the real image formed change 5vlhboq1 w+ q0xme4m 2
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a mate3 s*sqsx8nh ;urial with an index of refraction n = 1.30 In air, it is a converging lens. Will it still be a converging unqs*hs8;sx 3 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 convergbfxf65tf 3bty5x,w k8ing lens. If the nose and the tkytfx5 b, t b36ffxw58ail are each focused 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 cpf vbn 2u7(i4ktu5 a,fonverging lens. Under what circumstancesufak5v,b2 n4 (uip7tf (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?

Why, in Example 13, must the converging lens have awazj(a9iv m 3, shorter focal length than the diverging lens if the latter’s focal length is to m3ia a(wv,9j zbe determined by combining them?

Explain how you could have a virtual o u:ormz4/5)t hm o:zgubject.

  An unsymmetrical lens (say, planoconvex) forms an image of a nearby object. Doe418gt *fxbvah qmaegs-4bw -h:*psg- s the image poi m-4egg4f-pw8ahh:s-1x bqtg*a*svb nt change 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, tdw, s7 9e)kzuf2ksmq8he sh2ksf, ku)d e9smw8 7qzorter its focal length for a given lens diameter. Explain.

Consider two converging lenses70k, u jh(zon k:+finepady+8 l9-uvo separated by some distance. An object is placed so that the image from the first lens lies exactpoju0,9 hl++7-e:fk8 and vunoy(kz ily at the focal point of the second lens. Will this combination produce an image? If so, where? If not, why not?

  Suppose that you want to take a photograph of yourself.ea k cx)4xc-b as you look at your image in acxxk)- 4.bc ae flat mirror 2.5 m away. For what distance should the camera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mi jh4d+:)cfns xwk* o-jrror, you see the same amount of your body whethewdo h x4jjn: k+*f-s)cr you are close to the mirror or far away. (Try it and see.) Use ray diagrams to show why this should be true.

  Two mirrors meet at a 13orc.cb*w s/tjqa-5 8k5$^{\circ}\,$ 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 fldc6k vb49r) .a. vd7dt5rtu qnoor stands 2.20 m in front of a vertical ) rrv5..c4tq7dbdn atu9dk6 vplane 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 planeak k+rme36u6o mirror. 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 dma+r63 oku6 keiameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mzs2s//mtc-xfollv jx a (y)sj8d.+3 xirrors 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 the Sun, foc1o,q*6ilmjah ue8.l mq:i;sl co) qmkh4 7s1nuses the Sun’s rays 18.0 cm in front of the mirror. What is the c4nqmohq u6q17s l :ohlml mei.* k81jia;)s,radius of the spherical surface from which the mirror was made?    cm

  How far from a concave mirr egr1kr2o qk93or (radius 23.0 cm) must an object be placed if its image is to be at infinity? kgor3q9k 2 er1   cm

  If you look at yourself i:wcs/18fgat7 e2 g xiin a shiny Christmas tree ball with a diameter of 9.0 cm when your face is 30.0 cm away from it, where/1 2wftgcs:i g7 exai8 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 amuseme6rax3a+jzjf- nt park shows an upright image of any person who stands 1.4 m in front of it. If the image is three timeszafj +r3x6-ja the person’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror that, when 2.20 c 9ku sg1,5hhkym 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 ac gt44u.l ulgv 2d56zt:i;yrcars behind you that are smaller than they would be if the mirror were u v.5i:lcagtgt 4uy;4 2zrdl6 flat. Are the mirrors concave or convex? 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 high is placed 20.0 cm from a, dg,gfh,+6zi xtp4drf6fj8 p convex mirror of radius of curvatuzp68,dxf gt,, gj6d+p4hff ir re 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 conv/fhh/ug 9,jldex security mirror in a store. You estimate the height of your image to be half j/ h,u/gdlf9hof your actual height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object be placed in front of a concave mirror so that izik0(fa(8v3;v q k ffat produces an image at the same lo vkffaik((q0f 3 ;azv8cation 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 w j.moo:iqu)o trb). l50d;bkfhen viewed in a curved mirror. The image appears to be 18.0 cm behind the mirror. What kind of mirror is it, and what i )oo) j dqu.;fkbtolmibr :5.0s its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different tetn 0 36y7k1cz hxk-ywvchniques,
(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 convex mirror d. c87 ijg38imdx222 g5olek xihzf.k 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 equation, Eq. 23–2, is valid for a convwhh6* tm54 u rv*exd/lex mirror as long as f is consideree*4m h*6 txl wrudh5v/d negative.

  The magnification of a convex mirror isqdbmk nh 43w(ymmuw u210)a5b $+0.65\times$ 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 cmtxdfntn5 3 gh ztxysz s -u-993 g1al9gi1s45q in front of a spherical mirror. It is desired to produce a virtual image that is upright and 3.5 cm tall. q1un - sgh4gd t9 sgz-t3 3z91nxax5iflt5y9s
(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 w:5u1kmuw 9 akfactor of 1.33 when your face is place:1w w9u5mk kuad 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 in +wxon46 bwasv94s e lhd:rmlz3 (6jt;
(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 i za5lbggk(ycg( g g(:(ce 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% of its value in water. Wha; gegmdqimpj;8) -6qu l+z0 y mzi5;ayt is the index of re+y;i) ep-a0zdmz giu l;qmmq6y j85g;fraction of this substance? n =   

  A flashlight beam strikes the surface of a pane of glass (n = 1.58) at a p01 m1736ytdh bjl-i1 .x* blpfemnna 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashlight upward from q09g (ngoe5xp)ges 1e 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 an underwater spotlight exits the water at an angleg ycq,7c0 4(ap.jpwjzut 2 z0q hdi(,b of 66.0,0cz7qp czih((t ,y4 u.da qjjgpw2b0$^{\circ}\,$ 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 i 7v5,mxq f h(e,jzq(vseen 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*sxc:r .e n(v,9skqwds3 b/iojo(0wr flat glass sides whose index of refraction is 1.52. A r nj w/e* d ckss,soq9x3vw:0rb(oi.(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 beam o9.d z) zwkizmrsha/8qf66, ydf 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, measured fro.z/z6y wf8d k dzrs6i,)ha 9qmm the wall beneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equilateral gmg p)7q 2mftk,f 8f6)ic szcf.lass 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) d;4,xs*jix jv;rusl,and is partially reflected and partially refracted. Find the angle of incis,*ujl ;4 ;vxd,ji rsxdence if the angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam incident on a u,:u-pdoy zak0.d ,d gxn2nd+dniform layer of transparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the incident beam, independent of the incident angldd.a+y d n:kdz-,uoxp2d0g, ne $\theta$. Assume air on both sides of the glass.

A light ray is incident on a flat piecea qlfbze7+v4f/:zhbqgy/ s7 4 of glass with index of refraction n as in (Fig. Below). Show that if the i qhbqf74zg:fb4 v el /a7ys/+zncident 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 ip 07u4rhw /imhnterface between water and Lucite? To be totally internally ruh 07/wimprh 4eflected, the light must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–air sur+lwrprcq;p( 9 face is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in a pool of water from a deptgkby;a3 gz 2bf s+ei98h of 62.0 cm. Where must it strike the air–water interface, relati bzabei9;3 8f2 gskyg+ve to the spot directly above it, in order that the light does not exit the water?    cm

  A beam of light is emitted 8.0 cm beneath the surface of a liquid and ssv-plxi u3t 5fp8pxuq-n/ 0u7trikes the surface 7.0 cm from the point directly above the source. If total internal reflection occurs, what can you say about the index of refra8iptx vsf7xuppu-3l0 n-q5/ uction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikek,tn jo 5if/3xs the left face of 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 fibebvuv m.0yf0ca* 5gjzhbf*/g. r 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 the light beam reflects back igg /vm0 bc0fha* b5.* .yfuzvjnto the material at point a.

  (a) What is the minimum index of refraction for a gl+ 1h d+e*zub beohe: olxqmfe-;7i4z/ass or plastic prism to be used in binoculars (Fig. Below) so that total internal reflecolbo+dm 1h7/beei4zf uhz :-+xqe e*;tion 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 convtxf4 ac+4i fw;cryy 0y9foj). erging lens. Find 4)t;yaif wf9o c0f+j yycx4.r the object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a poimp+a d21 (iykfxx9p5rnt 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 li*s3fj /p ewl:xght from an object 2.75 m away as an image 48.3 cm on the other side of the lens. What type of lens is it and what is its focal length? Is the image real or virpj fwxe/:ls*3tual?  ----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-focal-lenv /f3),;t5o1yjx /g e( 6tunaeiu0mzfr(dz xagth 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 convergin ni*hrgwr4j*i t-9zl 4wvl2v.g lens with focal length 24 cm to view a stamp 1r4 rnlg l*z4*vii2.h-9wt wvj8 cm 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 from an oble2p9z a :r h-ycruc4;ject 4.0 mm high. What are the position, t2 ;cr l4pceuza9r:- hyype, and height of the image?
   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. Tun1 j v wju6fyx39o))whe maximum distance allowe)uw j v96)xf3oy1 jwund between the lens and the film 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 magnify reading)j 9c6)( yp iry*,:mtkcrqhuh material by a factor of 2.5× when a book is placed 8.0 cm behindquih cmr6 y,9yt:(pkhc))*jr 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 froq3yb0hq7k c;ra v2jz 8m an 8.0-D lens. By how much does the image move irqkv78 h23; yjqbca0z f the object 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 a3h 4f/ipo2.ehh oedj.ci1lz9 focal length of 25 cm should an object be placed to produce a real image which is the samp do1o9hf ci.he.ljhie3 z42/e size as the object?    cm

  (a) How far from a 50.cr npu )+bc);y0-mm-focal-length lens must an object be placed if its image is to be magnified 2.0;u+)y rcbnpc)0× 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- 9(a ( lhr/flmrj0fpx)length lens must an object be placed if its image is to be magnified jml rlf9)p0/hfa( (xr2.00× 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 1.2vy a)bwn)(2)rzjg pp*pg9(x w 0 m from a 135-mm-focal-length lens. Where is thepp x z*)n)( rbg(gjpa w92w)vy image, 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- iz+vs/*r:g3m1 ah*j1.ls,edy jv9v jg9cn brcm-focal-length converging lens if the image is 2.5× larger than the object a3vvm jzj,+1 9vrr sy1lb: 9anidc*.g/gsehj*nd is real?    m

  A bright object and a viewing screen are separated;niznsb : 2vtjhodi*tjw 321g/ + fl/p by a distance of 66.0 cm. At what location(s) between the object and the screen should a lens of fo sdtob1j://;*g v thiwnf+22ni zjpl3cal 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 placed 16.5 cm apart. An objec2t4.ec oq 4 ,sd 6gwlos1om+lut is placed 36.0 cm in frosu. eo6tldg2omcs ,o4l4qw+1 nt of one lens. Where 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 withp nhgspydu8 :e-0co*f2p b/ 8n $f=-31.5\mathrm{~cm}$ 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 converging8;pus+-xkf)2j rmf tw 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 focals;jw -+fk8tfu r)xp m2 length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Example 23–12t47+zyo(rc.jm0f r r v are now placed only 20.0 cm apart. The objecvr+( .cyj t0m47orzf rt is still 60.0 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. The focal length of the leei6 4rup9xkt2 hw)pns ka9f0 9ns 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 and located halfway between the two lenses. How far to the left of the 15.0-cm nf k06w 2hki9)esxrtupap949-focal-length lens is the original object?    cm

  A diverging lens withpo u5c3v6 )kv9slfaia ay64 a4 a focal length of is placed 12 cm to the right of a converging lens with a focal length o454ia)caa9o 6u pv3yfv6k sal f 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 (c9 - pp c2uohau zbj()fli;t+with focal length 20.0 cm and one diverging with focal length are placed 25.0 cm apar+;jz9ciautocl h b u((p-)p2f t. An object is placed 60.0 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 plac cso03 tysis w a2r1:6d6xq2 lui0k0cxed next to a converging 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 of 34.2 cm and 23.8 cm. What is th kohb9q40e4q9t,q w( r6mabxy.st d5 ve focal length wmqhb ,y9 oa59rv4 e(bq6q x.tt04sdk if n = 1.52?    cm

  Both surfaces of a double convex lens have rad n /cl+hbth h9jt.q916mc+ uhhii of 31.0 cm. If the focal length is 28.9 cm, what is the index9 . h+hl+h6ch htunqj/b1tmc9 of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a fonan fqd. )- 0vzyef6w-cal length of -23.4cm. What is the radius of thq ne-w- fy n.zv)af60de concave surface?    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat surface and th6n1fe o5rpax gk x8-,ue other has R 8a6xr5negok p , f1u-x= -18.4 cm. What is the focal length?    cm

  A symmetric double convex lens with a focal length of 256l5etv w4(n ae,l5dti.0 cm is to be made from glass with an index of refraction of 1.52. What shouldi 4eae6t(,d55n ltw vl be the radius of curvature for each surface?    cm

  A prescription for a corrective lens calls for +1.50D. 3myn)r3emlq c3 (w9p d,:cfak The lensmaker grinds the lens from a “blank” with n=1.56 and a preformed convex front surface pn ckra3y mq (d3ef:m,9w3)lcof radius of 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:av u d:9)2o9)apx wzalh (r5y7gls1othsl s- (Fig. Below). You stand 1.5 m away from one of these mirrors and look into it. You will see m1w)a9ya ()o:vsruph2:tl9d 5a zshglx l7s -oultiple 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 swimmqfj 8dzv+b1b. ing pool filled with water. We measure the width (x=5.50m) and then note that the bottom ef 8 zb+jvbq1.ddge of the pool is just visible at 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 certain piece of plasticyv2yd(;3l11wvk3 i d*dns crq 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 (qxxy*m16tesx6 wc2-425wq d*ioz6t xuvknt case of a spherical mirror. Specnz s t uqm(*w6ktey2*x25-1vxoqxi4cd x w66tify what 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 fore/l:zi, kn8 ls .ki+q,zyrj b,m 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 diverginw(o.u 1 ac*tau0k:sq xg lens can never form a real image of a real object. Can you describe a situatioxuu*co. tsk:(a0q aw1 n in which a diverging lens can form a real image?

  Each student in a physics lab is assigned tbfwvw118)iyq vc*p-mwwu)( u o find the 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 thev c u*v1b(ywuwi1-)qw) 8mpwfy 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 prism dpf (su:0/xa qis $\phi=72^\circ$ 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 cylind1z;j7nc;y ;awymrz l2rical 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 conv6q+lqsvw 34 v s0lwoj6erging 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 converging lens of fepap-wtxu7 m 3 h gk)il.o)i.*ocal length f, and a whitekm)ea.io w)il-*3 uxt7g p.hp screen for viewing 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, the film acts as the object whoe.3 g h d7,;oqsdac8cbse 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,a;d83h7edc.g osq cb, how far from the lens should the slide be? If the slide is 36 mm wide, how wide will the picture be on the screen? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (picture size is actually 24 by 36 mm) is to be projecteb +k0*ot wqczj b28;cqd on a screen 1.80 m by 2.70 m placedk*jt2o +wbcc 0;qz8qb 7.50 m from the projector. What focal-length lens should be used if the image is to cover the screen?    cm

Show analytically that the image formed by a converging lens xpc0i ws*k 0p1 tw o-xhm;oxr1e0(gx,is real and inverted if the object is beyond the focal pointepx0i rms 1x0 gw,h;p(wx1*-tx0co ko $(d_0>f),$ 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 rc4 a5v1 ou9vogx ,ej1eeporter shooting pictures 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 the subject was the reporteg45 ve1exu ovj,91a ocr standing?    m

  How large is the image of the Sun on fpjg94.pi9xm ,epz n4+8jcwqy2 w dfk;ilm 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.

  (a) An object 34.5 cm in front of a cer5(pyxo yldk3a(i + bp:9vl aj4itp2+rtain lens is imaged 8.20 cm in front of that lens yo25ap k p(l4bjt i(l9av:3iyxpd r++(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)

  When an object is placed 60.0 cm from a certain converging lens, it -xfxfkm 9t w7;forms a real image. When the w-x;mxkf9 7tf object is moved to 40.0 cm from the lens, the image moves 10.0 cm farther from the lens. Find the focal length of this lens.    cm