What would be the appearance of the Mp dy; +g -7y-zcsnegy1oon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned thx5ej) ;b1ds dqqsi4k8e whole Roman fleet in the harbor of Syracuse by focusing the rays qq8di dx)5s4;bkesj1 of the Sun with a huge spherical mirror. Is this reasonable?

Although a plane mirror appears79a(niy eti c0 to reverse left and right, it doesn’t reverse up and down. Expliy 70tieanc9 (ain.

If a concave mirror produces a real image, is the image nece skj +kk74p txr3y vgu1xoc5c)r; *hm)ssarily inverted? Exr+t jkgo h mpc)v ky)u*cs3r; k5xx174plain.

An object is placed along the principal axis of a spherical mirror. The e4+ hubvjcqlr 02gk2/e0:tdi magnification of the object is -3.0 Is the image real orgj +chiv 0eq/blr0d2e:4ku2 t virtual, inverted 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 discuss2 b5bd-d ya6opuvoq13ed with reference to (Fig. Below a), draw ray 2 for (Fig. Belowda3duv5obb1 y- qo 2p6 b).
(a)
(b)

What is the focal length of a plane mirror?i+si8, ivaez, What is the magnification of a plane mirror?sv8iz+i e, ia,

When you look at the Moon’s reflection from a ripply sea, it -m 2kgqf60bbbappears elongated . Explain.b fbq 2b0g-6km

What is the angle of 2 fw*7q8smguzrefraction when a light ray meets the boundary between two materials perpendicularl gswu8m fq*7z2y?

How might you determine the speed of light in a solid, recm,p , kcqf7bn3-;aoys:u/c j ptangular, transparent objfy;koc qpbua-s7, 3n:,p/j cm ect?

When you look down into a swimming pool or a lake,)+c:pgjd w- gx are you likely to underestimate or overestimate its depthc:g)x+ w-jdp g? Explain. How does the apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks benn p,fg;a0o. 2wohm stjz .uu7/t when part of it is under watera2w0mg/ ufhto,osp z j ;un..7 (Fig. Below).

Your eye looks into an aquarium and views a fish inside. One4umfv m-7kjr- az5b(id4zid m7 k /l0d ray of light that emerges from the tank is shown in (Fig. Below), as well as the apparent position of the fish. In the drawing, indicate the approximate position - f4kd(mum/zr 0i zbdj577dvmk ia-4lof the actual fish. Briefly justify your answer.

How can you “see” a round drop of water on a table even though the water is tr)w9w/vyc s0j/uf: a anzb8fmj-*a7v gansparent fzwg vn:cub7ymj9/0 avsj)w f-a* a/8and colorless?

When you look up at an object in air from beneath sxup1twcp(va8:5n3- ooj f0e the surface in a swimming pooln1 u :3-axpj(fp ots80cveow5, does the object appear to be the same size as when you see it directly in air? Explain.

How can a spherical mirror hav;t; 6xo7lb. om1a1ovi.cev hbe a negative object distance?

Light rays from stars (including our Sun) always bend toward the vertical dirihujf vyg l8d9 /bp ea(l71gbx7.r qs*w)/ gh/ection as they pass through the Earth’s atmosphere. )p/xh7w/ qag. f lb18yed7gr*ju 9(hi sgbl/v
(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 sharp imfhdkdm 6-lalgx.6 9 6kage of an object l9h -k66m d.kladg6fxvery far away?

What type of mirror is sho 9h rp(s4v xmb8k5uj3kwn in (Fig. Below)? Explain.

A photographer moveseb3w;8 ujnlabl 3a(3e closer to his subject and then refocuses. Does the camera lens moe;e ba(8j3u3 l3albnwve farther from or closer to the film? Explain.

Can a diverging lens form a real imwsdjng0 g)l-kmym- 3.age under any circumstances? Explain.

Use ray diagrams to show that a real image formed by a thin e65 hno+b f)azlens is always inverted, whereas a virtual image is always upright ia+ob e)h 5zfn6f the object is real.

Light rays are said to be “rv 4*5ri aytri.nt:5 hreversible.” Is this consistent with the thin lens equation? Explai5t.aviy 4tr r 5hnr*i:n.

Can real images be projected on a screen? Can virtual images? Can either be phofz.w uo;nq 7 l,k(6/vemeaiy+tographed? Discuss careful6auon,zev /( e+ylqwmk7.fi; ly.

A thin converging lens is moved closer to a nearby od2xew ;i1zwz7 wd9korf6yz4 )bject. Does the real image formed chrz7oyifwd1 )x6w ;dkz 92ezw4ange
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index rhl)7qc5z(j y j1dzk,p6b h/ iof refraction n = 1.30 In air, it is a converlczz qphb6rik5/h )jd j71, (yging lens. Will 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 the nose and4)*qy/phhjbc svp-3 m the tail are each focused o4c-/ p hq*ymhbsv)j3 pn a screen in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facin 254nqvglay9ng a converging lens. Under what circumstances (if any) would the image of the nose be virtual and4qynl25ga9 vn 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 a sho bc5f4(ns)sm)eemy) crter focal length than the diverging lensm ync))es4mc( 5bf) es if the latter’s focal length is to be determined by combining them?

Explain how you could have a virtual ob/gzbjl.y2rd ep;1 )kt ject.

  An unsymmetrical lens (say, planoconvex) formxo/ t1wmz3nj, s an image of a nearby object. Does the imageo1jtw xn/ 3z,m point 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, the:jeo4bmsopl ru+1 9r4 shorter its focalrbo4ou sj :lm1p+ 9r4e length for a given lens diameter. Explain.

Consider two converging lenses separated by some distance. Anhm. e q-jt1s miwq54r3 object is placed so that the image from the f-q4e h3 mri 5.qmstw1jirst lens lies exactly 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 as you look at your imag5jl j. o*8p4+bs kjkxor/l v9t+g;jqn*7 acpre in a fjrvqcpb5 j 8l.+/ol *pkj;+4n9so7akg jt x r*lat mirror 2.5 m away. For what distance should the camera lens be focused?    m

When you look at yoursel582gphgd5cju9m9 ann+u pt s6f 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 g9uns5pnmhpu d 9g+26 5jac8tray diagrams to show why this should be true.

  Two mirrors meet at a 135rza43foov9 7v $^{\circ}\,$ 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 4 4ihe28rbnrcw3w5r x2o holf0v (a(habove the floor stands 2.20 m in front of a vertical plane mirror whose bottom edge is 43 cm above the floor, (Fig. Below). What is the horizontal distan2f a0 rx4h w3vh4o5bwr(l(c oh2 rnie8ce 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 mirrot nds9s g,f,svw;:s -kr is used to ref s-s,n:s;gkw ftsd9, vlect the rays entering one eye from a point on the tip of your nose if your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors mejb+r9dj c06j/+ik aniet 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, reallyf6s2m2w h k*i0n zbph/ a concave mirror pointed at the Sun, focuses the Sun’s rays 18.0 cm in front of the mirror. What is the radius of the spherical surface fros / h2kwb*z 20finhp6mm which the mirror was made?    cm

  How far from a concave mirror (radius 23.0w+cgwbn86y c kg18m*2bxo. cs cm) must an object be placed if its image is to be at infinity?*w ywgc+k8x2mcc8o 1bn6 g.bs    cm

  If you look at yourself in a shintqmcm3.k 5x8d y Christmas tree ball with a diameter of 9.0 cm when your face is 30.0 cm away from it, where is your image? Is it real or virtual? Is it uprigh8m35t xkd.q mct 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 stan aqynwu zgoe22 fzu3+k*(fs7.ds 1.4 m in front of it. If the image is three times tf2u37equk*sn a+yw(fz zgo2 .he person’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror that, when 2.20 cm from a toozg 6t7xb5azp 6n.j3ld gy6,xjth, 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 pg4kbretd8b* /*idqhb8lq e6,+oty ( produce images of cars behind you that are smaller than they would be if the mirror were flat. Are the mirroq(y4del, 6bbei 8p t *8*ghb rtd/qk+ors 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 20.0mfwb0e8f.5 tmq05ba1 id4uy h cm from a convex mirror of radius of curvaty4fqtbhbiem5w0ma0 u 1d 5.f8ure 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 sto-i)r)1oa ( fkosczzc5 re. You estimate the height of your image to be half of your actual height. Estimate the radius of cur ioz())cfs1 co z5a-krvature of the mirror.    m

  (a) Where should an object be 2,j3 -xvgfxtc)xu1xh:.c l ic placed in front of a concave mirror so that it produces an image at the xxu- f3hv1 :.ccx)l igxtc2,jsame 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 distau1 va4u r4dcb9nt tree is virtual and very small when viewed in a curved mirror. The image appears to be 18.0 cm behind the mirror. What kind of mirror is it, 4c 1 rbuadu49vand what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniques, 9 emzz/.s 6p cujyk:ifr.q 75b
(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 x)x u(afnvi* 7q5di 58yo2hsc 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 equation, Eq. 23–2, is va av iq9g)uhyiz;(g 7q-b6pm2 blid for a convex mirror as long as f iiqq 2hm;gup7i()y9g bzb a -6vs considered negative.

  The magnification of a convex mirrorv29*u9vnn( j 5a brvn ::h-qgcbrkw4hzb w2* r 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 plac-l ;curt : 3b)ccpy.ic fj9rg+ed 28 cm in front of a spherical mirror. It is desired to producubi ry) -j c;3c+p:g9ftrlc. ce 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 1.33 whes.6*kfj oe:7xqphyncz0 lu m0l8w ,*wn your face is placed,u08fkjmo*cs*ll:phy 7.xznweq06w 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 7y ; b4f5co -mo+ timkulcw.;sam 7*ae
(a) crown glass,    $ \times10^{8 }\;m/s$
(b) Lucite,    $ \times10^{8 }\;m/s$
(c) ethyl alcohol?    $ \times10^{8 }\;m/s$

  The speed of light inq )p/n8+4adt ydgp(mppd z2e3 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 3+8. fhouxs0sku86w i iud8dq is 89% of its value in water. What is the index of refractio 36d0whi888x.i+ouq suuk fdsn of this substance? n =   

  A flashlight beam strikes the surface of a pane5 monhis6j1)wit c*y)/ px r6a 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 flashlight upward from beneath the water .7o, wrnwtt9vat 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 spotligkmyp 4 o3c*8mrht exits the water at an angle of 66.*yo rpm4c 3k8m0$^{\circ}\,$ 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 a 312lzmpl mct:(s4 xul/* .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 dd.0zzn3k e5i hy12ivy (.ig gof refraction is 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 angl dzgiy( d3v n.z.i2 he1gki5y0e 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 cm :nb k(z50hl4mp:gxw7 s-4r5 swizi pool at night, a watchman shines a narrow beam of light from his flashlight, 1.3 m above the water level, onto isgxkn w:ws(zmlmz405rphc5- b7 : i4the 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 from the wall beneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equilateral glas5,2ofzojck -0pzxi6 us 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) and is partiall- eowls. auvbh *fu7 (+ryv6v7y reflected and partially refracted. Find the angle of incidence if the angle of reflection is twic.fo7 yl- * +b(uasr76hv wevvue the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beyuwzi( j 1bf3gvg0i0p 0h bw):am incident on a uniform layer of transparent material, ai30i uw1gyfb 0:v) jghb0w (zps 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 a flat piece of glass wit -wdfkpb,li,f :ymxi 8rd -s89h index of refraction n as in (Fig.bwf-f ,9y s8:pidi -rm,dxk8l Below). Show that if 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 n xqo :-1)ach1 6onopswater and Lucite? To be totally internally)xpha1 cqos n16:o-no reflected, the light must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–air surface ijp ympm v,7epa*kuk73 ys l7l(e::)ku s 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in a pool of waxpjri6 4:d6)57ofqrqh m g e9jter from a depth of 62.0 cm. Where must it strike the air–water interface, relative to the spot directly above it, ix4p7: femjd6 9) rhiqo5jrqg 6n order that the light does not exit the water?    cm

  A beam of light is emitted 8.0 cm benr(61y(l tnr8j7 qnbhy eath the surface of a liquid and strikes the sur ylthn(r6nr( 1q78by jface 7.0 cm from the point directly above the source. If total internal 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) atri hkxs/(-v :wru,u6qnk c-7w 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 fpeit1f .v fg4a7;;b(hy(a hx aiber 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.((bp th.eh;gff;iyv 1aa4x7 a42. In other words, regardless of the angle the light beam reflects back into the material at point a.

  (a) What is the minimum index ovmn(pss1 zz/r;+df; wf refraction for a glass or plastic prism to be used in binoculars (Fig. Below) (s+;vznr w dpz1/s;mf so that total 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 mmtbn+;mosf.d dp3v/ gqr,ubk( z0;x2u behind a 65.0-mm-focal-length converging lens. F;z ktvrqxudg;,bs3n / .d fom b0(2+upind the object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed t;oicm5/pc9mup a(5jnlh 6u, ao 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 w.qc 6yzsal35away 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 virtulqw.5y3 zc6 asal?  ----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-fo cisax sxv;8bp387f p,cal-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 stamp,/fhow o.ii. e 18 cm i, of.e.hoi/wi n 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 object 4.0 mm high. What are the posi 26(yb *f;0wlv n kzwmpp/bzt,tion, type, and height of bzl,z;(*fbt0/pkpw ymnv 26w 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.wl-(2vhnmffj a45ai; The maximum distance allowed betwe(n- m2 ;fif 4walah5jven 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 material by a factor of )7/om))se vyr ggya6o2.5× when a book is placed 8.0 cm behind a a/yrem)oog))v6 yg 7s 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 q5xl; phr2uu1 t5ug/hs:y6 ythow much does the image move if the objec5/y526r:s thgxutpu ;1l y qhut 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 lpo0 ldp6:dy, a5o1sipr 9zt 3fal2g 1jens with a focal length of 25 cm should an object be placed to produce a real image which is the sapp1asfltp,gyjd:35o 2016ril 9odz ame size as the object?    cm

  (a) How far from a 50.2w q 7w*7oknriqmj46k1i4g ik0-mm-focal-length lens must an object be placed if its image is to be magnified 2.00× and be real?6*n k4wkgkq1qrjw imi727io 4    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 c9 i)uf lt;4zdan object be placed if its image is to be magnified 2.00× and be)u;dlti9zf 4c 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 if mtxw / 3,6dgjpuwz*s*nlj- *q2kyj6 nsect is 1.20 m from a 135-mm-focal-length lens. Where is the imagu kx**6qwjgz nys -,2fw 6*mj/ ltd3jpe, 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 obj/t89w q)oabl fect and an image formed by a 75-cm-focal-length converging lens if afbw o)qt9/l8the image is 2.5× larger than the object and is real?    m

  A bright object and a viewing screen are separated by a distance of 66.0 cm. At ekg (*5yrjd bxf4oa+*7-x wdk what location(s) between the object and the screen should a lens of focal length 12.5 cm be placed in order to produce a crispdwjx xg4(kb5fr*oae- 7+y dk * 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 conve jhquwouv.v910kz+gdjdx::+ eni- 4 krging lenses are placed 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 located? What is the total magnificationgxdv+4hj .k0d zjo 9: -v+:ie uwknuq1?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens withs xpufmswg4r 09f2d x0a*;0tw $f=-31.5\mathrm{~cm}$ 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 beh*uciysm1 ,m231oqr v plnx;,hind 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 ray diagcso;hxi1rmpm, 21, uy* vql3n ram.]    cm

  The two converging lenses of Example 23–12 are now placed onl el .k;l;eom3 3 dd1qc/*sqziky 20.0 cm apart. The object is still 60.0 cm in front of the first lens as in (Fig. Below). In this case, dete;3k msi3l;1 o.q/k qd cld*ezermine
(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 lenst 7.kpyqdtp8ilrn/) ej4 k t;wqqjyc, ,.f,6q 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-focal-lengthqw,rql.; q/teqj ,kj)f p8 i.pky 4,ntc76ytd lens is the original object?    cm

  A diverging lens with a focal length of is placed 12 cm to the )pxyrv; 7 hwc(right of a converging lens with a focal length of 18 cm. An object is placed 33 cr v7h) x;y(pwcm 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 diverging *p+c o7sf-xcdwith focal length are placed 25.0 cm apart. An object is placed 60.0 cm in front of the converging lens. Det+cdpxs* -cof7 ermine
(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 c ,6vm*xz/xumehv3gn/ onverging 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 len0b +uly okr b 6bwl1zxe40i bb6vx6n-2yqj l+:s has surface radii of 34.2 cm and 23.8 cm. What is the focal length if n = 1.52?+ w1zr +62qn60xllv6b4-bi k:b eblyo0byxuj    cm

  Both surfaces of a djx:z3g nq ezi xo97)b,ouble convex lens have radii of 31.0 cm. If the focal length is 28.9 xnz9,q )o:7 3jxibegzcm, what is the index of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal lc5dvd m75/bk kjh:6y- c0 iidoength of -23.4cm. What is the radius of the concave surfad b v:5cm/h6dkikjo0 7idc-y5 ce?    cm

  A Lucite planoconcave lens (see Fig. Beqznjo59 *ztb6low) has one flat surface and the other has R = -18.4 cm. What is the focnbq96otj5 * zzal length?    cm

  A symmetric double convex lens with w/vnmbs0cz f;:w- f ujf,2p;*fd a bd-a focal length of 25.0 cm is to be made from *-2;mff: pd 0b,- czfsd;b/wjavnf uwglass with an index of refraction of 1.52. What should be the radius of curvature for each surface?    cm

  A prescription for a corrective lens calls for +1.50Dc(p5s-4/jzxs5 a at6,wehkc q . The lensmaker grinds the lensqpaaczh5x c/(, t5-weks 4 js6 from a “blank” with n=1.56 and a preformed convex front surface of 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 (Fig. Below). You stand tgdzl o d.sqz08d1)2;hyo;4iubu 0vm1.5 m away from one of these mirrors and look into it. You will see multiple imagsuit 0 h lgdd0dzmyq;8vzb2 ;1o).4oues 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 water. We meal8lkinhz3i0) 8nc 7t zsure the width (x=5.50m) and th8 0lzniit37 h8zcnk )len note that the bottom edge 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 cerolh 728 . hn5xs)nabomtain 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 lib ;xxdhg5t mb,p99r (mmiting case of a spherical mirror. Specify what dtxphm; 5 rgx99bm,b(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 sokd(6ti +( 2 mvbx3d u/w46oq rprdmf,e they form 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 cqpr -kq-2dj4 ean never form a real image of a real object. Can you describe a situation in which a div-p4 e -jkq2drqerging lens can form a real image?

  Each student in a physics lab is assigned to find the5: 8lj evntntpx(x 7;1 )qzuy5iuoa,t location where a bright object may bev:q1t)ptaune i8zx n(; 7joty5u 5lx, 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 need to repeat the lab, and justify your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of a prism is 5nbh,c.k s0fto skm7 ;$\phi=72^\circ$ 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 cylindjh 0;q)4eoll+77x/u qnhias4 ga8 hvufi4t2jrical 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 converging lens of focal leng-0;w c7ymejc nv, br2ith $f_1=15\mathrm{~cm},$ 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 8 ej/ij5gt l8jm4xpe*exw7simm55 5 1;d rnqra converging lens of focal length f, and a white screen for viewing the image is on the oppos5 rgx4 nexm5w*je 87m1dp;l erm i8j5 s5/qijtite 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 whose image i: e/a q)wgxvwk;y52:e ghxf9is 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 theq f/)gyieg x 5: k9;h:wav2wxe screen? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (picture size is actually 24 by 36 mm) is to be proje;in..ix-s jkkqjg i52n2 anl64rf c f7cted 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 tok6fnna2 j.i .cfrq2-j7 5kxl si ;4ing cover the screen?    cm

Show analytically that the image formed by a converging lens is realv)-obz y2kwl/ and inverted if the object is beyond the focal poi y2)l w-vb/zoknt $(d_0>f),$ 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 pictures of her at home. She claims the4dol4eo-:v k2 .gja1vz8td k s 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 fos4z: ja go12 v4e8lt.-okddkvcal 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 cameraf0/dzax +kkkx 9n n(xi9+sk9u-a) vi p 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 certain lenscf fwb8(9 wcm0+kiayd* i -cr7 is imaged 8.20 cm in front of that lens (on the same side as the object). What type of lens is this, and what is its focal lekyimc i +*arwf-8cwb ( cfd079ngth? 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)