What would be the appearance of k)3uwv ,dsk.mza k(h8 vv n/3rthe Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fleet in the harbor yy(2ykhs4xx k. oa+4m of Syracuse by focusing the rays of the Sun with a huge spherical m 24ykkoys+mx .a(y 4hxirror. Is this reasonable?

Although a plane mirror appears to reverse left and right, it doesn’t reverse umya y2e1k/7 fah*(zbqp and down. Explainy 2fqhy/1amka(* e 7zb.

If a concave mirror produces a real image, is the image necessarily inverted? w f/fec;,fka:Explckafefwf;, : /ain.

An object is placed along the principal axis of a scfq1e) mb .fwgoq.1b- pherical mirror. The magnification of the object is -3.0 Is 11q -ewcmb qobf.)g f.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 rays discussedsen2 y*7 pnm5l:o )mzo with reference to (Fig. Below a), draw ray 2 for (Fig. Below b). *n:p)mnym e 57s2zlo o
(a)
(b)

What is the focal length of a plane mirror? What is the ma8jyo l1(o+ gcxgnification of a plane mir+1yj oxl8cgo (ror?

When you look at the Moon’s reflection f q(9hns+yipkfq778maj -t7 rdrom a ripply sea, it appears elongated . Expl-ks8h and+pq97y7( ftrqmi7 j ain.

What is the angle of refy;:3j , fpqzeg9a.pux raction when a light ray meets the boundary between two materials perpendicularly?f ua:j.,yp3qez; x9pg

How might you determine the speed of light in a solid, rectangular, transn5b h **xe*e4juzngn 2parent obje2*x e u4njnbez*g n*h5ct?

When you look down into a swimming pool or a lake, are you likely to underestimdytq-ty33 5zoate or overestimate its depth? Explain. How does t- 3z5tdoqyy t3he 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 unde;wg,1r :u0 sdj 1qx n6pht-enir water (Fig. Beleq d0 n1 nu;gpwt1:h 6ixrjs-,ow).

Your eye looks into an aquarium and views a fi;k :o*rsv8cmb sh 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 drawingk8*;scv r bo:m, indicate the approximate position of the actual fish. Briefly justify your answer.

How can you “see” a round du qy1m*assls a/)tdzah-t8 -/rop of water on a table even though the water is transparentus lysa*-)s-m ha qdz8at/1t / and colorless?

When you look up at an object in air from beneath 5h2v ;szt.r (q7vhfjj the surface in a swimming pool, does the object appear to be the same size as when you see it j2h;vqz5(r t 7hsv.fjdirectly in air? Explain.

How can a spherical mirror have a negatidflue8 -:z ,on+e5gimve object distance?

Light rays from stars (including our Sun) always ben zyjjf 6(,xq3xd toward the vertical direction as they py( xjzq3j ,x6fass through the 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 3)2d2o9tsywdofv ac 6 a camera lens is to make a sharp image of an object ver2a9yf6co ) tvdds2wo3y far away?

What type of mirror is shown in (Fig. Below)?+rki :cjh3x7 gpp+or2oc + pl( Explain.

A photographer moves closer to his subject and then refocuses. Doejd4i .ki 0jxo6s the camera lens move farther from or clk xjii6o. dj04oser to the film? Explain.

Can a diverging lens form a real image under any c ) +wmblxo0z;circumstances? Explain.

Use ray diagrams to show that a real image formed by a thin lens is k9o5rtb5,/ i*tl ;jsfp)q 7lbuux6fu always inverted, uf)p;fl r5x6utoqu9b*k/75,islt jb whereas a virtual image is always upright if the object is real.

Light rays are said to be “revers8+frav y3l qi9ihdabds27 xy.* hllw. 2) 3bgsible.” Is this consistent with the thin lens equation? Explawsbl3d8 hl2+a9idx*b 3l v yash 7f.y.2ir q)gin.

Can real images be projected on a screen? Can virtual imagesh2d:gt7n8-v+cn r 45od jg vkt:dtu 7r? Can either be photographed? Discuss carefug tvnr78 t7o th:k5:dcjudgr-ndv4+2lly.

A thin converging lens is moved closer to a nearby8fj-a6d9kvy) tx3qfv1 e 6svq object. Does the real image form-1k vvaqfq 9)6x 68y3dejtf vsed 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 a w4z,r.kidenlwh97d, mj mc14ir, it is a converging lens. Will rel97mk4cw.mi,,dd 4z1j wnh 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 convh2o -,fbl4y e4gktau q4,: o6s o-dlgqerging lens. If the nose and the tail are each focused on a screen in turn, which will have the greater magnifu t4 4 kqs6lhy:,qgf-,a-g2l o4boed oication? ----待选择----nosetail 

A cat with its tail in the air stands facing a converging lens. Under wha ny7 c*1q(mi*awqry0z t circumstances (if any) would the image of the nose be virtual and the image of the tail be 1q cr0nwa(y mi*zy* 7qreal? Where would the image of the rest of the cat be?

Why, in Example 13, must the converging lens have a shorter focal length than t 7.:s40uvava:gg( 7 uvbczk drhe duvg7 kv.b:garuda(70 4zs cv:iverging lens if the latter’s focal length is to be determined by combining them?

Explain how you could havehhwdl 48gisd/ fwtfh*5w- 93e a virtual object.

  An unsymmetrical lens (say, planoconvex) forms an image of a nearby obje-w o (p:t kabimnac6*9ct. Does the image point change if the lens man (-i kpba9cw:o6*t is turned around? ----待选择----yesno 

The thicker a double congi wvie3j2q)9-9vq p ivex lens is in the center as compared to its edges, the shorter its focal length for a given lens diam2qi)pv w9i-gie39 qj veter. Explain.

Consider two converging lenses sepaoc3mo 4g0f t4d41wdqqcqw+ n+rated by some distance. An object is placed so 4ntg4dofo3+w+cm dqqwc 14q 0that the image from the first lens lies exactly at the focal point of the second lens. Will this combination produce an image? If so, where? If not, why not?

  Suppose that you want to take a photograph of your0egz320 zmtsh x+l,7log wl8e self as you look at your image in a flat mirror 2.5 m away. For what distance should th0ew0, lts xo lhgel zg2z38m+7e camera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mirhro5(ulc z9l9ror, 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 show why this should be true l95zc9 lo(rhu.

  Two mirrors meet at a 13rzu++tj2f .7ve e8kh 7o 2zqdb5$^{\circ}\,$ 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 of a ve.9gxtyiz :9p ki/ hzvt-6jj(frtical plane mirror whose bottom edge is 43 cm above the floor, (Fig. Below). What is the horizontal zfg9xh6vjt.i-:/zjp(t k9 iydistance 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 mik-3 (bof56krz1 /f k qbedcj:error. What area of the mirror is used to reflect the rays enrq13e co-df6:j/ zk5k b(fke btering one eye from a point on the tip of your nose if your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors meet at an a5pn( 0 nedf eh, l793/enwparingle $\phi$. 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,llox0 y- d* s,5bionn, focuses the Sun’s rays 18.0 cm in front of the mirror. What is the radius of thed,0 -o o ,nysl*nblix5 spherical surface from which the mirror was made?    cm

  How far from a concave mirror /vtbbk s24 aw6dty9u ((radius 23.0 cm) must an object be placed if its image is to be at ktv9 tu2b6y( s/4wd abinfinity?    cm

  If you look at yourself in a shiny Christmas tree ball wb1ea9o qm 4o(q ac1a)jn.trs y+c.f*yith a diameter of 9.0 cm when your face is 30.0 cm away from*jqfr1eq4ay 1)somctb. an( y oa9+c . 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 uprigh)b chcg (qe42wt 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 of curvaq b c2hgcwe)4(ture?    cm

  A dentist wants a small mt. +qq;xogl.yzdh,a;s *k fj6irror 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 imayweb.86kz+27zugw hdou0h 66m f )art .slu,iges of cars behind you that are smaller than they would be if the mirror were flat. Are thohik. ,z6e dbuh06 8 ) 7uwf+r.wy 62tgszulame mirrors concave or convex? What is a mirror’s radius of curvature if cars 20.0 m away appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is placed 20.0 cm from a convex mirror *px73ice yx.t 0 lr0lxof radius of curvarxxi37 lp*.0c tx yel0ture 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. Y,nu4sot1mrmo.i k-s*ou estimate the height of your image to be half of your actual height. Estimate the radius of curvature ofok. mr1,t-imuso4n* s the mirror.    m

  (a) Where should an object be placed in front of a concave mirror sofashyv8 2b 4tzq;xb8 3(t 9hxx that it produces an image3(tvhhb ;2qz t48xf s8xax9by at the same location as the object?
(b) Is the image real or virtual?  ----待选择----realvirtual 
(c) Is the image inverted or upright?  ----待选择----invertedupright 
(d) What is the magnification of the image?   

  The image of a distant tree is virtual and very small when viewed in a curvea*zam ;: se:9ibhl 3bed mirror. The image appears to be 18.0 cm behind the mirror. What kind of ;shb3eamlai9ez:*: b mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniques,8hr2g xvr*+ 2m ,ytdwr
(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 diagqvi4*qgr,8 k iram, that 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 show that the mirror equr.w-fdbgb/) 7lmu j4t ation, Eq. 23–2, is valid for a convex mirror as long as f is considered negativ)fg7/tm. b rwlbuj4d-e.

  The magnification of a convex mg1 ).(/hp1(rtqgfn dq7sf emb irror 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 5xjm2,jn0 j;sr cjoheb9a5ea0-x 7m dplaced 28 cm in front of a spherical mirror. It is desired to produce a virtuaa5a2j jc-hbr,em7n5j m dj0 o; 0esx9xl 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 designedgl+:dv q mih/7z g9c fwnwhg,mc8 76.m to magnify your face by a factor of 1.33 when your face is placedmv67fmn7 :c c8zi wg+qgm,.glh9d/wh 20.0 cm in front of it.
(a) What type of mirror is it?  ----待选择----convex mirrorconcave mirror 
(b) Describe the type of image that it makes of your face.
(c) Calculate the required radius of curvature for the mirror. r =    cm

  What is the speed of light in lx * s:ctqkd5k6 u+ my1xtpj;8
(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 o4)d9dj o hntr8 7que7ice is $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in l ypj(dq qlx4ip 9+g..a certain substance is 89% of its value in water. What is the index of refractionq.9i.( gp +j4y dqpllx of this substance? n =   

  A flashlight beam strikes the surface of a pane of glass (npo :,w guq.ph2yl*.uw = 1.58) at a 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashlight upkml :r r.c(. dnhm;v/bward from beneath the water at a 42.5$^{\circ}\,$ angle to the vertical. At what angle does the light leave the water? $\theta_2$ =    $^{\circ}\,$

  A light beam coming from an undef1 b(uhfn,cn y+ /0fbdrwater spotlight exits the water at an angle of 60u + d /cyf(bnhbf1n,f6.0$^{\circ}\,$ 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 see.qy hx+r2-k1(gdt gg dn 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 whose index of rx/egmzk*/m ), dd ih*wefraction is 1.52. A beam of light from outside the aquarium strikes / de*xm,gi/*hdk)zwm 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 bott m3 ml33i b-9f;urfggeom of a pool at night, a 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 of the pool, measured from l3m3bf i;ef-3 9r ggmuthe wall beneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equilateral glass prism at a 45 uzolb jg4,ab-j)dj j.fp/ l/1.0$^{\circ}\,$ angle to one face, (Fig. Below). Calculate the angle at which light emerges from the opposite face. Assume that n = 1.58.    $^{\circ}\,$ from the normal

  A beam of light in air strikes a slab of glass (n = 1.52) and is pieu9*f8 jgkdh ebo r*h,61w2c artially reflected anbgf6k, 8 or21u jdcw h9hie**ed 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 incident on a unifcve9u3 6krw,e13 snauhc -9blorm layer of transparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the incident beam, independent of the ica,u 1ecr39b-9u 6ehl v3snwkncident angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on c qtaw524tapv:a:djx ( 4ofo (:as ni7a flat piece of glass with index of refraction n as in (Fig. Below). Show that if the inna4oa:q td a47 op 5:f(axcvw2sij:(t cident 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 inbm)0 ey)o2 zrh blkc20terface between water and Lucite? To be totally internally reflected, the light must strho20ybz)mc)b0 ek 2 lart in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certaz8x rd(bfo3 qh++uwd +l z0c8v0 tz9suin liquid–air surface is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in rt o /hwbl wixw1m1 apxj :m(1kl68+0ka 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 or6xb/0xil w1 hj+1kww1 8m tolk :mar(pder 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 haog;-v aj6/vj8h2mdp s*e0w the surface 7.0 cm from the point directly above the source. If total internal reflection occurs, what ca*/g0m -hh8oavs v 6 pjad;ejw2n you say about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face of the prism in (Fig. Be.f g5.qjs ;o+51rjgv q ,hu fobzh24gilow) 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 ;s idqof9dskk2rh:bx y)9s4vy:8g 0da 4s.xb end of 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 greater than about 1.42. In other words, regardless of the angle the lx.q0ks 4: 9ygx4bks 9 ydo)v;8afdrd: 2s shbiight beam reflects back into the material at point a.

  (a) What is the minimum index of refraction for a glass or plastic prism to be x zaibh6hnak+-f)x, -used in binoculars (Fig. Below) so that total internal reflection occnx6xz h-bfk ,) +aha-iurs at 45$^{\circ}\,$? $n_1$ $\geq$   
(b) Will binoculars work if its prisms (assume n=1.50) are immersed in water?  ----待选择----totally reflectingtotally transmitting 
(c) What minimum n is needed if the prisms are immersed in water? $n_1$ $\geq$   

  A sharp image is located 78.0 mm behind a 65.0-mm-focal-length conv e*eav * i0-mfo3 l)3hwuxq-vuerging lens. Find the objectmh -i v)3u-*u3 w0lxqeoafv*e distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus* mjhl e,nyr+uj.znsn6 t;c)) 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 agjs+vy -kd.r pi7+l 0js an image 48.3 cm on the -j+i7vk0+ dy rjp.s lgother side of the 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 powe/zz igm7zhhw1+/ r/ qfr of 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 lens with foc;84dzlzm6ou rk l3v34sky p4oal length 24 cm to view a stamp 18 cm r4od3 osp v6l3zuylz4mk;k4 8in 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 objj:y ugxw(yr(3m-- ao6eug xv+ ect 4.0 mm high. What are the position, type, and -exmg( 3+ gx-uv:yjoa6w (uryheight of the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to focus an image on the film ok6ib 0;ripmle7e* pn+ f a camera. The maximum distance allowedi l m0iep;b7*e nkrp+6 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 rls2nu( ud5 -vxeading material by a factor of 2.5× when a book is placed 8.0 cm behd (uxln2vu s-5ind 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 fstl8 wz; -u6qfrom an 8.0-D lens. By how much does the image move if the object is moved fu8-qtzl 6sw;
(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 lgo2v6hn c)a x5 h14ppwith a focal length of 25 cm should an object be placen5a1 24 vpg6xhphcl )od to produce a real image which is the same size as the object?    cm

  (a) How far from a 50.0-mm-focalb+q1vn.v +v lmm)t j1+s qz6aj-length lens must an object be placed if its image is to be magnified 2.00× and be real)v +jqs1zlv1 mm n6v+.a+bqt j?    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 a3 /vo hb+kplt,n object be placed if its image 3kb+pl,othv/is to 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-ldd3a;;8z.9xnu j vdwg ength lens. Where is the image, how high isz; ddwag9nu 3.jd8vx ; 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 upb98 f6y+ ejbvq u.p9(i0oey-focal-length converging lens if the image is 2.5× largere(.pe i+9bj6quuy0fy8v bop 9 than the object and is real?    m

  A bright object and a viewing screen are separated by ,wz.uwo8 z d65efn b*ka distance of 66.0 cm. At what location(s) between the object and the screen should a lens of focal lefw.,zn*b zkduo we6 58ngth 12.5 cm be placed in order to produce a crisp image on the screen? [Hint: first draw a diagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length converging lenses are placed 16.5 cm jrb*kr 46d3eoapart. An object is placed 36.0 cm in front of one lens. Where will the final image formed by the s jder*b34 6orkecond lens be located? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens with gum 8 foui,tynr..- j4$f=-31.5\mathrm{~cm}$ 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;r3xk i-07ynzmkm * ywf,/ gea diverging lens. Parallel light strikes the diverging lens. After passin xyk0wi *ea-/mnmrf7 ,3yzk;gg 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 *py2)w-j,bxy02jcja s0mqcydf )qn .ii eu-; placed only 20.0 cm apart. The object is still 60.0 cm in front of the first lens as in (Fig. Below). In this case, determine)2)qs;m uxw.ji jba 0 y -eqjn-y,*ic2dfcp0y
(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. Th;il* .6oix;0.aaud*tyrdug h e focal length of the lens on the right is 20.0 cm, and the focal length of the lens .hidu da6 a*g;l.yu;otx*0r i 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 lecfe::*wv ima6 o97e+ 5caxr eungth of is placed 12 cm to the right of a converging lens with a focal length of 18 cm. An object is placed 33 cm to the lefteeu5+:v afemcirx9ca 6: 7*w o of the converging lens.
(a) Where will the final image be located?    cm to the left of the converging lens
(b) Where will the image be if the diverging lens is 38 cm from the converging lens?    cm to the right of the diverging lens

  Two lenses, one converging with focal length 20.0 cm and one diverging with frs ogq6le1w9 2 66ku fj5vnpu;ocal length are place 6jevugl qp6;5run 1kos96w2fd 25.0 cm apart. An object is placed 60.0 cm in front of the converging lens. Determine
(a) the position    cm to the right of the diverging lens
(b) the magnification of the final image formed.   
(c) Sketch a ray diagram for this system.

A diverging lens is placed next to a converging rf ew*wp; l),te+xin -xcc51p)vmwq,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 len7(;m epk 3rp;w9sszzas has surface radii of 34.2 cm and 23.8 cm. What is the focal length if n = 1.52? 3epzs; 9z;sa( 7k wmpr   cm

  Both surfaces of a do/ d.kuajf9jw ruz -+;utk/y1k uble convex lens have radii of 31.0 cm. If the focal length is 28u jk k//j1z+;ft ukudraw9.y-.9 cm, what 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 r epdelsekw-v.z4/ h) 9adius of the conc9p).-/zh sdk4veewe lave surface?    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat surfac lub,xu9v,r q6y*i0ffe and the other has R = -18.4 cm. What is the focal length?v0 qb*u,9f ,xl6uyf ir    cm

  A symmetric double convex lens with a focal length of 25.0 cm is to bowim2u tcy+bckf /*8k+b49c fe made from glass with an index of refraction of 1.52. What should be the radius of28+kocbb mfc w/u4+tkfc iy9* curvature for each surface?    cm

  A prescription for a corrective lens calls for +1.j 6ah4frm0 u6g6b9nhg50D. The lensmaker grinds the lens from a “blank” with n=1.56 and a preform 9m6ru bhfgha60n64jg ed 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.b7he5af-oulvd, 2s*o) v.8n chm:qpw Below). You stand 1.5 m away from one of these mirrors and whvh8m7 fu ) ceo*2sa5lb dpqnov-:,. look into it. You will see multiple images of yourself.
(a) How far away from you are the first three images in the mirror in front of you?
$d_1$ =    m
$d_2$ =    m
$d_3$ =    m
(b) Are these first three images facing toward you or away from you?
the first image is facing  ----待选择----toward youaway from you ;
the second image is facing  ----待选择----toward youaway from you ;
the third image is facing  ----待选择----toward youaway from you .

  We wish to determine the depth of a swimming pool filled with water. We 1lwjzne*q0l9 measure the width (x=5.50m) and then note that the bottom edge of the pool ilj*qlew z910n s 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 ofs ro1s 8cv*n4hzw 2w6gu0lxja;qga 6 ( 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 lk+m;x m:4ff/ke h,upconsidered a limiting case of a spherical mirror. Specm;hukp ,xl /:ke4 ff+mify what this limit is.
(b) Determine an equation that relates the image and object distances in this limit of a plane mirror.
(c) Determine the magnification of a plane mirror in this same limit.
(d) Are your results in parts (b) and (c) consistent with the discussion of Section 23–2 on plane mirrors?

Stand up two plane mirrobb8p 1kb78zig rs so they form a 90$^{\circ}\,$ angle as in (Fig. Below). When you look into this double mirror, you see yourself as others see you, instead of reversed as in a single mirror. Make a careful ray diagram to show how this occurs.

Show analytically that a diverging lens can6nwt:m / mrj2+jymum 4 never form a real image of a real object. Can you describe mmwt/j6 4uynj +rm:2ma situation in which a diverging lens can form a real image?

  Each student in a physics lab is zx1c57jpel -dassigned 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 iden x7e5z1 cd-pjltical equipment, but when they compare notes later, they discover that their answers for the object distance are not the same. Explain why they do not necessarily need to repeat the lab, and justify your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of a prism.r-z( r lcrkx*w:r,*ld 4rge c 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 cylind q;io5yfd;1 v4doql*b rical 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 lenlb si ;xkclgjo 4.:82ag0n:b qs 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 jkq8z0vn;l.gp3z 5 lj lens of focal length f, and a white screen for viewing the image n0 jl3vgkj 8p; z.z5lqis 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 fil v6ev yra2rp-cm3 mtb 8q1j0/om acts as the object whose image is projected on a screen (Fig. Below). If a 105-mm-focal-length lens is to project an image on a screen 8.00 mbq06e2otr/vmrjv cy38pa m1 - 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 actually 25+iala00/ipws y/25wv wp ay d4 by 36 mm) is to be projected on a screen 1.80 m by 2.70 m placed 7.50 m from the projector. What focal-length lens should be used if 0 pl2vis /aw +iaya5p/wy5 0wdthe image is to cover the screen?    cm

Show analytically that the image formed by a converging lens is real and invertex x s(v3:b;ylg8ohmd3d if the object is beyo;(bm lsdovh:y8xx 3g 3nd the 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 her at hxl /iw(i9 d0aoome. She claims the reporter was trespassing. To prove her point, she gives as 0 /9owi( xliadevidence 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 ofxxr/0ke ;nb0m the Sun 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 fron7 perp(rl4o 8nw,hou5 xf iy+oy(t*3qt of a certain lens is imaged 8.20 cm in front of that lens (on the same side as the object). What type of lens is this, and what is its focal length? Is the image real or virtuihp5pw,l47(u3r 8ro *yyot o+ nq(fexal?    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 f ::kxgsn j9;0ab0xtu from a certain 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 9; 0:0xkxsbnaftgu:j lens. Find the focal length of this lens.    cm