What would be the apl/l ig-c yq.4.mby khl3.r0s8y qjrf* pearance of the Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Rom9wa k: +utrnoqtb 6h.6an fleet in the harbor of Syracuse by focusing the rays of the Sun with a huge spherical mirror. Is this rea b:u.+6h tkn tqor6w9asonable?

Although a plane mirror appears to reverse lefml yu 55l8/23m:lqp3ixtwcbit and right, it doesn’t reverse up and down. Explainqy/l5bx83 cl5ul mi 2wpm i3:t.

If a concave mirror produces a real image, is th1 r9kwoudbmim.w qmbv+ fv9-27nkzh9 nb/: 5ee image necessarily inverted? Explain9i1h m kb2.b9 vq f :vzbrm9nnwwe5dm-u +7ok/.

An object is placed along the principal axis of a spherical mirror. The magyl /zluxm:)3o3ut pd5nification of the object ll3pudz: 5t/o3umy )xis -3.0 Is the image real or virtual, inverted or upright? Is the mirror concave or convex? On which side of the mirror is the image located?

Using the rules for the three rag.tirk fmqk3 i/7+h,d ys discussed with reference to (Fig. Below a), draw ray 2 for (Fig. Below b).,t7rg.h m3ki /k fi+dq
(a)
(b)

What is the focal length of a plane mirror? What is the magnification:, +xa*ayw ry uus -1ppys6ut; of a plane mirruu*sys,paat+y y-u;1: p6rxwor?

When you look at the Moon’s reflection from a ripply sea, it5zdp (, spkb6n:5joy -ozw3jm appears elongated . Eny 5z,o3opp5 6dks m(:b jz-wjxplain.

What is the angle of refraction when a4j8hgupx3*8hqs xc-z wcb+;z ut s) t: light ray meets the boundary between two materials perpendicularlyu sqhx;ubw zxgc34 h)jt-c: 8+s8pt* z?

How might you determine the speed of light in a solid, r 5z2yawn xqj./r+a;*dlwcdn3ectangular, transparent objea +5w;x qn/lwyjdnz3 ad2*.crct?

When you look down into a swimming pool or a lake, are you likely to unno0 5n,wu)zf( ork6ou3qkn;z.mq ef6 derestimate or overestimate its dezk,ferwo6 u k f6oq( nonz 53.qnmu0);pth? Explain. How does the apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks bent when part of it is undert+z i,n8nmol*j5*1fo fyh 2ns water (Fig. Below). j5z2i*,ho ot*lmfsn+1 n8 nfy

Your eye looks into an aquarium and views a fish insi31x6x p7a z3)w :yoryu ar vb(wypk;j0de. 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 drawingwx a0x:1y633 k wbojarv)7pup;z(r yy, 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 tho 5b mrts1*s0 jrxhm76e water is transpa5 1hmt7 srr *s6jb0mxorent and colorless?

When you look up at an object in al*w-t6( 5hvdvlw7os)b i)i fzir from beneath the surface in a swimming pool, does the object appear to be*i)zowvv hltw5) - 7d ifl(s6b the same size as when you see it directly in air? Explain.

How can a spherical mih*x0n:dnn*gl dkjqs5yd8, 8 trror have a negative object distance?

Light rays from stars (including our Sun) always bend 9-/*ehl3eu xgaso :vxtoward the vertical direction as they pass through the Earth’s atmosphex* :39eog vs/lhx-eaure.
(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 cameig /6;f daiisvb+ x*azy75 l luf:/qm(ra lens is to make a sharp image of an objecf:dugsim(/;z/*x bif ylva i6 +7a5l qt very far away?

What type of mirror is shown in (Fig. Ber+ij7aoz6k,qpry l: 5 low)? Explain.

A photographer moves closer to his subj5h c0s w:hhchnb870ot )7mtsiect and then refocuses. Does the camera lens move fa 0)c5b:tm7t chs7nhso8hwh0irther from or closer to the film? Explain.

Can a diverging lens formsjju: c-)cl ont( .pd0 a real image under any circumstances? Explain.

Use ray diagrams to show that a i4s3qtsg 8g ax*69 z8hhuk2mq real image formed by a thin lens is always inverted, whereas a viku 4h g38sg68azqx9*hms2 itqrtual image is always upright if the object is real.

Light rays are said to+o cospl)awg56s e0q0o5mo:o: intg: be “reversible.” Is this consistent with the thin lens equation? ) t5peg:m:60no+i sco5:lwag oqs0ooExplain.

Can real images be projected on a screen? Can virtual images? Can er(xnrsh * / 1p*fvsdj9ither be photographed? Discuss carefully. rphj1vrf*(dnx* /9 ss

A thin converging lens is moved closer to a nea*6r 3mz/u92povcbq e k 36f7 0femtocjrby object. Does the real image foro6*3e zf/p mcmc2o6fv7 kq9eu0t 3br jmed 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 In a0 cvl 6jx e85k65aeptdgfn/h1ir, it is a convergick 6 e a8dn/5lvh6f0gj p1txe5ng 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 st izh6.u9sv: 2cibsjg2hjfq/7ands facing a converging lens. If the nose and the tail are each focused on a screen in turn, which will have the greater magj cz7iqh/22uij96h:bfvg s s. nification? ----待选择----nosetail 

A cat with its tail in the air stands facing a converging lens. Under wha4f srsiq nuc:f)asq qn8*q7, 3t circumstances (if any) would the image of the nose be virtual and the image of the tail be real? Where would the image of the rest of the cat be?8n7 3s u*iqfsc:f4,sqqaq nr)

Why, in Example 13, must the con yl05z)otrxd*0gdxma l:7ch.l 4jp, sverging lens have a shorter focal length than the diverging lens if the latter’s focaja x5)cto l7 0ld0*yzdr.xlgh,p4:sm l length is to be determined by combining them?

Explain how you could have a virtual objwp /xn3hw 9f2gj0yrz2ect.

  An unsymmetrical lens (say, planoco-r n,v fqz9(*x7dke9lxt 4 sh6mlzi0unvex) forms an image of a nearby object. Does the image point change if the lens is turned arlu , v4e7i xx9sq lr9nf- 6t0(kzdzmh*ound? ----待选择----yesno 

The thicker a doubleo y)i7w ;:t u4 k2ds+,fssxcoj convex lens is in the center as compared to its edges, the shorter its focal length for a given lens diameter. Explit js 47:s+,oc;u2yfkw xd) osain.

Consider two convergingq.:7o8jl/ )jid3md5z cxx wahezk o8 * lenses separated by some distance. An object is placed so that the image from the first lens lies exactly at the focal point of the second lens. Will this combination produce an image?*z 3 d hcjdq)x/8oa.imkwxez8:j75 ol If so, where? If not, why not?

  Suppose that you want to take a photograph of yourseluhv0cx8mk) g.f as you look at your image in a flat mirror 2.5 m away. For what dista 0u.kg8c)mvhxnce should the camera lens be focused?    m

When you look at yourself in at0:e,joq qv kh db,l/,j *xjsn/ my:f; 60-cm-tall plane mirror, you see the same amount of y:tfe:* y/q j,mn 0,dsqlbjok;hjx v,/our body whether 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 135b2y 8imd xqx,,$^{\circ}\,$ 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 sta7e ;x oydum:gy6k3sk, nds 2.20 m in front of a vertical plane mirror whose bottom edge is 43 cm above the floor, (Fig. y3u: ex ymk;,gdsk67oBelow). What is the horizontal distance x to the base of the wall supporting the mirror of the nearest point on the floor that can be seen reflected in the mirror?    cm

  Suppose you are 90 cm from a plane mirror. What ar (kuu3ucsdxj m33c gh*jk 60l-xia18vea of the mirror is used to reflect the rays entering one eye from a point on the tip of your nose if your pupil diameter hisax1j6m03 c83kcd (gk*j-u vuu lx3is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors meet at an 0otfc-( vwo .wangle $\phi$. 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, fo :;zz5f 5k8fbikyznt)cuses the Sun’s rays 18.0 cm in front of the mirror. What is the radikbit)yff5 n5;z8 zkz:us of the spherical surface from which the mirror was made?    cm

  How far from a concavz,ieg0 rmsfs a j8cwh877 s2hr(l;r6+r;mw cde mirror (radius 23.0 cm) must an object be placed if its image is to be atrs hz;s02 lai(h7,ge6f7r8ww;mm +8rrcjsdc infinity?    cm

  If you look at yourself in a shiny Christmas tree ball with a dia+wtdj/h3b(kq* 6 mr7ba 0z afxmeter of 9.0 cm when your face is 30.0 6tzm +x f/37ajw0qb bdka(* rhcm away from it, where is your image? Is it real or virtual? Is it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amuseq4d w 2ai(m*.)go oocrment park shows an upright image of any person who stands 1.4 m in front of it. If the image is three times the perso 4omow 2 qor*g(d)aic.n’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror that, when 2.20j j,(, u,6vk yar18h 6)jbopz3x8lm v npn(tsw 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 carse(:s bphbcixc4 q-/wgq.0p.i behind you that are smaller than they would be if the mirror were flat. Are the mirrors concave or convex? What is a mirror’s radius of curvature if cars 2-ibsw/ h.xqc(q0gbi c .4 :ppe0.0 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 conv -uj yd0: aa52vj(l88uqsm12ligrvixxjb:; i ex mirror of radius oji u: dl5yv qgj-v 28;r:0 u1x(lxi sj8a2imabf curvature 20.0 cm.
(a) Show by ray tracing that the image is virtual, and estimate the image distance.    cm
(b) Show that the (negative) image distance can be computed from Eq. 23–2 using a focal length of -10.0cm
(c) Compute the image size, using Eq. 23–3.    mm

  You are standing 3.0 m from a convex security mirror in a store. Y2 -bidnej /bwqtv ;u1 3j*rpjnx8 k8t5ou estimate the height ovtnqu- i8w;p/ej*n2 tb5kbj 8drx31j f your image to be half of your actual height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object be placed in front of a concave mirror so that itnc bqukc4ak3(t2(c a , produces an image at the same location as the object? (kbc2 knqac (3at,uc 4
(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 ( h qav hrf,18)ziut*itree is virtual and very small when viewed in a curved mirror. The image appears to be 18.0 cm behind the mirror. What kif1*iq8h)r,u ta vh( zind of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniqu(/pu mego*,nyes,
(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 mp*fw9yz9sgzh ; ,ur13udw0nxi9ca4 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. 232p;2absp b5lg –2, is valid for a convexgpsb2 alb5;p2 mirror as long as f is considered negative.

  The magnification of a conjt1y85p 509f asztbwg vex mirror is $+0.65\times$ for objects 2.2 m from the mirror. What is the focal length of this mirror? $\theta_2$ =    $^{\circ}\,$

  A 4.5-cm-tall object is placed 28 cm in front of a spherical mirror. Iv)ut) n krmp:6d34 fc+iph.b3p) egeyt is desired to produce a virtual image that is upfk)ge3t. p nip36v)c)h:4dpyme ur +bright 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 f :(u mz,j,wwt n1by s,2yr+zfcactor of 1.33 when ynu(zm1jt cz,fyw, sy,+2b:r wour face is placed 20.0 cm in front of it.
(a) What type of mirror is it?  ----待选择----convex mirrorconcave mirror 
(b) Describe the type of image that it makes of your face.
(c) Calculate the required radius of curvature for the mirror. r =    cm

  What is the speed of o3t .+a g,sm21uwnl vwlight 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 icem 40 yir02r l6qrz3*zt3p sytg is $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain subs cjw1y)y d)ux*tance is 89% of its value in water. What is the index of refraction of ))ycwj*d1y uxthis substance? n =   

  A flashlight beam strikes the surface of a pane of gl.3i/h jb2v.a pcdscl+ass (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 9g-he+o(pf i ;e6 efdethe 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 spotlig;1rv)r df2834xpd xdqz 0 yzmlht exits the water at an angle of 66.0pmr ld f4qd2d;z3 01)xr8 yxvz$^{\circ}\,$ 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)0e g1;xc:x .ula o n ,;ma+mnd*now q83azkce to make a 31.0$^{\circ}\,$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?    $^{\circ}\,$

  An aquarium filled with water has flat glass sides whc0wcvt .z-t: xose index of 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 a w0 z-xcvtc:t.ngle 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, e9)/ ar7wymeg j8s -dtty 123uepj :dea watchman shines a narrow beam of light from his flashlight, 1.3 m above the water level, onto the surface of the water at a point 2.7 m from the edge of the pool (Fig. Below). Where does the spot of light hit the bottom / 3j-j71ep)e9 e syugtmtyder:daw28of the pool, measured from the wall beneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equila8y qhaew+dbc)i 55gm(teral glass prism at a 45.0$^{\circ}\,$ angle to one face, (Fig. Below). Calculate the angle at which light emerges from the opposite face. Assume that n = 1.58.    $^{\circ}\,$ from the normal

  A beam of light in air strikes a slab of glass (n = 1.52) dgq33 8 vg2tydand is partially reflectqvd8gty3gd32 ed and partially refracted. 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)u+6ym)n(*h;bps c(g v ooxnu incident on a uniform layer of transparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the incident beam, i6bhx u gnno ums(vp;o y)*(+)cndependent 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 inde:l a6pape.s: mx of refraction n as in (Fig. Below). Show that if the incid.ame6:pal ps: ent 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 ikcob3g4uv.zt( wn*) between water and Lucite? To be totally internally reflected, the light must start in which materialt*i cvk4 bwg u(o3zn.)?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–aii ju9 r*q;o2xmr surface 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 frof() nmd hy2epv0ir(ihf6t cb2l --p e4m a depth of 62.0 cm. Where must it strike the air–water interface, relative to the spot directly eb i-ym lvehp t622 (4fi) dcrp0f-nh(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 lirx.6g.sgv6e8dtx lv g z))/sbquid and strikes 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 refraction ofv6sb.lx)s. ed6gg vg )xt/z8r the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face of the pt -47328mpok6gawu l)tx d sfarism 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 ofn enwi:;.c2tp an optic fiber as shown in (Fig. Below). Show that we can guarantee total internal reflection at the side surface of the material (at point a), if the index of refraction is etp;2n i.nw:cgreater than about 1.42. In other words, regardless of the angle the light beam reflects back into the material at point a.

  (a) What is the minimum index of refraction for a glass-ajqd i6(b+:kgkz3 ,iky n3om or plastic prism to be used in binoculars (Fig. Belowbiyozj3m3(k 6-+ qgik kd na:,) 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 mm behind a 65.0-mm-focal-y c,f xa)y jb4s,r53zclength converging lens. Find 53ac4j,c)bys ,frz xythe object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focjjyjf9 31pn6 kus at a point 18.5 cm behind a lens.
(a) What kind of lens is it?  ----待选择----converging lensdiverging lens 
(b) What is its power in diopters? P =    D

  A certain lens focuses light from an object 2.75 m away zp,kum,o o9 1pas an image 48.3 cm on the other side of the lens. What type of lens is it and what is itkou, pm9zp, 1os 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 =a0v duabe:. ze64sq,ap 7fzv4    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 con.lor kl-ao /+o/ehl g 1fzppsgp; *+c+verging lens with focal length 24 cm to view a stamp 18 cm in fron;fos1pho+-repcgz/ / +pa .kol*l gl+ t 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 tf cp 726vl-4 .ohntmdu 0y2bxpt+s(jcm from an object 4.0 mm high. What are the position, type,ttb(7sh m+.jyctxp2 f4luovp60nd 2- and height of the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to f*u6ybog /1*rlgv pv8 focus an image on the film of a camera. The maximum distance allowbg *y*6op1g uv /l8vfred 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 material by a facto n4th(sqq+2lb r of 2.5× when a book is placed 8.0 cm behqbsh+4n tq (2lind 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 fro : meoog-;6qfum an 8.0-D lens. By how much does the image move if the object is movqo u-;g:6efomed
(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 converg7kr 5uux 0x8rzing lens with a focal length of 25 cm should an object be placed to produce a real image which is the xx0 urz85r7uk same size as the object?    cm

  (a) How far from a 50.0-mm-focal-lenqtwk59v (b7) ,tfpo il-fsp y3gth lens must an object be placed if its image is to be magnified 2.0p-bs lqpk9vyoti) ff5 3w7 t,(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-length lens must an +92xewrps aixitdz8 367vn q/+af :j dll) n-robject be placed if its image is to be magn+jf lltd qie 8:7v/z6- +s 3 niarp9d)w2rnxxaified 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 g.ntc7nyfnogsx2 -8t; 2rq;z 1.20 m from a 135-mm-focal-length lens. Where is the image, how high isg2- oztt78cqr2nysfg n.;;xn 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 ahcac5.ye2e 2zjc my(-nd an image formed by a 75-cm-focal-length converging lens -c.a2cy52meez j( yh cif the image is 2.5× larger than the object and is real?    m

  A bright object and a viewing screc*q5mwkm5rovi hw48r6 6 9zw-wmp3uren are separated 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 or3rw9 uqrm i6cwpm56hv* 5mok8-4z ww rder 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 object c.ti:k,cvb 9t r) wk8o/q9j vgis placic9)jkv,b go:v9 .rt qc8ktw/ed 36.0 cm in front 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 witvk3i4j8 a/3y +4v6y zgzjvd)ph /ptvzh $f=-31.5\mathrm{~cm}$ 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 l pkw,2lmp )*6kme mk 8lw*7vlvens. Parallel light strikes the diverging lens. )lp6m2v kk7,e mklvwm*8w*p lAfter 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 onlii; rv 2 5z2k5 gu;tmvj(cf.4)mxqqp by 20.0 cm apart. The object is still 60.0 cm in front of the first lens as in (Fig. Below)52mc 5u(;v. gzrjvq;2 qfkt p4mbxi) i. 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 lenses3jua b 1,p5x nsp9x*sb are placed 30.0 cm apart. The focal length of the lens on the right is sb*aj xp 391spubx,n 520.0 cm, and the focal length of the lens on the left is 15.0 cm. An object is placed to the left of the 15.0-cm-focal-length lens. A final image from both lenses is inverted and located halfway between the two lenses. How far to the left of the 15.0-cm-focal-length lens is the original object?    cm

  A diverging lens with a focal length of is placed 12 cm to the right of a con duibp*t8d m/6e1ou thf9q m*5verging lens with a focal length of 18 cm. An object is placed 33 cm to f u1om i69tb dd/eq**ut58pmhthe 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 lengthdjll 3 :,:vvnqmk,-gv+y /klz 20.0 cm and one diverging with focal length are placed 25.0 cm apart. :l+-gy 3v q nvv,l/jm: klk,zdAn 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 placed next to a 1 ucz cp(8j2unry05bxconverging 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 andck2 17ug(lcur(h 8di f 23.8 cm. What is the focalu2u gr c((dkl1i8c 7hf length if n = 1.52?    cm

  Both surfaces of a double convex lens have radii of 31 7p:wj* t;eeygt:ak7a .0 cm. If the focal length is 28.9 cm, what is the index of refraction of the lens materak;taj 7w e:p :y*et7gial?    cm

  A planoconcave lens (n=1.50) has a focal lengtp uxoa9c+, ,i87qsc+r .l heffh of -23.4cm. What is the radius of the9. 8if+p u,ceohfrql+s7, axc concave surface?    cm

  A Lucite planoconcave lens (see Fig. Beloi(;ew7 y8ux 2eqmvfc9w) has one flat surface and the other has R = -18.4 cm. What is the focalx;u eq7 fmw(icy892ve length?    cm

  A symmetric double convex lens with a focal length of 25.0 cm is to be made r6x bu-iqm d7,8:alkwfrom glass with an index of refraction of 1.52. What should be the radius of curvature for each surface? rx,liu8m ab:k6- wq7d    cm

  A prescription for a corrective lel6)hit 1angh0 *nty64jj*l kuns calls for +1.50D. The lensmaker grinds the lens from a “blank”nhk1ugta0yjih*l6t*46)j n l 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. Belo rtfs3gj,hqmtxw10(.at gp.0qt j :g4 w). You stand 1.5 m away from one of these mirrors and look into it. You will see multiple imag10j (g, g:wr3.0 tqa xgtqt4jp.stfmhes 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 t ts v2wrqlumlfqgi)v.54+dg: 5) 4nulhe depth of a swimming pool filled with water. We measure the wivw4v u.f45 um5 srig )lltn)d gq:l2q+dth (x=5.50m) and then 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 certain pie)v65uwph f55om q f8bzce 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 lim/ly6yahe 3c7 ojlkawl0o6o1+iting case of a spherical mirror. Specify what this lim7k/lhcly0loa+o66wa y ej3o 1 it 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 form a 9 ml4 bocosqy/ .h,m1t+z1(rdl0$^{\circ}\,$ 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 *+kpk-p7ch/jrfi) u b diverging lens can never form a real image of a real object. Can yok /cb- i)*krfuj+7pphu describe a situation in which a diverging lens can form a real image?

  Each student in a physicy+fq -5znx 5;kjng/*f n oiz,hs lab is assigned 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 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 calzn f-5kz +njno xhfiy/ ;,q*g5culation.
$d_o$ =    cm    cm

  If the apex angle of a p.ke dm67trqmyqna:. 2rism 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 rod x :kh 7l,03lhomkj bgpr5w 84m$(n=1.54)$ 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 plaewm6bzel + 7k(ced 33 cm in front of a converging lens of focal length $f_1=15\mathrm{~cm},$ which in turn is 55 cm in front of another converging lens of focal length $f_1=15\mathrm{~cm},$ (see Fig. Below).
(a) Draw a ray diagram and estimate the location and the relative size of the final image.
(b) Calculate the position and relative size of the final image.

A bright object is plugg fi/z5r m3w d iqjh2.s7v25aced on one side of a converging lens of focal length f, and a white screen for vsiw25 2jgi3mfdzvrhgu/5q7 . iewing 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 hb 6 eof2kd/tk8kq*4 wfilm acts as the object whose image is projected on a screen (Fig. Below). If a 105-mm-focal-length lens is t*qbkh6w/kk2otf 8d e4o project an image on a screen 8.00 m away, how far from the lens should the slide be? If the slide is 36 mm wide, how wide will the picture be on the screen? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (picture size is ac+7zn:wqa vn *lgh0zt 4tually 24 by 36 mm) is to be projected on a screen 1.80 m by 2.70 m placed 7.t 0+*4h aznw: qgzn7vl50 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 forecuhu * .fsa4r/+x- ucmed by a converging lens is real and inverted if the object is beyond x-*r fucs4 u uch.a/+ethe focal point $(d_0>f),$ and is virtual and upright if the object is within the focal point $(d_0>f),$ Describe the image if the object is itself an image, formed by another lens, so its position is beyond the lens, for which $-d_0>f$, and for which $0$<$-d_0$<$f$.

  A movie star catches a reporter shooting pictures of h ack(lt 4vklbc u39.2der at home. She claims the reporter was ld.vl2tba(4k3k c9cutrespassing. 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 reporter standing?    m

  How large is the image of the Sun on film used in a cameral-tfwu (d.w*d; f amh6n7*avs 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 lmwlauo 1ay)x+1 c+xq ntzd/6nzsz21 7ens is imaged 8.20 cm in front of that lens (on the same side as the object). What type of lens is this, nw1xacla1yq z xd+o1usz z 72n6m/ )t+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 certaz8v,(sj :rnd ain converging lens, it forms a real image. When the object is moved to 40.0 cm from the lens, the image moves 10.0 cm farther from the lens. Find the focal lengv8d: sar,jzn (th of this lens.    cm