What would be the ap3wi7qosss02 , 6beqvupearance of the Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fleet in th gc)l- ktw*c.r7, -ex l8kp/ prfklf*f+ygq+ne harbor of Syracuse by focusing the rays of th*cx ,.p+frg8gf) q7fe+p- kcr/nwtlllk*y- k e Sun with a huge spherical mirror. Is this reasonable?

Although a plane mirror appears to reverse left andhcjhkzax j9d .5/5y-p right, it doesn’t reverse up and h5kcxdy9a5j j ph .-z/down. Explain.

If a concave mirror produces a real image, is the image necessarily invc9;+ gf y2udgmerted? Expg29+dcymgu ;flain.

An object is placed along the principal axis of a spherical mirror. The ma0 uxz/yc8x.bed/ *6cjn sxi7ignification 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 mirror7de/c xi/n xc8xzsyi *b 0uj.6 is the image located?

Using the rules for the three rays discussed with reference tob-;haos k. 5;g5 dmocmixy:/d (Fig. Below a), draw ray 2 for (F; bdgcmd5; xkmsao . yi/-h:5oig. Below b).
(a)
(b)

What is the focal length of a plane mirror? What is the magnification of a +ldp ocx5.q)splane mi +5)xsqo.p dclrror?

When you look at the Moon’sc- n u5r85- erfhmf/vk reflection from a ripply sea, it appears elongated . vf8-rem rnk-c/5uf5hExplain.

What is the angle of reth 3fr+.z nv)m ;rco 62p wbe/mh-nm0s.e /iqqfraction when a light ray meets the boundary between two materials perpen2i hp-e/zr ;6m).v o/f+csqwnbrhe 3 q.m0tmndicularly?

How might you determine the speed of light in a solid, rectzc /a,tify/4ryp y 4:yangular, transparent objy , / c/irya4fyyz4t:pect?

When you look down into a swimming pool onm xnr 150gg x3sx-qp)n 43ey 3hhqse-r a lake, are you likely to underestimate or overestimate its depth? Explain. How does the apparent depth vary with the viewing angle? (Use ray dqnh ph esxy1x me3n3x3)ng s0-4-r5qgiagrams.)

Draw a ray diagram to show why*j:s.2 ui6tyso:row-h 7w pxn a stick looks bent when part of it is under water jywnti: w6 p27sou-hx*:r so.(Fig. Below).

Your eye looks into an aquarium and vi,dk(w-lrky nr: gj:s ;ews a fish inside. One ray of light that emerges from the tank is shown in (Fig. Below), as well as the apparent position of the fish. In the drawing, y;:rs- d,wjgr kn(k:l indicate the approximate position of the actual fish. Briefly justify your answer.

How can you “see” a round drr7hoof,x* p;2i fi7 fxop of water on a table even though the water is transparent and colorless? i o7 ffrio;xh27f*px,

When you look up at ahhu/6 klw8m tr-ik77 gn object in air from beneath the surface in a swimming pool, does the lwug 7-h78kt/kr6imh object appear to be the same size as when you see it directly in air? Explain.

How can a spherical mirror have a negative object dismsulj.3lx/f..i )z yttance?

Light rays from stars (includa ud9 6g*u wio(wle;f0guyv63ing our Sun) always bend toward the vertical directu* 66w u9(ifa;dg wu gyvo30leion as they pass 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 a camera lens is to make a sharp imagefn amcs:o )ao*b5hr; + of an object very far n* m+s)aobc: a5ofr;h away?

What type of mirror is shown in (Fig.b*ua9ol t q5)vy:bvf+g/ 85lu-q ebre :( xnug Below)? Explain.

A photographer moves closer to his subject and then refocuses. Does thelsye 29pr, t7b 6cqjl; camera lens move farther from or closer to q7;2y pc,l erbsjt9 l6the film? Explain.

Can a diverging lens form a real ima-c ad;voy xyec3y (+v+ge under any circumstances? Explain.

Use ray diagrams to show that a real image formed by a thin lens 6;fdat ianb./is always inverted, whereas a virtual ima f.d/; btina6age is always upright if the object is real.

Light rays are said to be “reversible.” Is th1 xpri4. x*bg2 +qe1c*kw rovjphqh(9 is consistent with the thin lens equatio ov1eq4pkhpriq* b1 +.xh9w(jgcr*2xn? Explain.

Can real images be projected on a screen? Can virtual images?+zd.u)s mt0mvdk-h4c Can either be photographed? Discuss carefullyud)4z-0cmd v+smt.kh .

A thin converging lens is moved closer to a nearby obn4 cz4 gh7fnx5f1v:hjmw-de3 ject. Does the real image formed change-d 1hn4n 4h57ffcg wxev:mz 3j
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a r/n,oof h,xw x-9r2jl material with an index of refraction n = 1.30 In air, it is a converging lens. Will it stih -xnx2w9 j,l/rof r,oll be a converging lens if placed in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in shi35ekj;j9 wthe air stands facing a converging lens. If the nose and the tail are each focused on a screen in turn, which will have the gwi ;3ej5s jhk9reater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facing a converging lens. Under what2y .kaw04f 5ydcv yqxk+cag */ circumstances (if any) would the image of the nose be virtual and the image of the tail be real? Where would the image of the rest of the ck y*cdf.aqax+ 0 /y4k gwcv2y5at be?

Why, in Example 13, must the converging lens have a shorter focal len h6q 6lrb1tfxsr4;+r chu60wzgth than thetu61 w ; r+lcrbhqs4h0zxf6r6 diverging lens if the latter’s focal length is to be determined by combining them?

Explain how you could have a virtual objeys iz6-bgr58ect.

  An unsymmetrical lens (say7zr1y ;g1 cm,xg e4:ddl:uzby, planoconvex) forms an image of a nearby object. Does the image poiny:4;duxl cgz17 :g mdr,zeb1yt change if the lens is turned around? ----待选择----yesno 

The thicker a double convex lo* hn-5sazoa60hj;p q ens is in the center as compared to its edges, the shorter its focal lengthhsn*o0q a hoa5p;-j6 z for a given lens diameter. Explain.

Consider two converging lenses separ,0 vyb-r6aeeu lng9 p*ated by some distance. An object is placed so that the image from brluge ,* y6a9n -0pvethe 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 yourself as you loq(i sc+c0ysz3/ nhx2nok at your image in a flat mirror 2.5 m away. Fnq/cz0s i(3ysxh2nc +or what distance should the camera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mirror, you seesy 3bztva4afp:k pps3t* sau)8b1 (5y the same amount of your body whether you are close to the mirror or far away. (Trabs3z351yppf vsa (pu8ty k b4t:* )asy it and see.) Use ray diagrams to show why this should be true.

  Two mirrors meet at a 1kr bv(x ,7yl3c35$^{\circ}\,$ 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 s rdsayhk g60wn8srh1g/ 1q)entiz,+ 7 tands 2.20 m in front of a vertical plane mirror whose bottom edge is 43 cm above the f6 e a/dsh ,z0r8 hq1gkgnins7w ty)1+rloor, (Fig. Below). What is the horizontal distance x to the base of the wall supporting the mirror of the nearest point on the floor that can be seen reflected in the mirror?    cm

  Suppose you are 90 cm from 39az*( n2:ar uro*tyhzi5t ac a plane mirror. What area of the mirror is used to reflect the rays entering one eye from a point on the tip of your nose if your pupil diameter *:o ayrc uz3zar(tin5* at92his 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two planaflb 9 bqxyoj(u;5b79 e mirrors 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 mirri d(3;aikge oj8/pffjjdc08 1 or pointed at the Sun, focuses the Sun’s rays 18.0 cm in front of the mirror.1 8 f8(e ijkjgj/ipa3o;0 dfdc What is the radius of the spherical surface from which the mirror was made?    cm

  How far from a concave mirror (radius 23.0 cm) m+(nlnox4 fkh.ci8 x,yust an object be placed if its imagkl8 i (onhx4 xcn.+yf,e is to be at infinity?    cm

  If you look at yourself in a shiny Christmas tree ball wit cszixw)tqk:uw .95hrofl :.b4 5vhu -h a diameter of 9.0 cm when your falt5cqfw u5u-ho bi9k s.zw.r :v4 h:)xce 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 pers az)9:pt +hcq je6ebe(on who stands 1.4 m in front of it. If the image is three times the perz :c ()he ej9+6etabpqson’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror that, when 2.20 cm from a tootha-lzvg+) n)ln, 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 tha (k2a*tqflq8i n they would be if the mirror were flat. Are the mirrorkqq2* f8ita (ls 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 of ralvj 4dclpi5 p4621mbi6mnyv 5tvbw1 0g92rb adius of curvature 20.0 cmvy50w pip 6c 6abbg vvb9l21dl in4tm4r5m 12j.
(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 sto/nr-cg/ z k1uqi,lp;z re. You estimate the height of your image to be half of y1/, inqk p glzz/;-cruour actual height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object be placed in front of a concav(f1 6z.wo2r o +oiiilmee1 0dte mirror so that it produces an image at the same location as+i2 df w1emoro1zoet6i 0l(.i 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 curvedr 4ijrq o.c7)d mirror. The image appears to be 18.0 cm behind the mirroc i)qdr or.74jr. What kind of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniques,h-kf wm;s ry/wn8*)p 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, that the magnification m of a convex mirror ii8q ;fe0pz 5xhk ocn4xf/)y9 vs $m=-d_\mathrm{i}/d_\mathrm{o},$ 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 eq+mae vpk2; j)n x2:n7) oqk*yejmur 6vuation, Eq. 23–2, is valid for a convex mirror as long7j e)nqxpk)j k22 o:myu*6n+vvearm; as f is considered negative.

  The magnification of a5sud7 uh-srbtb ( k:)l 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 sphery(jj.we zx x;3ical mirror. It is desired to produce a virtual image that is uzjxx ey (w;j.3pright 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 ::pvc q w.+7;umcorxxyy7-miyour face by a factor of 1.33 when your face is uipc: +cxxy7vmqo-y: ;wmr.7placed 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 n:jk1:,vz+dc af c6ko 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 ic, ,znk0e4bf;2umgwtc:zkx nk - lzb08e is $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certainny3 sh-ek si+3 2soj,.wg1d6fk lu7fl substance is 89% of its value in water. What is the index of refraction of this substssw uik2f,d7j.hlelo6s 3n+-13gy kfance? n =   

  A flashlight beam strikes the surface of ajn(g9apx u + be-z ax+-l25phy pane of glass (n = 1.58) at a 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashlight upward from beneath the water at a y 7v6-znitt8yx y*i8*oazb 3m42.5$^{\circ}\,$ angle to the vertical. At what angle does the light leave the water? $\theta_2$ =    $^{\circ}\,$

  A light beam coming from an underw fjkam:w0 d*b)ater spotlight exits the water at an angle of 66.00k*a:m)b wfd j$^{\circ}\,$ to the vertical. At what angle of incidence does it hit the air–water interface from below the surface? $\theta_1$ =    $^{\circ}\,$

  Rays of the Sun are seen to hed79oa1cjfj 6pahs- rj./*smake 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 hascbrsj;zs;aii/b,f5 . flat glass sides whose index of refraction is 1.52. A beam of light frb5rb;.;aziijcs,/ f som outside the aquarium strikes the glass at a 43.5° angle to the perpendicular (Fig. Below). What is the angle of this light ray when it enters
(a) the glass, $\theta_2$ =    $^{\circ}\,$
(b) the water? $\theta_3$ =    $^{\circ}\,$
(c) What would be the refracted angle if the ray entered the water directly? $\theta_3'$ =    $^{\circ}\,$

  In searching the bottom of a pool at night, a watc)bp29dkfgk ,-1 2tkcr l ffj7xhman 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 li1 g,l9dt jkbkkc xff72-f p)r2ght 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 e j-zhhl8q nzkas;(;d4i92q fxquilateral glass prism at a 45.0$^{\circ}\,$ angle to one face, (Fig. Below). Calculate the angle at which light emerges from the opposite face. Assume that n = 1.58.    $^{\circ}\,$ from the normal

  A beam of light in air strikes a slab of glass (n = 1.52) av 5fsiheofewvk1z6hsw 4. (7+nd is partially reflected and partially refracted. Find the angle of incidence if tv+17i. 4o hhk6ewsf (5 svzfewhe angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a lightpdre9r y vjsc) kmp0/s ks9:3rer 5;1u beam incident on a uniform layer of transparent material, as in (Fig. Below), the directiove 0drrm ues 3r;9k9 s5)r/p:jpskc1 yn of the emerging beam is parallel to the incident beam, independent of the incident angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on a flat piece of glass with index of refraction.gipy18u o qov))tz 6n n as in (Fig. Below). Show that if the incident ano)og p )i8yzq.nt16 uvgle $\theta$ 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 be7ai67 jab. qco6ipg w+tween water and Lucite? To be totally internally reflected, the light mus+i.7o6 g q7p aibcj6wat start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liq5laa *c8ns)c15vd ox ouid–air surface is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted lhfhredl ;0j1z ;3k:qf1p6dmin a pool of water from a depth of 62.0 cm. Where must it strike the air–water interface, relative to the spot directly above it, in order that the light does not exit fmp dze 016hqhld:1f;kr3;j lthe water?    cm

  A beam of light is emitted 8j clikc(l0z 5/v ab0:t.0 cm beneath the surface of a liquid and strikes the surface 7.050lt /c ab0j clv:zi(k cm from the point directly above the source. If total internal reflection occurs, what can you say about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the lefrqxyps1 d /22bc1s jr/lru l n4k/z/b3t face of the 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 enterjtgpaz dgz3 3v/0not1(r t/-f s the 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 3 t0/zg-tofjagn(z/pdv 3t r1 the light beam reflects back into the material at point a.

  (a) What is the minimum index oxyzjx, *f-z6 yf refraction for a glass or plastic prism to be used in binoculars (Fig. Below) so that total internal reflyf *xz6jyxz ,-ection 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 tf8gzaz.6 e3l a 65.0-mm-focal-length converging lens. Find za 3f.teglz86 the object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at )hx4t5-xcb hqa 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 /snb+ nr6(pmk object 2.75 m away as an image 48.3 cm on the other side of the lens. What type ofk+/ n bpsmrn(6 lens is it and what is its focal length? Is the image real or virtual?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the power of a 20.5-cmx88 p s-p6m3+,k ajbtm j/yqyh-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 21/*idhhzwm. h , .+nk*te* b+caiquya4 cm to view a stamp 18 cm in fro.,mqh+ky bi c.1h /u+entdahizw***a nt 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 heldf1jsq wst37 (d 14.0 cm from an object 4.0 mm high. What are the position, type, and height of ts( 7d3sf w1tjqhe image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to fekk (1 u9r: f/wy4d)mkhu/yu uocus an image on the film of a camera. The maximum distance allowed between the lens and the film pl9u)(k4ry u//: mkhdu1 ye fwukane 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 r0i1xhvdom. ue z-rmw v;4 it/:eading material by a factor of 2.5× when a book is placed 8.0 c-ur .:/40; ovvem tmi wd1zxhim 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 -jf- 52x :c0lnnp2 eosdeit *grx8 .mrmove if the object is movox.- d-mr0pnrxle:jn c*e2i2gf5ts 8ed
(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 37jl2 9bmn;ws2g2l m jz4el iez-7rehlength of 25 cm should an object be placed to produce a real image wh 72jwel rs-l7 z 2j2gb3ehmmn;z94ileich is the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an object be plae.re.25w en loced if its image is to be magnified 2.00.e5ln. wee 2or× 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 qrlljq) ,qcbt61t .fg,l0 . eslens must an object be placed if its image is to be magnified 2. c tq1fs 0t),l.gl6b,j.qr qle00× 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 is t pa392 buuj(vhhe image, how high is it, and what tuajb3(2u p9vh ype 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-cmudg2 +7uj/i og:ga9k hp73vjyzme/,w -focal-length converging lens if the image is 2.5× lar z kuy,a+gvjog 9ui7w//3gph 2 7:jdmeger than the object and is real?    m

  A bright object and a viewing screen are separated by a distance of 66(w /v4ivm/e4) cklaes ;qtxp;fl/fz :.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? [Hint: first draw a diagrame lxplv4/4:w ia/ cqeft vz/m;k(f;s).] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length converging lenses are placed 16.5 cm apart. An objq5un cn m p8edx+n;n19ect is placem d; n9c+1nepqu 8nxn5d 36.0 cm in front of one lens. Where will the final image formed by the second lens be located? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens with,t)/vxy.7ajb ks 4my;bnz 1 yb $f=-31.5\mathrm{~cm}$ 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 isyjrw5.0svl s*h)pc( 2w nat4e 21.0 cm behind a diverging lens. Parallel light strikes the diverging lens. After passing thrw(0t)w.aln*e4h jvyc2 rsps 5 ough the converging lens, the light is again parallel. What is the focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Example 23–12 are now placed only 20.0 ( gg(v0nn5fop cm apart. The object is still 60.0 cm in front of the first lens as in (Fig. Below). In this case, g5f0nvn(pgo ( 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. Tx5e,z(.m elrnk *zu03*vlrg ahe focal length of the lens 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 gz(0 3m .lez,5vnxr*ruea *klthe left of the 15.0-cm-focal-length lens. A final image from both lenses is inverted and located halfway between the two lenses. How far to the left of the 15.0-cm-focal-length lens is the original object?    cm

  A diverging lens with a focal length of is placed 12 cm to the ri)ao oamk v3.pa8tm*:i4rihpm z0)wv7ght of a converging lens kmor0)itai )*8hz7w3avm: .ovpapm 4with 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 l-rx(y5akg97wv(f2i/y v xgq.ea5fsv ength 20.0 cm and one diverging with focal length are placed 25.0 cm apart. An object is placed 60.w5ygvar-k ( 2 f.viax/5sf7(exvq 9gy0 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 convejr9m3hd6b x +mrging lens of focal length $f_C$ as in (Fig. Below). If $f_T$ represents the focal length of the combination, show that the focal length of the diverging lens, $f_D$, is given by
$\frac{1}{f_\mathrm{D}}=\frac{1}{f_\mathrm{T}}-\frac{1}{f_\mathrm{C}}.$

  A double concave lens has surface ru t+* t(z:d/c+uynap pep/ :m.r ilrj)adii of 34.2 cm and 23.8 cm. What is the focal ljzp:/.a tm+c :/+u*r (ynle) p ritpudength if n = 1.52?    cm

  Both surfaces of a doublehu nn r-.mvk5ut e;7d.,vh b.b convex lens have radii of 31.0 cm. If the focal length is 28.9 cm, what is the inde un5vd-e vr.h .n,mu;k t7b.bhx of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal length ofn.tn fo*6dj3 soet/p 6 -23.4cm. What is the radius of the con*n6tenofd3 6 p/ojts. cave surface?    cm

  A Lucite planoconcave lens (see yo)c+eq d2nsq5v79 wq2x-g vkFig. Below) has one flat surface and the other has R = -18.4 cm. What is the focal lenx9co5d+y2 k)qq gv7s nqv- we2gth?    cm

  A symmetric double convex lens with a foh(dkysz5t k 4)+q7:woxw/no ocal length of 25.0 cm is to be made from glass with an index of refraction of 1.52. What should be the radius ofo4nho7(xsy)wz+dw q5/k :k to curvature for each surface?    cm

  A prescription for a corrective lens calls for +1.50D. The lenmu ykt(ub:*/in5vk6 h smaker grinds the lens from a “blank” with n=1.56 and a preformed convex front surfacym/ih v 6nkk:*u(ut5be 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. B7 g rmeb5dnfvumgh o :kp10;1*elow). You stand 1.5 m away from one of these mirrors and look into it. You will see multipdu1 *hgm: kv0pen 71ofrgm5;ble 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 swi97poqtb..z mibxs 9 ef;2cr9hmming pool filled with water. We measure the witeq9x2 b hms. o79b;iz9. cprfdth (x=5.50m) and then note that the bottom edge of the pool is just visible at an angle of 14.0$^{\circ}\,$ above the horizontal as shown in (Fig. Below). Calculate the depth of the pool.    m

  The critical angle of a cert s 3vy;kh4 iyjn-u4 qnryo0-,rain 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 limiting case of a spherical mirror. 4ulkic/ ;vvz (:cybm+Specify what this limit is vi: l4v(c b/kc;z+myu.
(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 fobr wx 6hl9m/u vo.ruw6+y-9 strm 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 ajxy; aa ln6av.z7yx4 9 real image of a real object. Can you descrizaa;9yvx4jy7a nx 6. lbe a situation in which a diverging lens can form a real image?

  Each student in a physics lab is a1v0wfa4a ur)ha eh;8hssigned to find the location where a bright object may be placed in order that a concave mirror with radius of curvature r = 40 cm will produce an image three times the size of the object. Two students complete the assignment at different times using identical equipment, but when they compare notes later, they discover that their answers for the object distance are not the same. Expl8aw)ha1 u0f4v rhe h;aain 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 x3ano);*t0kh r3ot jxprism is $\phi=72^\circ$ see (Fig. Below), what is the minimum incident angle for a ray if it is to emerge from the opposite side (i.e., not be totally internally reflected), given $\mathrm{n=1.50~?}$ $\theta_1$$\geq$    $^{\circ}\,$

The end faces of a cylindrical qfl9 j8 7d. s02.ymt undlj;wqfx+ e4iglass 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 pv3 -lpbvwkiz90)3knxo eihll1uqp s ;05-h0f laced 33 cm in front of a converging lens of focal length $f_1=15\mathrm{~cm},$ which in turn is 55 cm in front of another converging lens of focal length $f_1=15\mathrm{~cm},$ (see Fig. Below).
(a) Draw a ray diagram and estimate the location and the relative size of the final image.
(b) Calculate the position and relative size of the final image.

A bright object is placed on one side of a conve0aflkv + + rmsb10ncwa:mv6j2 rging lens of focal length f, and a white screen for viewing the image is on the opposite side. The distabjkv 6mfr a0ncvsm0wal2+1: +nce $d_T=d_i+d_o$ 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 8l h6(,axo *afhhr ccy8d) -lqimage is projected on a screen (Fig. Below). If a 105-mm-focal-length lens is to project an image on a screen 8.00 m away, how faf8xay c c(h ahl,q*6h)8dor-lr 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 sizei 09pt/p xbo3o is actually 24 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 to9t3ix p0/ob phe image is to cover the screen?    cm

Show analytically that the image formed by a converging lens i cn9m9yy)ydpi cp/nuy yy292)s real and inverted if the obyd9yiu2/ mc )2y)yn n9cpp9 yyject is beyond 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 home. Shemau 7u*dpfw6 f68kq z0 claims the reporter was trespassing. To prove her point, she gives as evidence the f6 fufwpmd 7kuz6*8aq 0ilm she seized. Her 1.75-m height is 8.25 mm high on the film, and the focal length of the camera lens was 210 mm. How far away from the subject was the reporter standing?    m

  How large is the image of the Sun on film used in a camera with9g8:/+ .qkgyuhvu vzq 1/ kb6bjlms2u
(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 czvf. vm6d9,yjw gcz7l,nq0- agn s1: am in 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, and what is its focal length,nm0d6n9g y7-:zvsj.al af 1vgcz,wq? 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)