What would be the appearance of tr j4bsn 89qy c/rrz65jhe Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the nlj 8bu 7e;3tmwhole Roman fleet in the harbor of Syracuse by focusing the rays of t;8jb elun3m t7he Sun with a huge spherical mirror. Is this reasonable?

Although a plane mirror appears toaxj /e *1rmxhnmyk834 reverse left and right, it doesn’t reverse up and down. Explain.je r*8xm n41hmxy3 ak/

If a concave mirror produces a realn+q sq/.cmq p- image, is the image necessarily inverted? Explmqn- ./+q cspqain.

An object is placed along the principal axis of a spherical mirror. Thegc x w f 7om7xd7u9k8e1ef.u)q magnification of the object is -3.0 Is the image real or virtual, 7qe.mx7 u)fw7ecgf19 d8xo kuinverted or upright? Is the mirror concave or convex? On which side of the mirror is the image located?

Using the rules for thewy1r(3 jr (p ;lxf5gtw cdk /y+np4-k9nfie5r three rays discussed with reference to (Fig. Below a), draw ray 2 for (wfn j4 lp/5nekrk;-yg3f y dp(r+ 1r9iwc5(xtFig. Below b).
(a)
(b)

What is the focal length of a plane mirror? What is th.koi. x v2d(elj)w9yr n -lv6et-w7wfe magnification of a plane mirrftl-y) n.l v 6-kd(2r9o7. w ewejxivwor?

When you look at the Moon’s reflection from a ripply sea, it a rv2ub4 )/ceoms)l7qjppears elongated . Expla bj4r)cemv ul)s2q7 /oin.

What is the angle of refraction when a light ray meets the bkj0 +mour4vv8r)2i,yl g gce x* +ido:oundary between two matel*)28vd +xv j ,:g+u0krio o4 ygcimrerials perpendicularly?

How might you determine the speed of light in a solid, rectangular, transparenv gk( z0t,ii9ht obj0tghk9ii,v (z ect?

When you look down into a swimming pool or a lake, aogn ;dtae++ii, q1 0klg, b*jjre you likely to underestimate or overestimate its depth? Explain. How does the apparent depth vary with the viewing angle? (Use ray diagrag,id*+qi; na1 jejbk+g tl,0oms.)

Draw a ray diagram to show why a stick looks bd1f05 k dyj)zgent when part of it is under water (Fig.zfk0gydd1 )j 5 Below).

Your eye looks into an aquarium and views :(nzn(u4m dxz a fish inside. One 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 of thxdnz: (nm(4 uze actual fish. Briefly justify your answer.

How can you “see” a round drop of water on a table ev6zs ktuie/5 ( gzk;t0den though the water is transparent 65ez(0/d gzut kst; kiand colorless?

When you look up at an gl4 )jr.i* znux/rv3 xie6:d robject in air from beneath the surface in a swimming pool, does the object appear to be the same size as when you see it directly in air? Explai jx6rg )3rnue r4vx*:.ii/zdln.

How can a spherical mi 4-fgh-+-kzfb/s /fb7 uqi lwjrror have a negative object distance?

Light rays from stars (/w0x6 a7xrv 8jaq2( png- kcghincluding our Sun) always bend toward the vertical direction as they pass through thexq/ agcg p 6 hr-8(j2axvw7n0k 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 v+e b pcz0*/yilpy 5f+is to make a sharp image of an object very far away/5vbpp z0i+fyel+* cy?

What type of mirror is shown in (Ffn/ 02ye7rmfc ; uxj-jig. Below)? Explain.

A photographer moves closer to his subject and then refocuses. Does the came(wepmf4na2 e3q7 h7u dra lens move farther from or clos4ue w72e 7a(qhm fnp3der to the film? Explain.

Can a diverging lens form a real imagev)mpz++:nu8/4td wxbt( (z0aleu oh n under any circumstances? Explain.

Use ray diagrams to show that a real image formed by a thin lens i5qy86wp l.bok s always inverted, whereas a virtual image is always yol5w 86. bqkpupright if the object is real.

Light rays are said to be “reversible.” Is this consil7b;6 ml oy m/j/3wuidstent with the thin lens equation? Ew/67lbyi;3m lomd j/u xplain.

Can real images be projected on a screen? C py,8gip+.vesan virtual images? Can either be photographed? Dis8pse.g+vyp i ,cuss carefully.

A thin converging lens is moved closer to a nearby object. Does the reah(g3m6s+ppc j da**e ol image formd *hsap(co* 3+6jmpg eed change
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of refraction n = 1.30/bit d e/j8e66w czwaoj+qt(4 ev82sz In air, it is a converging lens. Will it still be cq//+odw8sw j8 6jv6(b2ztetee 4ai za 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 conver,xy.i-f6q t f zu-b3tknh+0t vging lens. If the nose and the tail are each focused on a screen in turn, which will have the greater magnificfk v-tiz,tbt fh - n+6q30x.uyation? ----待选择----nosetail 

A cat with its tail in the air stands facing a converginr:jguibx6c6iioatx ),2rl 9 2g lens. Under what circumstances (if any) would th b29x )cjo:i,6tgrir luia 26xe 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 a shorter focal 4jbtsw +l2t* klength than the diverging lens if the latter’s focal length is to be dt wjsbl*+k4t 2etermined by combining them?

Explain how you could havew(phta3zm7 v+: o /wgh a virtual object.

  An unsymmetrical lens (say, planoconvex) f+)mqt0 dqmnl77l9ga morms an image of a nearby object. Does the image point change if t0tl9l7gnmaq dmm +7q)he lens is turned around? ----待选择----yesno 

The thicker a double conlo9fn wb54b3m fn/3b gvex lens is in the center as compared to its edges, the shorter its focal length for a given lens di bwf g/bbf394n5mn3loameter. Explain.

Consider two converging lenses separated by some distance. An objec6ezpp0 uj)lu; t is placed so that the image from the first lens lies exactly at the focal point of the se; u06jze l)uppcond lens. Will this combination produce an image? If so, where? If not, why not?

  Suppose that you want to take a photograph of yoursah( 1zi a-wi sqnl*zb4b5qwe4g, t yhxm )w2-9elf as you look at your image in a flat mirror 2.5 m away. For i1lh n4yz-2qti,h m*(q9a w-zw)5gsaweb4 bxwhat distance should the camera lens be focused?    m

When you look at yourself ip 4pnt640*ozpctcf .en a 60-cm-tall plane mirror, you see the same amount of your body whetherce4pzttcn*po 64f. p0 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 0*cy u tm;x-xanugy.; 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 stands 2.20 m in front ov ;2j7wr:onbgf a vertical plane mirror whose bottom edge is 43 cm above the floor, (Fig. Below). What is the horizontal oj:nr2;wb v7gdistance 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 fo r8vmi )geu03nb sq a8nnx: h:5v;r1mirror is used to reflect the rays entering one eye from a point on the tip of your nose if your pupil diameghnueas o5ix0)1 8v :f vmq8nr n:;rb3ter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrl 75hp/i gsvbv0+ *kbr) dfno;)bhm- hors 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 mirrrmjds ,6bzy58 or pointed at the Sun, focuses the Sun’s rays 18.0 cm in front of the mirror. 6 bm5r z8,ydsjWhat is the radius of the spherical surface from which the mirror was made?    cm

  How far from a concave mirror (rae5rsq 32acm k7dius 23.0 cm) must an object be placed if its image r7es3 ak2q5m cis to be at infinity?    cm

  If you look at yourself in a shiny Christmas tree ball with a diameter of 9,(fpqvndc80 haev 9u, .0 cm when your face is 30.0 cm away from it, where is your image? Is it real or virtual? Is it eh,c09 8nuaqp,dv( vf upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shkj cj; c1nc9;nows an upright image of any person who stands 1.4 m in front of it. If the image is three times the person’s height, what is the radius o ;;cjn1kn 9cjcf curvature?    cm

  A dentist wants a small mirror that, when 2.2gq1g 0zos-:t) a*wlp m0 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 smaller than th zxc8z51i,xv xey would be if the mirror were flat. Are the mirrors concave or convex? What is a mirror’s radius of curvature if cars 20.0 m awaz xx5ivzx,1 8cy appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is placed 20.0 (0 pvs,h(scmk z-f.k ccm from a convex mirror of radius of curvature 20.0 cms(czkscm hf, 0(k. v-p.
(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. You estimate thrlc*rhq.c3r yti.)k*9 shuxv;v) jw)e height of your image to be half of your actual height. Estimate the radius of curvature of)i;wrvr*h) *rlt.q y. c)9hc xk3ujvs the mirror.    m

  (a) Where should an object be placed in fb)k/x*)xx ko front of a concave mirror so that it produces an image at the same locabx o kf/x))*kxtion 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 vtf9d,u 8 -bmahery small when viewed in a curved mirror. The image appears to be 1- dhmabu, 8ft98.0 cm behind the mirror. What kind of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniques )9cwq-cumnu lbhogv ,zf*,73 ,
(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 convex4:pq wask/vd: 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 valid for an n; zyjoz,mj/ws8:ko5+cdot2 dv j / -tv9h.z convex mirror as long as f is considered zcj vd.;5jn,t8jh9tmow/oo k-+sn :z2/zyvd negative.

  The magnification of a convex mirror is r2xa:z5l0g3 qnc;g p v$+0.65\times$ 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 frok 6e,h-z )s*; 9wrjuky*fwzvvnt of a spherical mirror. It is desired tozreykw*-uk9f,vvsh; 6w *zj ) produce 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 factoru.a x:)f kbl2e of 1.33 when your face is placed 20.0 cm in front of klex.2) :fu bait.
(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 light5et1-:iv jyss in
(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 * ega-xe(oz90m na mu9vf7n/h 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% of its valcip1 f eybm5)/+br9kw ue in water. What is the index of /5fr)cmbwk1 y9b e+ip refraction of this substance? n =   

  A flashlight beam strikes the surface w6-qqxuq n v:9/cygf*iwk+ 1vc( n) lmof a pane 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 at a )g*jv lf: n)hdrnjvhh *u 6yz+y8wd0342.5$^{\circ}\,$ angle to the vertical. At what angle does the light leave the water? $\theta_2$ =    $^{\circ}\,$

  A light beam coming frk50sq 69wx(:4 fta x+ur1 3eu hkqwdkfom an underwater spotlight exits the water at an angle of 66.k539d tqw0fah4s6fu erkkq w u( x:+1x0$^{\circ}\,$ 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 maketb.7r lo9/- zsuk-dv l 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 sides whose indeia1:4 v2nh4 pj6yzcgfx of refraction is 1.52. A beam n6ph1f 24yzv4j gica: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 shines769yexmyv;w g a narrow beam of light from his flash9m ye6 gv7xy;wlight, 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 from the wall beneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equilateral glass prism at a dm iut3ws6 j 03gs b9:fv0 9wh;bcapzh4g;b*z45.0$^{\circ}\,$ 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 (nu+q s) 9hij4nb = 1.52) and is partially reflected and partially refractejbqi 4+9su) hnd. Find the angle of incidence if the angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam incident on a uwom3/* x kjym oug/.t9niform layer of transparent material, as in (Fig. Below), the direction of the emerging beam is u9/o/xt. jgmy3mw *okparallel 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 with index of refce* di:n0p d*0ya j3tgraction n as in (Fe *adij00cgdny t*p3:ig. 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 interfapc:um 82 efx;zce between water and Lucite? To be totally internally reflected, the light must start in which materialc:e;xm 2pzu8 f?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for5wc rla6g :kumk+facukg6h249 e86ah a certain liquid–air surface is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is ema or8f7c d.h2m- dciou9+3pugitted 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 order that the light does nicgf3o p.m72u8c udrh9 ado+- ot exit the water?    cm

  A beam of light is emitted 8.0 cm beneath the surface ocmmr3c9z/4w pl to7*gf a liquid and strikes the surface 7.0 cm from the point directly above thp z7o/c*wm3rt4 cgl9me 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 izd8siz. lex8dgu ;h)ag/ z54hn (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 shown in (Fig. Below). Shmh (1; d+zlwl-0ubiblow that we can guarantee total internal reflection at the side sur0b;(h ibm 1u+wzl ld-lface 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 into the material at point a.

  (a) What is the minimum indekjiwo0zukj*: q.rs u5/. sr,r2k qyo3x of refraction for a glass or plastic prism to be used in binoculars ujs5 k,2:uiq /sro qz3jyo.kw0 *rr. k(Fig. Below) 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 locate y*wagt dez/j: z5*0ct k;n2mxd 78.0 mm behind a 65.0-mm-focal-length converging lens. t 0w:jdza;mx*c5 neytzg*/ k2Find the object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.5 cm behind m4 1zgnwx44hhw*b-ge 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 fxkr/ wfn:(fzs.r1*i image 48.3 cm on the other side of t *ffz xrik1.nw( rsf:/he lens. What type of lens is it and what is its focal length? Is the image real or virtual?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the power of a 20.5-cm-focal-length lens? P (*ozg.w e;ifogvgt //=    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 conve9n sb l7wf+le6a1t+yarging lens with focal length 24 cm to view a stamp 1nl+bsy6+l1w9 7aet af8 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 object 4.0 mm high. What are the po k-,9i 6vz6-ebywuw jlsition, type, and height of the im lb6ywj-w ezkivu,96-age?
   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. Tk;pe9 j oa6rxte5 ip2,he maximum distance allowed between the lex pta2p,5re oie9k;6jns 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 readingf - 3(nnsoc6hccii;gn4:i 6h e material by a factor of 2.5× when a book is placed 8.0 cm behind a le ;:3fg c6c6no nn4sihhi-ce (ins.
(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 ) oj *ui1 k )v9g: o3abq*pfjtidqi1/9pr)ehb8.0-D lens. By how much does the image move if tqqt:b9)*dp)oo1/)irj1 *gajeu hkf 9 pibvi3 he 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 a focal length of 25 cm shoulgt*gn/g v 6 c lvb)3z)lb*agbfqh9,k 8d an object be placed to proglk h*l,atgb b39v8)ngc)fb/z* v qg6duce a real image which is the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an object be :y . j g1:5ajqx6qkgceplaced if its image is to be magnify: g:c5eq. 6x kajqg1jied 2.00× and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm

  (a) How far from a 50.0-mm-focal-length lens must an object be placed if its43 0 don 2qdwkk6bga8u image is to be 34 g620aoqdw8kbdukn magnified 2.00× and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm (formed by some other piece of optics).]

  (a) A 2.00-cm-high insect is 1.20 m from a 135-mm-focal-length lens. Where x9io -ysv0n:cl8d8xy is the image, how :8 vxi0o -ycsnlyx 89dhigh 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 obl npc 8 5i9s/b0by5gy 5)zh,i8frq+xgqdm5psject and an image formed by a 75-cm-focal-length converging lcf i+bp,95ngisyr80z)ybg558md lq h /qp sx5ens if the image is 2.5× larger than the object and is real?    m

  A bright object and a viewing screen are q hfl4xqht* xyqmvv9:ci e7217: .kudseparated by a distance of 66.0 cm. At what location(s) between the object and the screen should a lens of focal length 12.5 cm be placed in order t7l*1qh:yeqm 7 xu qihd:4v xf9.ckt2 vo 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 objecz,w9fs:m r. zht 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 magnifz:r s zfw.m9h,ication?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens with -*ydw43, wx3d gykng l$f=-31.5\mathrm{~cm}$ is placed 14.0 cm behind a converging lens with $f=20.0\mathrm{~cm.}$ Where will an object at infinity be focused?  ----待选择----realvirtual ,    cm beyond second lens.

  A 31.0-cm-focal-length converging lens is 21.0 cm behind a diverging lens. Pa ratjrx f j)s99ocp 1pqcjr5xv*p9+(*rallel 9c fjo9pcjr jxv5 *x 1rsp*p(a+rqt9)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 diagram.]    cm

  The two converging lenses of Example 23–12 are now placed only 20.0 cmv *l . 4 yaay2rwz6,wjzz6iv;k apart. The object is still 60.0 cm in front of the first lens as in (Fig. Below). In6a j.r6,;lz v*kz i4wa2yzy vw 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 lens sit4bdgdpok9y v j78i ;d ,d(-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 v9iy-tk,o b 4s ddpgddij;78(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 foc-afxq/0j: exqn +2d egd6re/zal length of is placed 12 cm to the right of a converging lens with a focal length of 18 cm. An object is placed 33 -az/ngeqe dq6 e r0:fd+x/2 jxcm 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 an tjbo+xuyf+e)xm:-31u; t nbnsqe6 r *d one diverging with focal length are placed 25.0 cm apart. An object is placed 60.0 cm in front of the converg);:+njrm3ebf euy*+6x qn-bsoxt ut1 ing 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 aqs67 zc, po-pa 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 ux k1lg*n8/ uphas surface radii of 34.2 cm and 23.8 cm. What is the focal length if n = 1.52p/1ukl n*8gu x?    cm

  Both surfaces of a double convex lens have radii of 31.0 qdl9z42 +q l6g3 n2pivswg9vsmhdi6 :cm. If the focal lengths2:gipsi 663+vhv 92z9mlq q 4nglddw is 28.9 cm, what is the index of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has ice/y(b f(b0c w;db*9 3rjtdwa focal length of -23.4cm. What is the radius of the concave sur/w; b bew0c ( cbi3fr*d(y9jdtface?    cm

  A Lucite planoconcave lens (see Fig. Below) has web)gock*c :.,yss8g one flat surface and the other has R = -18.4 cm:sc,*ow g8y.gs ek b)c. What is the focal length?    cm

  A symmetric double convex ).t fb w4uw0wk5uknr2bg*u5e-yr ve a)eyj)6 lens with a focal length of 25.0 cm is to be made from glass with an indexk5)6na er bj4uby2gf)veueku.r5w*)w -wt 0 y of refraction of 1.52. What should be the radius of curvature for each surface?    cm

  A prescription for a corrective lene ftrt09x b(9rtpntk4u/rn 78s calls for +1.50D. The lensmaker grinds the lens from a “blank” with n=1.56 and a preformed convex front surface of radius of curvature of 40. /0rex f7trn n9t84b t(9pukrt0 cm. What should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fig. Below). You stand 1.5.hgwg8,0hbkp5md+e )gx a j o. m away from one of these mirrors and look into it. You will see multiple imme. h x0gpj g ,5kd+a8hw)go.bages 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 devx6r. l) nm;bypth of a swimming pool filled with water. We measure the width (x=5.50m) and then note that the)n6mx;rvyb.l 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 certain piece of plastic in air is ejo336 t 8xorv$\theta_{\mathrm{C}}=37.3^\circ.$ What is the critical angle of the same plastic if it is immersed in water?    $^{\circ}\,$

(a) A plane mirror can be considered kjqgs; k)5 p xvsp+qs4by/*/ra limiting case of a spherical mirror. Specify what this l4/k*q/qpkgsr5) xvb+ssp; j yimit 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 foreh 0 /8ov2 el tuh0lhvelo*l1,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 diverging lens can never jyvn6j nwgio2py 02/pd57ip 3 form a real image of a real object. Can you describe a situation in which a diverging lens can form a rep6j/ni02v 7pyjow32 ndgp5iyal image?

  Each student in a physics lab is assignnxt,,7p w ezjkk9i9ur4u2x3h ed to 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 erx947pe,3iwk n2 ,kuhtjzx9uquipment, 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 pri ga-vk v obn:tkylbhg* )c131 4z(xmp5sm is $\phi=72^\circ$ see (Fig. Below), what is the minimum incident angle for a ray if it is to emerge from the opposite side (i.e., not be totally internally reflected), given $\mathrm{n=1.50~?}$ $\theta_1$$\geq$    $^{\circ}\,$

The end faces of a cylindrical glass rodk 6kyjlk;my86ao/ t-i $(n=1.54)$ 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 p58yk9-ca +h riv. rusmlaced 33 cm in front of a converging lens of focal length $f_1=15\mathrm{~cm},$ which in turn is 55 cm in front of another converging lens of focal length $f_1=15\mathrm{~cm},$ (see Fig. Below).
(a) Draw a ray diagram and estimate the location and the relative size of the final image.
(b) Calculate the position and relative size of the final image.

A bright object is placed on one side of a converging lens of focal lt7( nn d0zu4,vt2* eaf,- kyn e0bopfiength f, and a white screen for vib* 2tunyf,4 af (ez n0,ndv-7ekop0itewing 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 whose image hh (vv-kj25c pw7k jqa1hq /-yis 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 slh(1vh7 h ka -py5wcqvjj2kq-/ide 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) isv w1wuc nzq./5/o1gvm to be projected on a screen 1.80 m by 2.70 m placed 7.50 m from thmvquv1 c n1ow. /gz/5we projector. What focal-length lens should be used if the image is to cover the screen?    cm

Show analytically that the image formed by hykk24 d/zlq14z;lxmmj zx5) a converging lens is real and inverted if the object is beyond the f)21m q;dly mk /jk5z4zx4lhx zocal 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 reporte4;wu :1+u k 18vdgmzngcd3 cufr 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 subjec1d3wc8cv u+fuk1gud z: ;nmg4t was the reporter standing?    m

  How large is the image of the b s4:vin/;8hgk tc: ddikq,+ dSun on film used in a camera with
(a) a 28-mm-focal-length lens,    mm
(b) a 50-mm-focal-length lens,    mm
(c) a 135-mm-focal-length lens?    mm
(d) If the 50-mm lens is considered normal for this camera, what relative magnification does each of the other two lenses provide? The Sun has diameter $1.4\times10^6\mathrm{~km},$ and it is $1.5\times10^8\mathrm{~km}$ away.    for the 28 mm lens    for the 135 mm lens.

  (a) An object 34.5 cm in front of a certain lens is imaged 8.20 cm (:6zt bpjtedlf r:z:)in front of that lens (on the same side as the object). What type of lens is this, and what is its focal length? Is the i:dpb :re6zl:j)tzf(t mage 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 certainc;4/ h7 j9vkssh(ilin converging lens, it forms a real image. When the object is moved to 40.0 cm from the lens, ti9vsl /is; 4n(kjch 7hhe image moves 10.0 cm farther from the lens. Find the focal length of this lens.    cm