What would be the appearance of p,zj1j+wl3zmkhfg(js x11u4the Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned t21uzx aw7p1qk +6;y.zpv up nahe whole Roman fleet in the harbor of Syracuse by focusing the rays of the Sun with a hp1 uzqk6xn+ 7vyuw1ppa z;.2auge spherical mirror. Is this reasonable?

Although a plane mirror appears to reverse left and right, it doesn’t ream bo99 5uct- rgjcml4m 1iq:nr+v69rverse up and down.6ai gu1mj9rlmmcq9+n vrrtc 5 b-:9o4 Explain.

If a concave mirror produces a real 1a .v 8hv-aknyimage, is the image necessarily inverted? Explai ynk h-.8vv1aan.

An object is placed along the principal axis of a ao::)ogn: vm p-ac-l aspherical mirror. The magnification of the object is -3.0 Is the image real or virtual, inverted or upright? Is the mirror concave or convex? On which side of the m)oav n :pa:o-:lc g-amirror is the image located?

Using the rules for the three rays discussed with reference to (Fig. Belo 8ev7rd:+vetu k+woze jk b:9+w a), draz t obv:+r7d:u+ ekwve+j9k e8w ray 2 for (Fig. Below b).
(a)
(b)

What is the focal length of a plane mirror? What is v1 se8i si0yl5the magnification of a plane mirror?i0sies518ly v

When you look at the Moon’s 14a.4pbx9l ukqo*o kb reflection from a ripply sea, it appears elongated . p1a4. qbx ku4kol9b*o Explain.

What is the angle of refraction when a light rae 3gkw h,98tjfdtl )n10rk:lgy meets the boundary between two materials perpendicularly?trhw 1l3ngk:lg0 ,9t)e jd8kf

How might you determine the speed of light in a 5yk+ e1bm9(irv+ ve7 gnt.qvq solid, rectangular, transparent objecyrimq+e(vetqk v9 7.vb+ 1 5gnt?

When you look down into a swimming pool or a lake,fx 1yuq8 ue+)z6bu i:u are you likely to underestimate or overestimate its depth? Explain. How does the apx)fz:1q uuu i+ye6ub8parent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram tojx9upwdui +uc ic+j0r582zw 5 show why a stick looks bent when part of it is under water (F xu c5wcudz5ijj++9wp2ui0 r8ig. Below).

Your eye looks into an aquarium and views a fish h, + pz:rslukc ca817hinside. One ray of light that emerges from the tank is shown in (Fig. Below), as welph 8 u:c7ksl+h,acz 1rl as the apparent position of the fish. In the drawing, indicate the approximate position of the actual fish. Briefly justify your answer.

How can you “see” a round drop of w2 m(/icu+ e4( izcoopiegtt// ater on a table even though the water is transparent andt g4eii/poo/uc(2eci+mt / z( colorless?

When you look up at an objeswl. sv.* bw:1pa(mx uct in air from beneath the surface in a swimming pool, does the object appear to be the same size as whenwvm( : w.ux s1a.b*lsp you see it directly in air? Explain.

How can a spherical mirror have a negative obc8 ausy6cest,di53 ; kject distance?

Light rays from stars (including our Sun) always bend toward the vero9y, 739 ixxwzev+vukzsn4p )tical direction as they pass through the Earth’z 4+e9p9si kvzn3v w)yx x,7ous atmosphere.
(a) Why does this make sense?
(b) What can you conclude about the apparent positions of stars as viewed from Earth?

Where must the film be placed if a camera lens is to make a shaxws+ /zx (wf:grp image of an ob:sx+(x wf/gzwject very far away?

What type of mirror is shown in (Fig. Below)? Expla w/u(yznv wmj 4.79 b 7nx,qelclm)2kmin.

A photographer moves closer to his subject and then aov+/b, gs;tibwp +;g:n x3uqrefocuses. Does the camera lennit+:pq , gu; +ogwbx;svab3 /s move farther from or closer to the film? Explain.

Can a diverging lens form a real image unf;bs-ag n2k55)qc njv(,,/oxrtn f jlder any circumstances? Explain.

Use ray diagrams to show kzxu r)* yfbcz-i4 e:hv;;j1qthat a real image formed by a thin lens is always inverted, whereas a virtual image is always upright if the object is re4rqev-*x b 1f:zjkyzc uh;)i ;al.

Light rays are said to be “reversible.” Is this consistent with4-hntbxyc;sua/ xs) u9g0;nt the thin lens equati ny4bg h-/)x0; ;nt x9suutascon? Explain.

Can real images be prw+ms wm yc)88cojected on a screen? Can virtual images? Can either be photographed? Discuss carefulwc+ 8ycmm8w) sly.

A thin converging lens is moved ckb.zq98se:15 . i7h+ m gdoiq rvl xeaksx:/+bloser to a nearby object. Does the real image formed change rx:qsi8g lobqk db.7e+k1v ex m/95z. si+ha:
(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 ld4-m le3 yn 53hbv/vcs43c mpair, it is a convec c- /3svp3lv43m5lyem bhdn4rging 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 tn5m; 5 xts)ownose and the tail are each focused on a swno)xt5m ;ts 5creen in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facing a converging lens. Under j at8 iqj4g72le( oijyb2xo92what circumstances (if any) would the image of the nose be virtual and the image of the tail be real? Where would4 lti2boa(y 722gqjj8 xej9oi the image of the rest of the cat be?

Why, in Example 13, must the converging lens ha9nma3k demz9hs0 2i 7ukg/b7gve a shorter focal length than the diverging lens if the 0e kk2uin7a /93b97zdmhm s gglatter’s focal length is to be determined by combining them?

Explain how you couldaait1)lin :m fj 31-v(.f(m; gdgsicm have a virtual object.

  An unsymmetrical lens (say, planoconvex) forms a39ef3ln ar) sw0sgb3qn image of a nearby object. Doesswb33qlsa3)9ef gnr 0 the image point change if the lens is turned around? ----待选择----yesno 

The thicker a double convex lens is in the center as l,obo3h7f5l 1 qw:rdacompared to its edges, the shorter its focafol dl7w 3bo 5h1ra:,ql length for a given lens diameter. Explain.

Consider two converging lenses separated by s4g; (mf s*uoxnome distance. An object is placed so that the image from the first lens lies exx*munso; (g f4actly 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 youynla21la9 *fj6 uot5 .q u o,lx*gexe/r image in a flat mirru out5 9 j1lxgef.2 q o6*eaya/n*llx,or 2.5 m away. For what distance should the camera lens be focused?    m

When you look at yourself in a i3tqxxy2v- elr5 +zna5uaj6+ 60-cm-tall plane mirror, you see the same amount of your body whether you are close to the mirror or far away. (Try it and see.) Use ray diagrams to stjxx6ayau v n+i3z+5-el 25q rhow why this should be true.

  Two mirrors meet at a 13i g4sxg *n042 kcl/fkq5$^{\circ}\,$ 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 fre *ctz*)an4gc ont of a vertical plane mirror whose bottom edge is 43 cm above the floor, (Fig. Below). What is ngt )*cz c*a4ethe 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 arqvz 58a q79duypw1c.j0gtb 8r uu ,d)xea of the mirror is used to reflect the rays entering one eye from a point on the tip of your nose if yoc x5urp7)wbu qj0ygd,d 9u a8 1.8vqtzur pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors v vb/oc2,t9sy meet at an angle $\phi$. a single ray reflected successively from both mirrors is deflected through an angle of $2\phi$ independent of the incident angle. Assume $\phi<90^{\circ}$ and that only two reflections, one from each mirror, take place.

  A solar cooker, really a concave mirror pointed at the Sun, focuses the Sun’s unt4 xy2s:nwt(b 8r7xrays 18.0 cm in front of the mirror. What is thrxntu(7bw28nx4s : ty e radius of the spherical surface from which the mirror was made?    cm

  How far from a concave mirror (ra tp0j8ry38ttd l37 g ndc4o*sodius 23.0 cm) must an object be placed if its image is to be at infinity?7843nr0yjo ptd go3d8* tsct l    cm

  If you look at yourself in j 393jte1,uaqh :,iyqsue*qs a shiny Christmas tree ball with a diameter of 9.0 cm when your face 9 *tuyj1ee3: ,qaqshjiqs3 u, is 30.0 cm away from it, where is your image? Is it real or virtual? Is it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shows an upright image of any person who s+r r1 d8no4ojttands 1.4 m r 1tor 4o+djn8in front of it. If the image is three times the person’s height, what is the radius of curvature?    cm

  A dentist wants a smaljzr2(060kiz8qdrzqm l mirror that, when 2.20 cm from a tooth, will produce a $\text{4.5×upright}$ image. What kind of mirror must be used and what must its radius of curvature be?
 ----待选择----convexconcave 
r =    m

  Some rearview mirrors produce images of cars behind you that are smaller th2 oul znc7bhoq -57on:an they would be if the mirror were flat. Are the mirrors conb q:7l 57ocnozh-ou2n cave 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 jk;db b 3peq10mm high is placed 20.0 cm from a convex mirror of radius of curvature 20.03 dpk; qe1bjb0 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 4 mtmvlo)lzq3j:5a8oa*qo8i+gd1c l security mirror in a store. You estimate the height of your image to be half of your actual heigh8a*3qmv) li:agz4od+ tl jmco8 l15oqt. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object be placed in front of a concave mirjqct6g;t+.g.xbk6r r(( jsgx ror so that it produces an image at the same locatio(6c.x g;t6rjqkxrsb g t+g(j.n as the object?
(b) Is the image real or virtual?  ----待选择----realvirtual 
(c) Is the image inverted or upright?  ----待选择----invertedupright 
(d) What is the magnification of the image?   

  The image of a distant tree is virtual and very small when viewed in a curveu1e3+ x+hica5ln bfpr3o 7za8d mirror. The image na+ 3ix 8+boa1r5zlhf up3ce7 appears to be 18.0 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, iw2y jf0co,n3is4u;q
(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, t0ivahb3 au16; bcw/qshat the magnification m of a convex mirror is $m=-d_\mathrm{i}/d_\mathrm{o},$ just as for a concave mirror. [Hint: consider a ray from the top of the object that reflects at the center of the mirror.]

Use ray diagrams to 9z -r5o)*h2orghbg mvshow that the mirror equation, Eq. 23–2, is valid for a convex mirror as longv -h)r gr9oob 2mhg*z5 as f is considered negative.

  The magnification of a convex mirror is05 mauha-a2d b ,poq2k $+0.65\times$ 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 ge.l(lx,7n(ou*g.xa x7 pqj sspherical mirror. It is desired to produce a virtual image that is uprielx ag 7j(.* psg7xnolx ,uq.(ght 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 miu h1n 0.4iju 3n;jnwxxna25gagnify your face by a factor of 1.33 when your face is placed 20.0 cm in front of it. 3nn; ihjx ijunn02w 4a51gux.
(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 lighh1hk *rzx:z5:i) fuqzt 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 ice ih1t;yqo+pa, dt5 8c bis $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certa:gn hvba6v5xua1+y e 4in substance is 89% of its value in water. What is the index of refractionv6na54 ue +x gha:vby1 of this substance? n =   

  A flashlight beam strikes the surface7fd2nx 66*lr o-gq4ysi: etvk of 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 psumv .5vp+ya dh 7,;j+t0cnbn x. -inwater at a 42.5$^{\circ}\,$ angle to the vertical. At what angle does the light leave the water? $\theta_2$ =    $^{\circ}\,$

  A light beam coming from an underwater spotlight exits 1nglo e-t)6txthe water at an angle of 66.0g 6oe-x t)l1tn$^{\circ}\,$ 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 tyb+zr)3vc xp73yx0 fro 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 wdo)wew)6;:a cgx6 dm)ituubro:h 0n0ith water has flat glass sides whose 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. Beloo )om :)wgi;en0 trw :ca60xb )dhud6uw). What is the angle of this light ray when it enters
(a) the glass, $\theta_2$ =    $^{\circ}\,$
(b) the water? $\theta_3$ =    $^{\circ}\,$
(c) What would be the refracted angle if the ray entered the water directly? $\theta_3'$ =    $^{\circ}\,$

  In searching the bottom of a pool at night, a watchman shines a nar5f jo,hz1q74kalu zc 79 mmvsk8vc6w5row 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 of the pool,6aoh f uzm v5jcs 8qkl,w174vzk5m79c measured from the wall beneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equilateral glass prisi :a .1v/ y0ih 4fc(;qlkemjypm 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 sdr frpk6.bfs ).i -/f= 1.52) and is partially reflected and partially refracted. Find the anf fdk.i.-6r r /s)pbfsgle 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 unifor o27zef- tuk6jw/ oba1,na*xq m layer of transparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the incident beam, independent of the incident angle 1n zta,jfox - ub/ew 6q72*aok$\theta$. Assume air on both sides of the glass.

A light ray is incidentg/bvbdd f jho;2ci) -4 on a flat piece of glass with index of refraction n as in (Fig. Below). Show o4;-2fd)c i/ bhb jdgvthat 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 water and Lucite? To mvwy ) e 0;hg4f;/ap(km+thbhbe totally internally reflected, the light must start inhw(pavmhe;+gkbm y; h0)f / t4 which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–air surfacbdh f( qkv6r/: rc--tqe is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in a pool of water from a depth of 6 (sf6givkoq r 8*7myt02.0 cm. Where must it strike the air–water interface, k(ti708vq6* gs yromf relative to the spot directly above it, in order that the light does not exit the water?    cm

  A beam of light is emitted 8.0 cm beneath the surface of a liquid and strikes tba4lg d*s el(/he surface 7.0 cm from the point directly above the source. If total internal reflection occurs, what can you say about the *egsbl(d a4/l index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face of the prism icqm5hxr+dt x;nv ,(l*m,u. wpn (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 t)y glg2 b 60m5sfi tv.9a 2s*x*+vu5dneyrfxzhe end of an optic fiber as shown in (Fig. Below). Show that we can guarantee total internal reflectiondbfs+6xzn*yx s ryt) e5 ia *fu59mvg220v. gl at the side surface of the material (at point a), if the index of refraction is greater than about 1.42. In other words, regardless of the angle the light beam reflects back into the material at point a.

  (a) What is the minimum index of refraction for a gla.otg4 5aqjw1zss or plastic prism to be used 1tj .4wza5goqin binoculars (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 located 78.0 mm behind a 65.0-mlh9qv ; y:.tzpm-focal-length converging lens. Find the ob:.;q 9zhlpvty ject distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed gutpyd/afn: 3 v,ikr m;5/d )zto 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 gb7ecdu; s( 3am away as an image 48.3 cm on the other side of the lens. What type of lens is it and what is its focal length? Is the image real or virtual? edab; s7gc3(u  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the power 4. m-qnak. oixof a 20.5-cm-focal-length lens? P =    D  ----待选择----converging diverging 
(b) What is the focal length of a lens? $f$ =    cm  ----待选择----converging diverging 
(c) Are these lenses converging or diverging?

  A stamp collector uses a converging (h jm-i8zo g1 rdb5obel5 w63alens with focal length 24 cm to view a stamp 18 cmie5g1m z5(-oodhwal b 8 3jr6b 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 mmb6f t,;.,31j zi pl.bziotkjz high. What are the position, type, and bip,z ,zjtl;k3z jit1f.o.6bheight of the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to focus an image on the filmf37tkdakg) l )i3uksv qn(o,- of a camera. The maximum distance allofqdn3)kl a(kgsui,t-ok 37 v)wed 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+66rjws si 5jiqre86xfs8u 6v factor of 2.5× when a book is placed 8.0 cm +xje68 w66ri6fij s5v8sr uq sbehind 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 from an 8.0- 0qy5 3 qbodzt.fn n,(oao):(zcj7jauu do/x1D lens. By how much does the image move if the o,zoa7 q)odo 0ntu z qdy:au5bn( c(/j3o xjf.1bject 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 should3 dcnpr74-puti6zzl ) an object be placed to produce a real image wh -4i)ul6ptr 7pn3zzc dich is the same size as the object?    cm

  (a) How far from a 50.0-mm-foc2ajd7*t 2v.xml9ij sde-8ljg al-length lens must an object be placed if its image is to d*ex2tm9g vi j8djajs72.l-lbe magnified 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 it.bs(m mnw)*l rub-pn h4n7;m ms image is tbp7n;l -wr hbms *(un4)mm.nmo be 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 isi8 rzi)(-nmz*3+j iq r7bvhgk the image, how highhi* n q-biir8gzm7k zr)vj3 +( is it, and what type is it?
$d_i$ =    mm (real,behind the lens) $h_1$ =    cm (inverted)
(b) What if $f=-135\mathrm{~mm}$?
$d_i$ =    mm (virtual,in front of the lens)
$h_1$ =    cm (upright)

  How far apart are an object and an image formed by a 75-cm-focal-length converz zz /,rv: 9rpq-irtm8ging lens if thmz vrt r/:piz8 -r,zq9e image is 2.5× larger than the object and is real?    m

  A bright object and a viewing screen are separated by a distanc vpa)jtpccp6; tqp+1-e 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 to produce a crisp image on the screen? [Hi61p-cv qpp +;jct )atpnt: first draw a diagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-lengtqo 4:oht-wvl2h converging 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 locav-t2l o4qoh:w ted? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens with 9:+q3ii*zwat w*x2ucc 1rf dh$f=-31.5\mathrm{~cm}$ 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 diverginist b-u0- ,shog 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 diagram.] hso-, -i0 sbut   cm

  The two converging lenses of Example 23–12 are now p/1on4 rw la:3tx1v ofts*rpf2laced only 20.0 cm apart. The object is still 6 a txo/wft1p2*r:onsrlv 4f1 30.0 cm in front of the first lens as in (Fig. Below). In this case, determine
(a) the position of the final image,    cm
(b) the overall magnification.    cm
(c) Sketch the ray diagram for this system.

  Two converging lenses are placed 30.0 cm apart. The focal length of the lenv6 a-u4twm4 bvn b+0*fvg 0sjbs 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 imv4 twfab4*-vvbnj0m 6 u0bsg +age 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 rightx+.hsjkgo5 nyc0 p e60 of a converxp k50g+. y e0ohjncs6ging lens with a focal length of 18 cm. An object is placed 33 cm to the left of the converging lens.
(a) Where will the final image be located?    cm to the left of the converging lens
(b) Where will the image be if the diverging lens is 38 cm from the converging lens?    cm to the right of the diverging lens

  Two lenses, one converging with focal length 20.0 cm and one0*ptfok0 6sut diverging with focal length are placed 25.0 cm apart. An object is placed 60.0 cm in front of the conv60ftskt *pu0oerging lens. Determine
(a) the position    cm to the right of the diverging lens
(b) the magnification of the final image formed.   
(c) Sketch a ray diagram for this system.

A diverging lens is placed next to a converging lens of focal l7r qvw/rs 7l;iength $f_C$ as in (Fig. Below). If $f_T$ represents the focal length of the combination, show that the focal length of the diverging lens, $f_D$, is given by
$\frac{1}{f_\mathrm{D}}=\frac{1}{f_\mathrm{T}}-\frac{1}{f_\mathrm{C}}.$

  A double concave lens has surface radii of 34.2 cm and 23.8 cm 9 i:tuanhtt0(xrdx5,. What is the focal length if t:h0u5an,t dixrx (9tn = 1.52?    cm

  Both surfaces of a double convex lens have radii of 31.0 cm. Ifbbu)4-1 bymlg the focal length is 28.9 cm, gy bum1b- )4lbwhat is the index of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm. What is the radius 9we 5hwqgvaqyf4 m0;/of the conw /q0q4ay m5;wgevh 9fcave surface?    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat surface and the oth305 yjvb s2rije thj13er has R = 1 5h2bvtri y33 sje0jj-18.4 cm. What is the focal length?    cm

  A symmetric double convex lens with a focal length of 25.0 cm ijcq rfqha+ 9+1s to be made from glass with an index of refraction of 1.52. What should be the radius of curvatu9fr+ cq+ hjqa1re for each surface?    cm

  A prescription for a correctiv3w;w9q 7ah z pb+j7gcqag h2,ie lens 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 40.0 cm. What should be the radiusp 9zb+7wiq;hq, a3 ajc 2g7hgw of curvature of the other surface?    m (convex)

  Two plane mirrors face each uvss w5n6fp(2o gf h21 l,vt2fother 2.0 m apart as in (Fig. Below). You stand 1.5 m away from one of these mirrors and look into it. You will see multiple imv26ff 5vu g2(, so psn2lth1fwages 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 determineob)3 4a6a(vbfdxmu w 9ogko-. the depth of a swimming pool filled with water. We measure the width (x=5.50m) and then note that the o3bv(mux 9oo awgb af)6d-4k. 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 isb(a3+ btk;waa $\theta_{\mathrm{C}}=37.3^\circ.$ What is the critical angle of the same plastic if it is immersed in water?    $^{\circ}\,$

(a) A plane mirror can be considered a limiting case of a spheesa6 guq-(3zogv;4 tprical mirror. Specify wv p-gz4o(s ;agt u3eq6hat this limit is.
(b) Determine an equation that relates the image and object distances in this limit of a plane mirror.
(c) Determine the magnification of a plane mirror in this same limit.
(d) Are your results in parts (b) and (c) consistent with the discussion of Section 23–2 on plane mirrors?

Stand up two plane mirrors so tf n5. sc5zojluk7+r-t hey 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 can never form a real image of a realrdv9tx6/k2wvxcl gbch 4 : e/+ object. Can you 4v29g+d tec wc/lbx6k/v :hrxdescribe a situation in which a diverging lens can form a real image?

  Each student in a physics lab is assigned to find t y +b ea:ssyit0ox.vged2(d6,he 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 usingt. s,gvea: e 6b d0y(do2syi+x 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 pr4y/wldqfmc+z u6 av) h2t um6h4f29coism 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 cylindrical0(kolj8gmcwpd ff(w9b6t+ts4p j6u9 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 lekgyj4. w kgj2*ngth $f_1=15\mathrm{~cm},$ 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 le8wlx5xr4n / 1+*cybuzbw8 ot prma:1vngth f, and a white screen for viewing the image is on the opposite side. bvptw/ m*18rnc a5uo xb 1lrzy+4 xw8: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 projectoxo7c u ulx)e9.jfr,/st p )9orr, the film acts as the object whose image is projected on x.uer)s l o9cjrfx 9t/p, )o7ua screen (Fig. Below). If a 105-mm-focal-length lens is to project an image on a screen 8.00 m away, how far from the lens should the slide be? If the slide is 36 mm wide, how wide will the picture be on the screen? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (pictuonni : +k(23 7xdjawnxre size is actually 24 by 36 mm) is to be projected on a screen 1.80 m by 2.70 m place nn7k:ix(n a+d3o2wxjd 7.50 m from the projector. What focal-length lens should be used if the image is to cover the screen?    cm

Show analytically that the image formn hm,*;/hxrhn xu m:h .3vjeb,ed by a converging lens is real and inverted if the object is beyond the focal point h3nx,x:muj rh/vh; .m*hn b, e$(d_0>f),$ 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 pictureje fb*tq+ 0q5jje8*acs of her at home. She claims the reporter was trespassing. To prove her point, she gives as evidence the0 tjc *e8qj*qfa 5+jbe 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 Sur k0 6yr:zszl:;. kssfn 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/y5x /2 pejoar cm 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 2re5op /yj/axmage 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)