What would be the appearance of the4ad do09xtfk/ 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 o9 spa dhb fv 0.41y(,odq95)idlkoep hf Syracuse by focusing the rays of the Sun with a huge spherical mirror. Is this reasonable?i.1d,pla9(vp94d5h o ksofby he q) 0d

Although a plane mirror appears to reverse left and ee* omzz37 c/sright, it doesn’t reverse up ee /moz3cz*7 sand down. Explain.

If a concave mirror produces 9*0eo4ufo z uwa real image, is the image necessarily inverted? Explauzefo4*o u w90in.

An object is placed along the principal axis of a sp0 kxxdm r(i2 a6o2p9dhherical mirror. The magnification of the object is -3.0 Is the image real or virtual, inverted or upright? Is thi62x m9hpk 2do da0(rxe mirror concave or convex? On which side of the mirror is the image located?

Using the rules for the three rlna2ozt( :qc.ays discussed with reference to (Fig. Below a), draw ray 2lz .tcq2n(oa : for (Fig. Below b).
(a)
(b)

What is the focal length of a plane mirror? What is the mb+g4da 2 qwv bpeo/c 8jnx(51yagnification of a planedbqg1vw e5 2 4(8xj+c/b ynopa mirror?

When you look at the((zsmo 3f y58mzf j2ev Moon’s reflection from a ripply sea, it appears elongated . Explain2ms(em(58 zv fj3 oyfz.

What is the angle of refraction when a light r0y3ra c*s jxbr,fcswa95n v,6ay meets the boundary between two materials perpendicularl,5c0xa9 snb3jcf 6w, r*vsyary?

How might you determine the speed of light in a solid, rectang*x9kr0bjtb8z yl9r*ycv)0 um6k ;b fq1f o)ovular, transparent object?rkb b01kyr fyb8qo cz0fm)9j; u6xvt*) o 9*vl

When you look down into a swimming pool or a lake, are yo,d s/zxsy+h(q(kk4 b yu likely to underestimate or overestimate its depth? Explain.sx/(,z 4kd(ysb k+hyq 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 under w86o hkzkj*b62 b8qv tkater (okbqk6 88vbhz6* kt2j Fig. Below).

Your eye looks into an aquarium and views a fish inside. Ogf;e 3 u80xjkwyk s);ine ray of light that emerges from the tank is shown in (Fig. Below), as well as the apparent position of the fish. In the drawing, indicate the approximate position of the actual fish. Brieflyex kg;wu83;y0 j)i sfk justify your answer.

How can you “see” a round d c2ruwntx4a0+ m(5 xqxrop of water on a table even though the water is transpatarw5q uxcnx42xm0(+rent and colorless?

When you look up at an object in airmn5d7z:9cx lsh0sv(gh /s0 nj from beneath the surface in a swimming pool, does the objecgs /n7d 0j: s9 lm0sxc(vz5nhht appear to be the same size as when you see it directly in air? Explain.

How can a spherical mirrorxf z*mqd ;t+8p/bro+n have a negative object distance?

Light rays from stars (including our Sun) always bend toward the vert73;pwig ft(t cical direction as they pass th(wfic 7;g3pt trough 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 a camera lens is to jv4-*m k.r5uooosy4l euuk 1)yo. h2f make a sharp image of an object veryyh ek1 s54 oovfm yu-u.l4j*.)kr2ouo far away?

What type of mirror is shown in (Fz; hig9;iym z82yy-o tig. Below)? Explain.

A photographer moves closxc.s;bec,ktm9a/)iw:f ) q 9xlx/ unqer to his subject and then refocuses. Does the camera lens xx;l c/ emcf9q),quib:) xa s /.tnwk9move farther from or closer to the film? Explain.

Can a diverging lens form a real image under any c7c0oxi4*w1gzce n aeu k 2qjj*0boaok 751xt-ircumstances? Explain.

Use ray diagrams to show that a(bny ;q8wwi:k real image formed by a thin lens is always inverted, whereas a virtual image is always upright if the object is ;nki bw (:wqy8real.

Light rays are said to be “reversible.” Is thibmt2y32jy g7u7bua* f s consistent with the thin lens equation? Explaba 27ut3uf gy ybj72m*in.

Can real images be projected on a scr o,t:t;8 xzopseen? Can virtual images? Can either be photographed? Discuss careful xs8po t;:zto,ly.

A thin converging lens is moved closer to a nearby object. Does the real *jdhgb .en;vrh+ *au/;bj *ydimage formed change d hb v e*a.hr+ djn/*;jgb*;yu
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of refraction n = 1.3r)ha xabxa(ke+/ 5nu.0 In air, it is a converging lens. Will it still be a converging lens if placed in water?n/xexu+5arh)a( .k ab ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands facing a converging lens. If tdh:z xx .w ci(s*6 nv1cofy.5she nose and the tail are each focused on a screen in turn, which will have the great onvx.hs*ywz:s1fc 5( 6ci x.der magnification? ----待选择----nosetail 

A cat with its tail w6j1h*bm:t5pvr w jz6in the air stands facing a converging lens. Under what circumstances (if any) would the image of the m:b*rh5 j jz6t6w1 pwvnose be virtual and the image of the tail be real? Where would the image of the rest of the cat be?

Why, in Example 13, must the converging lens have a short-tpo (iem ;s+tu5 j4zwer focal length than the diverging lens if the latter’s focal len-m +5i;ttpo(zjw e 4sugth is to be determined by combining them?

Explain how you could havet5a9woord l0um0;h k j2(n o(p a virtual object.

  An unsymmetrical lens (say, planoconvex) forms an image of a ne7b)ec; hj jgt9 0ou2c+yhi6 rsarby object. Does the image point chac ;6sy2gb)hheji7 jcu+0ot r9nge if the lens is turned around? ----待选择----yesno 

The thicker a double cot0j u1jxe*br1*e-hq ynvex lens is in the center as compared to its edges, the shorter its focal length for a given lens diameter. Explain. xh1 brju**j-q0t1eye

Consider two converging lenses separadkmzq. 1i-l ;,+cpd jpted by some distance. An object is placed so that the image from the first lens lies exactly at the focal point of the.p-,kj qldzim p c1+d; 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 pr,g;a i5 +oekb,lpq1 at your image in a fo;ag pl kpb riq1+5e,,lat mirror 2.5 m away. For what distance should the camera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mirror, you see the same am for8x,lx i r2sv1yhzw3a;qs.sq01j;b . r y6gount of your body whether you are close to the mirror or far away. (Try it and see.) Use ray di zr,;611srifgxhxbs v;ls0jr a qw3y. .2o q8yagrams to show why this should be true.

  Two mirrors meet at a 1q*xdaa-1z 85+ m rrjgm35$^{\circ}\,$ 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 fro vmki/k2nd1 ;znt of a vertical plane mirror whose bottom edge is 43 cm above the floor, (Fig. Below). What is the horizontal distance x to the base of the wall supporting the mirror of the nearest point on the flo1vm knzik d2/;or that can be seen reflected in the mirror?    cm

  Suppose you are 90 cm from a plane mirror. What area of the mirzpjwy2ia38x9pe n4 m+ ror is used to reflect the rays enterinj4 +ap8pxywmi 9 ne23zg 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 j,zv8f/8v hu vat 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 poinyuib4b 4xcjp us4 ) .e(i2m*dtted at the Sun, focuses the Sun’s rays 18.0 cm in front of the mirror. What is the radius of the spherical surface from which the mirror was maijb ptube4x4)(d4u i*c 2ysm. de?    cm

  How far from a concave mirror (radius 23.0 cm) must an object be pdm+32ono6, xo71axi1l 8 r*rfkb kcz ulaced if its image is taouo fr i*rd8mz12 1xclknb+3k67x, oo be at infinity?    cm

  If you look at yourself in a shiny Christmas tree bl j.dg0i0kit:ff5 zp/ all with a diameter of 9.0 cm when your face is 30.0 cm away from it, where is your image? Is it real or virtual? Is it upright or pkgl/ij i 0dt0ff:5z. inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shows an upright image of any pers( m68e3xqpdca on who stands 1.4 m in front of it. If the image is three times the person’s height, what is the radius d(m3q8 paec6xof curvature?    cm

  A dentist wants a small mirror that, when 2.20 cm from a l1l) 2q.wa n;ws1rv gp6scf2 stooth, 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 imagel2cxmk +z4sv8 s of cars 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 20.0 m away appear 4ml2vkcx+s8 z 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm h4gt- mbou:f a*igh is placed 20.0 cm from a convex mirror of radius of curvature 20.0 cm f*t :a-obmu4g.
(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 securc73pp (e.gdosz8sm2 ,usmny3ity mirror in a store. You estimate the height of your image to be half of your actual height. Estimate the radius of curvature of the mirror.mysgp(m327dep c3o.sn8 u, zs    m

  (a) Where should an object be placed in front of a concave mirror so thapv5pr-7uxlo 5m(k k1jsgck vtxw1:5 8t it produces an image atsp5kwox75v(kt 5 :url1k8mxgj1 c p-v 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 jlxrc1 p d0w0azs t q7q 7lr77+.3eka4j7 yongviewed in a curved mirror. The image appears to be 18.0 cm behind the mirror. What kind of mirror is it, and what is its radius of curvatu0.q a 70k1 s n77 374lxqatgoecrdjyzljw7 pr+re?
 ----待选择----convexconcave 
r =    cm

Use two different tec xm9f/ 1ad/ebwhniques,
(a) a ray diagram,
(b) the mirror equation, to show that the magnitude of the magnification of a concave mirror is less than 1 if the object is beyond the center of curvature $C\left(d_0>r\right),$ and is greater than 1 if the object is within $ C (d_0 < r) $.

Show, using a ray diagram, that the magnification m of a x6-zun,(3gmom qkyx8 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 mirro+ltv+b p rpmle4 l3;q;a9tagco0 3zo 1r equation, Eq. 23–2, is valid for a convex mirror as lono34 3 bt;tca 1z++plq r0;v 9pmealglog as f is considered negative.

  The magnification of a h fpj:wve3n/o(y2ph4 :5 v koavp-wc*convex 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.o3mw y0m6 n1w+fv hi sa8c0.lk It is desired to prf18o shw03+l .ikvmy0ncamw 6 oduce a virtual image that is upright and 3.5 cm tall.
(a) What type of mirror should be used?  ----待选择----convex mirrorconcave mirror 
(b) Where is the image located?    cm behind the surface
(c) What is the focal length of the mirror? $f$ =    cm
(d) What is the radius of curvature of the mirror? r =    cm

  A shaving/makeup mirror is designed to magnify your face by a factor omw s;nx.7s .)6xcceg tf 1.33 when your f6m s c xg)7wt..nec;xsace 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 ligcgt6dgcbs8 9 iz:*p7z ht 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 i3gspxc n6 uo5v w2x/u67(g iwqn ice is $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain substw4pyaw -hevq:5 zx6mq)ivxe4 qg.q* o.0(l ptance is 89% of its value in water. What is the index of refraction of this subsh(lq )q4px:m z-y.5 avvoww6 e4qgt*0qe. xi ptance? n =   

  A flashlight beam strikes the surface of a pane of n -qh9rfsr:w, otdx0zb 0y,i: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 ,gosfi h5zs o,,6o *0f vfqgu1beneath 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 underwater spotlight exits the wa+y my8bh-c l)wter at an angle of 6+8y-yb )hcw lm6.0$^{\circ}\,$ 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 seeomk his/.suuxr*dk/.i op,)/ n 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 whosebxqyt,f 8xih1* 1r tmov*w:/b index of refraction is 1.52. A beam of light from outside the aquarium strikes the glass at a 43.5° angle thbq 1,fwt8*ovmbi1 *rxx: y/ to the perpendicular (Fig. Below). What is the angle of this light ray when it enters
(a) the glass, $\theta_2$ =    $^{\circ}\,$
(b) the water? $\theta_3$ =    $^{\circ}\,$
(c) What would be the refracted angle if the ray entered the water directly? $\theta_3'$ =    $^{\circ}\,$

  In searching the bottom of a pool at night, a watchman shin9zi(;y,e ang f- apr)sr6qz:aes 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 thna)p:i, r e9razgs-azq(fy 6;e spot of light hit the bottom of the pool, measured from the wall beneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equilateral glass prism at a 45.0h*c9)xotb0 l nwakv (,$^{\circ}\,$ 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 ( )aqvbs. c-mv5n = 1.52) and is partially reflected and partialv)qbsa- m5v c.ly refracted. Find the angle of incidence if the angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that forb5rr4op prv6tml44s ) a light beam incident on a uniform layer of transparent material, as in (Fig. Below), the direction of the emerging beam is paralb5m4os6p rprv)4 l4rtlel to the incident beam, independent of the incident angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on a )wt)z palderl4 l3, 0pflat piece of glass with index of refraction n as in (Fig. Below). Show that if the incident a wtep4, ld)3l)l 0rzapngle $\theta$ 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 andd 9y:w;s+jae 4i: j itceea*m2 Lucite? To be totally internally reflected, the light must start in which ma42mai d9e t:e:ij *+ s;jacweyterial?
$\theta$ =    $^{\circ}\,$
 ----待选择----waterLucite 

  The critical angle for a certain liq5gaxz71ispg * uid–air 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 from a depth of 62.0 cm. W4h ujd5pj4u3 l9hoz) ghere must iudgh zj9u3l)oh45 jp4t strike the air–water interface, 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;9yxrmwb6c j0n 7k xo4 and strikes the surface 7.0 cm from the point directly above the source. If total internal reflection occurs, what canc nx;ko6 0m4w79xyrbj you say about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face of th,.e zj xacf-:ce prism 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 en4jf 68q-hak vhd of an optic fiber as shown in (Fig. Below). Show that we can guarantee total internal reflection at the side surface of thea 4-8jfkq hhv6 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 glass or plastic eug8 ng p-kpw/j4(*7 zs(m3 y4a8tibt.nimvn prism to be used in binocun/p7i jgsz(8*p.-atvbtm y84mi uwk gnn(34 elars (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-mm-focal-83j-)ix 9kq qgg b ,4w6gcogcmlength converging lens. Find the object dista-ki)w jg3g6m4xq ,98b qog ccgnce
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 1 bw5yn z*rnp3k:w3-qy8.5 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;7m0ot-j19fdmxt iv o m 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 -mo1t f90m ovx;tij7dlength? 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 20dx3)e 4hgg 8oc.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 focal length 24 cm to view u fpta1wowf 6/1p8cw (2y0f)qeie+ *z;cfzxha stamp 18 cm in y6pfice/xqfhz 1p+c8 0f *f;wo(a2uwe)w1tz front of the lens.
(a) Where is the image located?    cm behind the lens (virtual)
(b) What is the magnification? m =   

  A -5.5-D lens is held 14.0 cm from an object 4.0 mm high. What 1xnu0n i7jp dj;e) -pvare the position, jivd1e)xp0;nn p-u 7jtype, and height 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 of a camer,mfm8) fc-gs2uxj d :fa. The maximum dis ffxc8:2mm-g)fsdj , utance allowed 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 materiinkpufte-7 (.al by a factor of 2.5× when a book is placed 8.0 cm .feun k-t pi7(behind 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-D lens. By how much does the image moveo-z)rq;v3ac px a3o:c if thp-ov :x q 3aaorz)c;3ce object is moved
(a) 1.0 m closer to the lens,    cm away from the lens
(b) 1.0 m farther from the lens?    cm cm toward the lens

  How far from a converging lens with a focal length of 25up hi.q v 6:soj*e9anl94b /fr cm should an object be placed to pr hebna4 9 * ovsipqrj:96f/ul.oduce a real image which is the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an object be placed m8k- wn*kyp dvs e(uw9rn7 j0.if its image is . 0*vw-jk9msnwrn( 8pkd eyu7to be 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-lengf,a csi i1h.+xid9le4th lens must an object be placed if its image is to be magnif,s9fc1 +id xeial.4ih ied 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 5y0urzwfs ss(hk:l c*3zqz 8,-ujt/ba 135-mm-focal-length lens. Where is the image, how high is it, and what tyzf-,(z 3zqs: h0r5sbl* uus 8t/kjyw cpe 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 a3bhl/jk n-g k( 75-cm-focal-length converging lenskl3gjk bh(-n/ if the image is 2.5× larger than the object and is real?    m

  A bright object and a viewing screen are separated by a distance (*/hkhz act sc.3jfg .of 66.0 cm. At what location(s) between the object and the screen should a lens of focal length 12.j(.hz fs/hg 3c *aktc.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 comw69 /ct0jiel 2hbe9 jnverging lenses are placed 16.5 cm apart. An object is placed 36.0 cm in front of one lens. Where w9/ct0mb6w2i9 el ehj jill 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 withso*i:rp r9s:57 bvfxyd; 6y do $f=-31.5\mathrm{~cm}$ 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 convergi0a3(1jlie7 qjb xkc; rng lens is 21.0 cm behind a diverging lens. Parallel light strikes the diverging lens. After passing through the converging lens, the light is again parallel. What is the focal length of the d17(qr0ba 3ckj lexj;iiverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Example 23–12 are now placed only 20.0 cm azyhndduss e3z2xfq*:15 f.z +part. The object is still 60.0 cm in front of the first lens as in (Fig. Below). In this qzhsxfdzdfn uz.3y:+51 *e2s 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 apazq1 spb,efg6, 7ub xq0rt. The focal length of the lens on the right is 20.0 cm, and the focal length of the lens on the l, ,qxpfzbg1e0q7 6u bseft 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 h td-hxah2s yy+z,,/wto the right of a converging lens with a focal length oz2xdy/wt- shh,,yh +af 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 one dr ),pm enfdpk2 ym*)+riverging with focal length are e)k*nypf ) prr,m+ m2dplaced 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 lens of f+lxf ct15zu+ pfwjpng 0l;8 rhg-- f6jocal 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 4e)isnby j)) mi(i, biand 23.8 cm. What is the focal l4b )n,i i)m) (eyisibjength if n = 1.52?    cm

  Both surfaces of a double convex lens 0nnm* f 7wpj;k/j)dqy have radii of 31.0 cm. If the focal length is 28.9 cm, what is the index of refraction of the lens matm*)/nnyfdw0j kj;7 pqerial?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm. q5vaqers: s5pw 6l 93xWhat is the radius of the cw5qsp9x6q5sa3lvr e :oncave surface?    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat surface m1r hqiiaoe)/8ln k3t+x9h8 iand the other has R = -18.4 cm. What is 3 e i8oh1+ k8hm9rxn/a)q ltiithe focal length?    cm

  A symmetric double convex lens with a fop zk9f06m 0vaxcal length of 25.0 cm is to be made from glass with an index of refraction of 1.52. Wv6mf pa9k0zx0 hat should be the radius of curvature for each surface?    cm

  A prescription for a corrective lens calls for +1.50D. The lensmaker grinds gp1nf9az0pl3 the lens from a “blank” with n=1.56 and a preformed convex p1lap3zg0 nf9 front surface of radius of curvature of 40.0 cm. What should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fig. Below).qz1i)uq.1 xxs You stand 1.5 m away from one of these mirrors and look into it. You will see multiple images of you.uxis)x1z q1q rself.
(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 sw n35xml o3m.gtn88md oimming pool filled with water. We measure the width (x=5.50m) and then note that the bottom edge of the g5 x. dlnm3on3t 88mompool 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:vl b pmvdn/-6c h2sa certain piece of plastic in air is $\theta_{\mathrm{C}}=37.3^\circ.$ What is the critical angle of the same plastic if it is immersed in water?    $^{\circ}\,$

(a) A plane mirror can be considered a liml 9e5.vtcix r(z9g if0iting case of a spherical mirror. Specify what thiix9l5fct.vg er0 ( 9zis 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 they formr 2-on;-cjtx r 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 realj;nb, m ) 5iyrdc/.1;rrw k lzukb,fw4 object. Can you describe a situation in which a diverging lens can form a real ;5, /yznw4r w.udi; ,f1mrkkrbc jl)bimage?

  Each student in a physics lab is assigned to find the lokle o6y(7c,l bcation 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 th b67lye( ,kcloe object. Two students complete the assignment at different times using identical equipment, but when they compare notes later, they discover that their answers for the object distance are not the same. Explain why they do not necessarily need to repeat the lab, and justify your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of a prism so26ok)) qpnrg wk.t 5(jg fo8is $\phi=72^\circ$ 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 glas5*,qomp9+ pjuv/a bym fv91cp s 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 le*x mrqq953y 7 :ko6xg:mrhtjb 2d8fqeh53yx gns 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 pwyrg,c0 in,o)pr0 h4g: uzv 9zlaced on one side of a converging lens of focal length f, and a white screen for viewipionr )gryu w z,vz ch,09:0g4ng the image is on the opposite side. The distance $d_T=d_i+d_o$ between the object and the screen is kept fixed, but the lens can be moved.
(a) Show that if $d_{\mathrm{T}}>4f,$ there will be two positions where the lens can be placed and a sharp image will be produced on the screen.$d_T$>4$f$
(b) If $d_{\mathrm{T}}>4f,$ show that there will be no lens position where a sharp image is formed.
(c) Determine a formula for the distance between the two lens positions in part (a), and the ratio of the image sizes.

  In a slide or movie projector, the film acts as the object whose image is p-6zhcs fe v-8frojected on a screen (Fig. Below). If a 105-mm-focal-length lens is to project an image on a screen 8.00 m away, how far from the lens should the slide be? If the slide is 36 mm wide, hozvfefs6c- 8h -w wide will the picture be on the screen? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (picture size is actually 24 by 3j9b.*( (d8g4h wvl sp bvxi3ils-w8mp6 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 the image is to cpxp8w9wmshd3(b b (iv s- i 4ljv8*l.gover the screen?    cm

Show analytically that the image formed by a converging l(isgjqwi 4wxwo d+2q b fj1b62py+9i+ens is real and inverted if the object is beyond the focal p6qig xw 9 +pj2i2y(swwf++iod1 bqjb4 oint $(d_0>f),$ and is virtual and upright if the object is within the focal point $(d_0>f),$ Describe the image if the object is itself an image, formed by another lens, so its position is beyond the lens, for which $-d_0>f$, and for which $0$<$-d_0$<$f$.

  A movie star catches a reporter shooting pictures of her at home. She ct2djof -cqx,rv;g /d*ve6 vf*laims the reporter was trespassing. To prove her point, she gives as evidence the film she seized. Her 1.75-m height is 8.25 mm high on the film, and the focal length of the camera lense2; vcrv f,xf -6d*o*jvqd/tg was 210 mm. How far away from the subject was the reporter standing?    m

  How large is the image of the S ph+c88jmi bk)up(nu :un 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 iy3eed)wpl(c( n front 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, apd(l ()e 3eywcnd 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)