What would be the appearance of the Moon if it had tjyk 4o.nl p2igv98 *b
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned qt -kq; +zcft4d( m7quthe whole Roman fleet in the harbor of Syracuse by focusing th7q; qdu -q+k(cmzttf4 e rays of the Sun with a huge spherical mirror. Is this reasonable?

Although a plane mirror appears to reverse left and rekj h :;ffkrld* t8ba3g -*1yaight, it doesn’t reverse up and dafjf8kg hdy*rt k-a1e3*bl:;own. Explain.

If a concave mirror produces a real image, is the image necessarily invert*x jcys+pw8v/ ed? Expx yps8+ vjwc*/lain.

An object is placed along the principal axis of a t z (al:ho;yb/spherical mirror. The magnification of the object is -3.0 Is the image real or virtual, inverted or uprighoh(: zb;/ya ltt? Is the mirror concave or convex? On which side of the mirror is the image located?

Using the rules for the three rays discussed with reference to (Fig. B rrc+29) 4ptaclqnyt1elow a), draw ray 2 for (Fig. Be t 2l)rccq41ap9yn+rtlow b).
(a)
(b)

What is the focal length of a plane mirror? What is the magnification of a plan6mnbf4m5 gtx /e mirrog 4tn bfx/m5m6r?

When you look at the Moon’s reflection from .n ioh*.yku; . :lszlka ripply sea, it appears elongated . *s .k.h;o:inyluzk.l Explain.

What is the angle of refraction when a light ray meets the boundary bemu*;w/1r xu0cq v ect/tween two matu*t 0qvmcex/urc w1;/erials perpendicularly?

How might you determineg+ ,cyc5lz.no * 1tybg the speed of light in a solid, rectangular, transparent objtnyz yo*l+c1 cb gg5,.ect?

When you look down into a swimming pool or a lake, are you 4llq)x*e s:zubln+zpz 56j, olikely to underestimate or overestimate its depth? Explain. How does the apparent depth vary with the viewing angle? (Us)4usq ,l: bz *ozepz6j+llx5ne ray diagrams.)

Draw a ray diagram to show why a stick looks bent when part of it is fdp y2z96gg)xbc/pp , /fq1sr under water (Fig. Be yd2)zf,/g9c gpr 6pf 1spxb/qlow).

Your eye looks into an aquarium and views a fish inside. One rayk 0 rh58bbh3avo0l1 wp of light that emerges from the tank is shown in (Fig. Below)813wbh 0 lv5a0orh pkb, as well as the apparent position of the fish. In the drawing, indicate the approximate position of the actual fish. Briefly justify your answer.

How can you “see” a r41l akpoibe 7e;9cf,mound drop of water on a table even though the water is transparent a,4ec1 ombpe ;l iak79fnd colorless?

When you look up at an object in air from beneatkm 1ya c9.mwl,h the surface in a swimming pool, does the object appear to be the same size as when you see it dire.ycalw mmk 9,1ctly in air? Explain.

How can a spherical mirror have a negative object dzfe6.rlx6l l 4istance?

Light rays from stars (including our Sun) always bend toward the ve a+bz q3:r0eczrtical direction as they :b 3rc0za+ zqepass 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 cam pvgd/m:r)e85mz 3 obeera lens is to make a sharp image of an object veomp5 3)me8rdv /bz:gery far away?

What type of mirror is shown in (Fig. Below)? Exppk q(2e uwre89lain.

A photographer moves closeew2 d)idu0t3;l)mley p6bf u* r to his subject and then refocuses. Does the camera lens move farther frommd6;))fu2ibd pwuty0l* l e e3 or closer to the film? Explain.

Can a diverging lens form a real image under any c6wvng. 3h bofdh+3:3 n2p)fyb)g b jnbircumstances? Explain.

Use ray diagrams to show thatq hqmcbh*4*6 1ahr6 yr a real image formed by a thin lens is always inverted, whereas a virtual image is always upright if the object is r r* c*61hq6qhrbah4my eal.

Light rays are said to be “reversible.” Is this consisten jm 8ep1ksk 7.ku0ea2qt.+dz qt with the thin lens equation? Explaint0pq.k e u2jmse7z.d1 ak kq+8.

Can real images be projected on a screen? Can virtual images? Can8 .pvyhub 2cu+ either be photographed? Discussuu yb2p+c.hv8 carefully.

A thin converging lens is moved closer to a nearby object. Does the real i v;ks zh(;l7seq(9t hpmage formed change 7kstv (s;hq(9zel ph;
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of refractio+4l ng2ghvr+,6h3skwa4i wc an n = 1.30 In air, it is a converging lens. Will it still be aw g n+6kvgsr4l4,iawh+hca23 converging lens if placed in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the airq ,ua(g7x 0qde iogut8g0y: lf,1br,v stands facing a converging lens. If the nose and the tail are ,71avrt8:odfu,egl y u (0qxg,bg qi0 each focused on a screen in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facing a converging lens. Under wha qb pr+)kzvk+m 9ti98jt 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 ctkvbp9i+8j+m9qr k) zat be?

Why, in Example 13, must the converging lens have a shorter focal len7mhfxaj , -,nfle tlmkc *09;wgth than the diverging lens if the latter’s focal length is to be determined by combining 09c l,xwemham; - f,* 7tkfjnlthem?

Explain how you could have a lce h4/1vp)uavirtual object.

  An unsymmetrical lens (say, planoconvex) forms an h/vf+i ks)qb/ image of a nearby object. Does the image points/+ khv/qfib ) change if the lens is turned around? ----待选择----yesno 

The thicker a double convex lens is in the center as compared to its j769ces; fznyedges, the shorter its focal l ezyf;j7s6 nc9ength for a given lens diameter. Explain.

Consider two converging lenses separated by some distance. An ob blc76bs xc el7eo:(,gject is placed so that the image frbcl:6s(e7 gbc xol7e,om 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 yourself as you look at youru /bc23fzahxmuuhl: x17 f ()w+ nes.r image in a flat mirror 2.5 m away. For what dihb hl. / uu: acxfze)7(ns+wr13xf 2umstance should the camera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mirror, you set(7rv;tf )nifbhjhr4znb7 w75 c / yw*e the same amount of your body whether you are( tb7;f ) c7h75yfrnb/nhrv4 *jzwtwi close to the mirror or far away. (Try it and see.) Use ray diagrams to show why this should be true.

  Two mirrors meet at 3n3b7hu7ku/c cfajo g4: 0 ikea 135$^{\circ}\,$ 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.2o 4 mwr+hjpa in front 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 .w+rjm 2h a4poof the wall supporting the mirror of the nearest point on the floor that can be seen reflected in the mirror?    cm

  Suppose you are 90 cm from a plane mirror. What area of the mirror )uwactql 1y8 :wu.em+is used to refleu m w8wyce 1aq.ul:+t)ct the rays entering 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 planex3jkiv5hs.dxl,s2 j 0 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 mirror pointdgw0a ( ;62s8syzifbqed at the Sun, focuses the Sun’s rays 18.0 cm in front of the mirror. Wbyg0 2a fq6wz( dis;8shat is the radius of the spherical surface from which the mirror was made?    cm

  How far from a concave mirror (radius 23.0 cm) mus2;2(u ai rllvzq ip/;bsq8d vd,uoh0-p/y* u st an object be placed if its image is to be2isdpa8v2;z/yo p-u d/l r;qu (q biu0*hlsv, at infinity?    cm

  If you look at yourself in a shiny Chr9mr7uxkifr,m c 8.39. 9jvw7w 1aixq txvxw9m istmas tree ball with a diameter of 9.0 cm when your face jv78 r wm37m99xcwu, v imxwi99qx ftkr.a.x1is 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 ll1o.bi wbvej +ka0 7l; tvnyym.8h+i)3rhj- 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 curvatuj..m3;wy7l hlvlyn beo1ra+k+iv8h0bi) - tjre?    cm

  A dentist wants a small mirror that, when 2.20 cm from a toothl14n14ke .xs;ommqijvq n -1c , 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 os i9i* j9,,cqyxt.e wbehind 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 0.33× their norma,o, w99txi* j eqisc.yl size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is placed 20.0 cm from a convex miriwvkwh:rx7kt qht- 8 -m;3nw8 ror of radius of c-nk3 ht-:x;q88w7rwtkh mw iv urvature 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 9voi6rvkp*t ( from a convex security mirror in a store. You estimate the height of your image to be half of your actual height. Estimate the radiuk t9v p(iorv6*s of curvature of the mirror.    m

  (a) Where should an objectmr.fpu kdmp t0) j5k5ui*- a*p be placed in front of a concave mirror so that it produces an image at the same u.aj k- *mkp ir 5mp)td5*pf0ulocation 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 curved mif m1: 0 5is k9pfoalecst22em(il/(: 3ixyhfxrror. The image appears to be 18.0 cm behind the mirror. Whak2 iois9a 1lp((fmy 0ixl m3x25e:esthf/f:ct kind of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniques,k(-)jue i: ysae8kz(v
(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, k1ev *7f/ wzgj(jj8yk 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 sh;lb a/yxdav:ziz ..u+ ow that the mirror equation, Eq. 23–2, is valid for a convex mirror as long as fdb u.l:y+zi x;a zv./a is considered negative.

  The magnification of p 6hwds3pspnex(1c v+9g;7(pd lhx0g w z1av9a 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 btf:c3ns 5m3z/m9ck wof a spherical mirror. It is desired tmfst3m:cw b3k n/ 5zc9o produce 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 yourj :)y8 -fmvoluhtrrn ,:g5rq9 face by a factor of 1.33 when your fq5g,trlvrfr9 n)mh-8y:ju: oace 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 light in q.jr,sk 0n-dsmxaz,wm8 + jb+
(a) crown glass,    $ \times10^{8 }\;m/s$
(b) Lucite,    $ \times10^{8 }\;m/s$
(c) ethyl alcohol?    $ \times10^{8 }\;m/s$

  The speed of light in ice 7 de/or )ta/yd9vw/rikk0qtkez ;+/v is $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain substa q5r7 xlh p:d(ofby8m7nce is 89% of its value in water. What is the index of refractirp(yxfl 8d 5q :7hom7bon of this substance? n =   

  A flashlight beam strikes the surface of a pane of glass (n = 1.58) at a 6xg av 8)86(3aln cpze:1lvcgq3$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashligh;7c d p/ ya3sc7ut-ixat upward 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 underwater spotlight exits the water at 4wj w .ql*k-ujurl5o)an angle of l*- kw5.qlow4) ruj ju66.0$^{\circ}\,$ 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 th 2:6 su:tvw9y q7w6m49pu+nydw0+dtyjym yseen 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 refractii p- :m/rtc 3 m(wgo mmu;;y3mjyf-6rcon is 1.52. A beam of light fro (m:trf cmr mumpc;3oj-3w-iym y g;/6m 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 z;, q8rq pscdpu-7vo)cq7g*d 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 do ,-qr7g;cquv8 p7opq) c *ddszes the 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 equil,r 8z:f k1dtkn j;6zefateral 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 2uvn* zw(ioms5i+f1 va slab of glass (n = 1.52) and is partially reflected and partially refracted. Find the angle of incidence if the angle of reflection is twice the angle of refractiov( i51mvos+fn u*zw i2n.    $^{\circ}\,$

Prove in general that for a light beam inik7cg94a: me zcident on a uniform layer of transparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the incident beam, indepenm4ie9z ka :gc7dent 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 refh6s.,to ;rrf vraction n as in (Fig. B,.h r;vs6tofr elow). Show that if the incident angle $\theta$ is small, the emerging ray is displaced a distance $d=t\theta(n-1)/n$ from the incident ray, where t is the thickness of the glass and $\theta$ is in radians. [Hint: for small $\theta,\sin\theta\approx\tan\theta\approx\theta$ in radians.]

  What is the critical angle for the interface betweuw e:6r8lvt93wuzl v. qid.y 3en water and Lucite? To be totally internally reflected, the light must startedt 39.iyv uv68uz3w :lqlrw. in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle fora: p-tvplew4f kzx4xoqy)g52 8bv8k2 a certain 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 a pool of water from a depth of 62.0 cm. Wh ;t.xj3mh:: jalsq/rb w8ex(prph 9c+ttc0l(ere must it strike the air–water interface, relative to the spot directly above it, in order thatexp8jhxtcwl:aq(r:tt9j+bs rm/p ; 0h(.cl3 the light does not exit the water?    cm

  A beam of light is e 7gm(u(bl5t *fxbny ,ymitted 8.0 cm beneath the surface of a liquid and strikes the surface 7.0 cm from the point directly above the source. If total internal reflection occurs, what can you say about the index of refraction obx (( b* unf7g,tmyy5lf the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face of the prism in (Fig. v.ipfu:f4o ay5 frc+ y8 jy91uBelow) 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 e h/o:j1l 8scsz/lk;v 8k/qa lrp50ur ond of an optic fiber as shown in (Fig. Below). Show that we can guazl/rv8 hlj 8uol/c 15/;ok kr:asp0s qrantee 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 light beam reflects back into the material at point a.

  (a) What is the minimum index of refraction for a glass or plastic prism t)3 mit8vyn at. i-cz0ro be used in binoculars (Fig. Below) so that total inter.nyiv- 0)c8t m zai3trnal 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-iz59qarc;u-r lay7xhrth f;15bz 1 . ifocal-length converging lens. Find thiziclt9hr zrx 5;7y1r1u a5abh -f.;qe object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.5 cm behind a lensp* /u9y jyl)nn fo6g8i.
(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 as an image 48.q syl2hc4 07vq3 cm on the other side of the lens. What qch4y7s qvl20type 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 power of a 20*f ;ik4o k; r cun:rd+-rrwsf..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 coecig) ht4ofyn1mk;- 8nverging lens with focal length 24 cm to view a stamp 1otngi 8);y hmkf4c1 -e8 cm in front of the lens.
(a) Where is the image located?    cm behind the lens (virtual)
(b) What is the magnification? m =   

  A -5.5-D lens is held 14.0 cm f4c;e6fycuw67 domm 7brom an object 4.0 mm high. What are the position, type, and height of the imagc6mw7 4u6e mcdbo7;fy e?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used t+,k3mb. wpeij c9 1foyo focus an image on the film of a camera. The maximum distance allowed between o,m1.w3fk+iy9 epjbcthe 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 vcppw) ky;:p 0l-msqc 0;f4j fsq35namaterial by a factor of 2.5× when a book is placed 8.0 cm beh;:njfq fw3c5ks myp;lc0)psa -4q pv0 ind 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:pisvec(tu 53 . By how much does the image move if the ot3vsp(ecu5 :ibject 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 witevh s aezz q97fv)ek- x1r;:r+u)q :och a focal length of 25 cm should an object be placed to produce a real image which 1 sxkqz7 :r)-e zr c9 qfvv)+eae:o;uhis the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens(n b tu:9tc;q:lz*wbpgzd e*8 must an object be placed if its image is to be magnified 2buqz8:twpt 9 n(;zb:cgld*e *.00× and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm

  (a) How far from a 50.0-mm-focal-length lens must an object s6ps:n+p. e s(l)glut.wpf+dbe placed if its image is tg n+pp+.pe6 :d)uswl.tsfls (o 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-foca7 vpu jfi,:i udzsl2ly,d.9cts5;6bdl-length lens. Where is the image, how high is it, and what type is ts,dp7s.z:il6 jdul9;v5 ufb c ,id2yit?
$d_i$ =    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-cm7dnj kh;ezi7 ; 7g*jam-focal-length converging lens if *jkzin77dm jga ;7e;hthe image is 2.5× larger than the object and is real?    m

  A bright object and a viewing screen are separated by a distvod hxrhgl h7 )f*6uv)4d3-pwance of 66.0 cm. At what location(s) between the object and the screen should a lens of focal length 12.5 cm be placedhp6h7lud4 roh v)3 x*-wvd)gf 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 convergm3z*kqob(1ahbl0,4odrjja 0ing lenses are placed 16.5 cm apart. An object is placed r4kjj ao*q,zhobb3(dma0 1l0 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 gx.yx6 qe. .wcbwo5h:ak 2gu( $f=-31.5\mathrm{~cm}$ 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 21b ih ,j3k ,en53-nu- w*getxaq.0 cm behind a diverging lens. Parallel light strikes the diverging lens. After passing through the converging lens, the 3xn nka*-g, ,u3e5 qbi w-jhtelight is again parallel. What is the focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging l sazh-3/ g** yvtkve.tenses of Example 23–12 are now placed only 20.0 cm apart. The object is still 60.0 cm in front of the first lens zskh/t .yag*3t vv- e*as in (Fig. Below). In this case, determine
(a) the position of the final image,    cm
(b) the overall magnification.    cm
(c) Sketch the ray diagram for this system.

  Two converging lenses ai.s. ct/,cxum e n6e(wre placed 30.0 cm apart. The focal length of the lens on the right is 20(,xwsuitn6 mc/.ec.e .0 cm, and the focal length of the lens on the left is 15.0 cm. An object is placed to the left of the 15.0-cm-focal-length lens. A final image from both lenses is inverted and located halfway between the two lenses. How far to the left of the 15.0-cm-focal-length lens is the original object?    cm

  A diverging lens with a focal length of is/a ncgom ww/ /477bxcg9.lu st placed 12 cm to the right of a converging lengb9 s/c u/m/aw.tx47lw o7gc ns with a focal length of 18 cm. An object is placed 33 cm to the left of the converging lens.
(a) Where will the final image be located?    cm to the left of the converging lens
(b) Where will the image be if the diverging lens is 38 cm from the converging lens?    cm to the right of the diverging lens

  Two lenses, one converging with focal length 20.0 cm and one diverging withsw wpg,x+l. 46w 4a* hbkegcdxk531t z focal length are placed 25.0 cm apartxhkgpdawt 4*5g6c lbs.wze,4w +1k3x . 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 convergchp.an1u9a ef64+ cez 8xoh; bk rr0/ping lens of focal length $f_C$ as in (Fig. Below). If $f_T$ represents the focal length of the combination, show that the focal length of the diverging lens, $f_D$, is given by
$\frac{1}{f_\mathrm{D}}=\frac{1}{f_\mathrm{T}}-\frac{1}{f_\mathrm{C}}.$

  A double concave lens has surface radii of 3e 0 x+ 9lzf.ku-f1cjls+/ldv g4.2 cm and 23.8 cm. What is the focal length ikl10sfjl v9x g d./ce- +uzl+ff n = 1.52?    cm

  Both surfaces of a double convex lens have radii of 31.0 cm. If the fh vd9s1dy+ok0c ;/ 8thvz ky9tocal length is 28.9 cm, what is the index of refdty/8oy 9 +01dhtszvkh;k9 vcraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm. What is thkcr, q z6esjn:z(vk;/ e radius of the co:;, jzs knev q(/z6rkcncave surface?    cm

  A Lucite planoconcave lens (see Fig.qy5y0sg wo/9i v4l6xcvul+-q Below) has one flat surface and the other has R = -18.4 cm. What is the focal len5sg0yl iq+w/ol4vy- vqxc9 6ugth?    cm

  A symmetric double convex lens p8 r)yb zh n, so7dqrm.918pnxwith a focal length of 25.0 cm is to be made from glass with an index of refraction of 1.52. What should be the radius of s) .q9xrrnh mnp1p b7o,z y8d8curvature for each surface?    cm

  A prescription for a corrective lens calls for +1.50D. The lensmakpk.kpx um*z*+er grinds the lens from a “blank” with n=1.56 and a preformed convex front surface of radius of curvature of 40.0 cm. What should be the radius of curvature ofkm zp* +k*x.up the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fig. Below). You stad 7oj/6 haos)rnd 1.5 m away from one of these mirrors and look into it. You w6hj /d7a)o orsill 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 thg;n *o a /8/qmsrqeb-re depth of a swimming pool filled with water. We measure the width (x=5.50m) and then note that the bottom edge of the pool is just visibg q/*sr-b m;no qar8e/le at an angle of 14.0$^{\circ}\,$ above the horizontal as shown in (Fig. Below). Calculate the depth of the pool.    m

  The critical angle of a certain piece of plrku1-b 8c5 zeuo/rxxlzy3v+*astic 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 sphez1k5oz0 osin 3rical mirror. Specify what thisn3zi szo0 1k5o 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 thwx0vyxt 8i; d) v/1xp(6 j7,m. dhbxhs9smfqhey form a 90$^{\circ}\,$ angle as in (Fig. Below). When you look into this double mirror, you see yourself as others see you, instead of reversed as in a single mirror. Make a careful ray diagram to show how this occurs.

Show analytically that a diverging lens can never form a real image of az4m d 3uuv yt7/gj,rf; real object. Can you describe a situation in which a diverging lens can form a real imauzr/7dmugt jfv3 ;4 y,ge?

  Each student in a physics lab is assigned w:) wnf7hh jtkz14(0x,hpu fpto find the location where a bright object may be placed in order that a concave mirror with radius of curvature r = 40 cm will produce an image three times the size of the object. Two students complete the assignment at different times using identical equipment, but when they compare notes later, they discover that their answers for the object distance are not the same. Explain why they do not necessarily need to repeat the lab, and juwh0 j hpp:(1ztuxfnwf ,4)7hkstify your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of a prism if9*2ejr2zon h n/r(u)g dpik( s $\phi=72^\circ$ 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 cylindrickpuj2 *h789c 2i swyqzal glass rod $(n=1.54)$ are perpendicular to the sides. Show that a light ray entering an end face at any angle will be totally internally reflected inside the rod when the ray strikes the sides. Assume the rod is in air. What if it were in water?

A lighted candle is placed 33 cm in front of a converging lens of focal sbdl) vof o800length $f_1=15\mathrm{~cm},$ 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 plaux2j9e.mn*mi. g , syeced on one side of a converging lens of focal length f, and a white screen for viewing the image is on the opposite side. The distance n.*s, 2mj.xmeig 9 euy$d_T=d_i+d_o$ 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 prb*ggk9fh. zr7n7 qdu1 ojector, the film 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 m away, how far from the lens should the slide be? If the slide is 36 mm wide, how wide will the picturg.9b qr7*nh fgd7 ku1ze be on the screen? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (picture size is actually 24 by 36 mm) is to be projected on a 2 yf/j9eddw tce./9 vascreen 1.80 m by 2.702yw.t f/ d cd9e9a/jev m placed 7.50 m from the projector. What focal-length lens should be used if the image is to cover the screen?    cm

Show analytically that the image formed by s4zxa0ctm2i7 a converging lens is real and inverted if the object is beyond the focal poic7sm zxait 240nt $(d_0>f),$ 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 cftqg;:a-/f p;n)x sqpictures of her at home. She claims the reportef /n-p: acq xsq;t);gfr 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 lens was 210 mm. How far away from the subject was the reporter standing?    m

  How large is the image of the Sun on vknw6ne3h dl0 uq3wded5* :1 afilm used in a camera with
(a) a 28-mm-focal-length lens,    mm
(b) a 50-mm-focal-length lens,    mm
(c) a 135-mm-focal-length lens?    mm
(d) If the 50-mm lens is considered normal for this camera, what relative magnification does each of the other two lenses provide? The Sun has diameter $1.4\times10^6\mathrm{~km},$ and it is $1.5\times10^8\mathrm{~km}$ away.    for the 28 mm lens    for the 135 mm lens.

  (a) An object 34.5 cm in front-lf3 qa /oy5qb of a certain lens is imaged 8.20 cm in front of tlq3 b5a-fqy /ohat 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 virtual?    cm (diverging)  ----待选择----virtualreal 
(b) If the image were located, instead, 41.5 cm in front of the lens, what type of lens would it be and what focal length would it have?    cm (converging)

  When an object is pleqbo,l( bj+2q aced 60.0 cm from a certain converging lens, it forms a real imagq qbo bj,l+2e(e. When the object is moved to 40.0 cm from the lens, the image moves 10.0 cm farther from the lens. Find the focal length of this lens.    cm