What would be the appearance of thck . (n icp+7bm+m6otve Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to havlykl*c z5gu3*ys o)p3e burned the whole Roman fleet in the harbor of Syracuse by focusing 3p3oyk)y*l sc* u5gzlthe rays of the Sun with a huge spherical mirror. Is this reasonable?

Although a plane miry; :n7 -u8hl+og gcu96fxcttzror appears to reverse left and right, it doesn’t reverse up tfyun9 ouz+xc7c;6g t8 h:g-land down. Explain.

If a concave mirror pyrm *xhb95arki 4q 0q-o(2sdwroduces a real image, is the image necessarily inverted? Explai (o qmr40sdxikwq2ba9h -5*ry n.

An object is placed along the principj*xgna/85qhda./ cn+wmxazm4x r7 5val axis of a spherical mirror. The magnification of the object is -3.0 Is the image real or virtual, inverted or upright? Is the mirror concave or convex? On which side of the/mhja wan +/8*vr55q.xx4 dmz7xgnac mirror is the image located?

Using the rules for the three rays discuss)1yo ip7sy fm;xq-mf-ed with reference to (Fig. Below a), draw ray 2 for (Fig. Belo;-pf1ix o- y)7fmmsyqw b).
(a)
(b)

What is the focal lengtn x,ag 3/z8carh of a plane mirror? What is the magnification of a plane zn g8axc/,3armirror?

When you look at the Moon’s reflection from a ripply seiys4 2+u4lhm gjeudoy5 1mxw7*y9mi 4a, it appears elongated . Explain 9 ywex2i44hmjmlu4 +7syoi5 yud1 *mg.

What is the angle of re+n /zef7f qt5fd7nrr6fraction when a light ray meets the boundary between two materials 6d zrn5/ e7ntfqf7 rf+perpendicularly?

How might you determinev;el7yx -p z5i z;v*om the speed of light in a solid, rectangular, transparent object;7lm*z5;vi- xozpv ey ?

When you look down into a swimming pool or a lake, arf+bf wer))u*be you likely to underestimate or overestimate its depth? Explain. ef+fu w)r* )bbHow does the apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks beh ,e 0ysd4pat+nt when part of it is under water (Fig. Below).0,psade t4y h+

Your eye looks into an aquarium and views a fish inside. One rayzcpbwyfl 9gd)p ,+i+ecq o- g6.zfj6 5 of light that emerges from thzoje+6 bf dg,pcp)c gi. wz5 qy6-lf+9e 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. Briefly justify your answer.

How can you “see” a round drop of water on a table even though t35 *7mam.5ag6) fhx2ilc .m zlfrl meqhe water is transparent and colorless?l3*5 g .ammqla2x)l5 .7f6re fcmhizm

When you look up at an object n (3v0rmk,dazhn rm :/in air from beneath the surface in a swimming pool, does the object appear to be the same size as when you see it directly in ar3v0r/d a hm mnkz(n,:ir? Explain.

How can a spherical mirror have a negative object t *z*0bq:fdyv distance?

Light rays from stars (including our Sun) always bend ta*h mhz)pg * +,*syockkuiwh p-8 1,ssoward the vertical direction as they p,ik s)+czpok*ushwg*s, *h yp1a-8 mhass 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 atmr:.dlk .e 9b camera lens is to make a sharp image of an object very far awa:9dlrb. e m.kty?

What type of mirror is shown in (Fig. Below)? Expxlajpso8l 9 .92:vk1j5) v n)hxqkiry lain.

A photographer moves closer to his subject and then ru)el9zz 7y6 px( l)bafefocuses. Does the camera lens move farther from or closer to the film? Explain )lyx7)u(a9ezz l6pbf.

Can a diverging lens form a real image u,polu2 )ykja-kh-db7 nder any circumstances? Explain.

Use ray diagrams to show that a real image formed b.h0o6 nruy /xf)e/cp)c :ace8f qh5i vy a thin lens is always inverted, wyacri n :)x .evu/oecqh8f /56ch0 )fphereas a virtual image is always upright if the object is real.

Light rays are said to be “reversib4*uyo(u jp94b shw/vfle.” Is this consistent with the thin lens equation? Explai y9p*4 uo4/bhvusw(jfn.

Can real images be projected on a screen? Can virtual images? Can either )9cr: +jlz jxk/8kj/ *cft umr1yk;nbbe photogra9jkmjyt/xb *ku+ /jr ;l)rf81 cz:nkc phed? Discuss carefully.

A thin converging lens is moved closer tok;/l4p:pznd1, xit y v a nearby object. Does the real image forme:ypnzk ;x4/1 p,dvitld change
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an i 29d r2mkdhz5jndex of refraction n = 1.30 In air, it is a converging lens. Will it still be a converging lens if placed 95d2zjdhrm2k in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands faci7g-5z4y+ub ec+fjlx)ih.x yqyi n x)2 ng a converging lens. If the nose and the tail are each focused on a scrnujxfi2ql)e 7)+-4yg.x z+yx h5iycb een 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 v .x qwr o086fuogq(f3what circumstances (if any) would the image of the nose be virtual and the image of the tail be real? Where would the rq(f6 0o.quv8ow3 xfg image of the rest of the cat be?

Why, in Example 13, must the convergin yusmtj6 txw5u1 k8:;ng lens have a shorter focal length than the diverg6581wttu; uxyj mkns: ing lens if the latter’s focal length is to be determined by combining them?

Explain how you could have a virtup0 5qmql /i*voz4 fvx*al object.

  An unsymmetrical lens (say, planoconvex) f; ) mcfif-u lojfg;w5*g*6nasorms an image of a nearby object. Does the image point change if the lens is turned aro) -lc6n;*gj *ms w;if of5uafgund? ----待选择----yesno 

The thicker a double convex lens is in the cente+zys+.f fm0c6wwfw dhkb;. b8 r as compared to its edges, the shorter its focal length for a given lens diamet 0wsw+w +;mbc ff8dbhf6k .zy.er. Explain.

Consider two converging lenses separated by some distance. An object is placed s:ffxmnspu)m5 w.,ywrh ,d+erhis1 5: o that the image from the first lens lies exactly at the focal point of the second lens. Will this combinatiou:,) mh +hryw:5 d5m1.frfsexi, pn swn produce an image? If so, where? If not, why not?

  Suppose that you wankba1b 8 tv:ta1t to take a photograph of yourself as you look at your image in a flat mirror 2.5 m away. For what distance should the camera lt181a: tkab bvens be focused?    m

When you look at yourself in a 60-cm-tall plane mirror, you see the same epevk-fw su u6dx 2043amount of your body whether you are close to the mirror or far away. (Tryed24-0f uk xsevup36w it and see.) Use ray diagrams to show why this should be true.

  Two mirrors meet at a ikcmc+88 ( q3qvqfw(w135$^{\circ}\,$ angle, (Fig. Below). If light rays strike one mirror at 40$^{\circ}\,$ as shown, at what angle $\phi$ do they leave the second mirror?    $^{\circ}\,$

  A person whose eyes are 1.68 m above the floor stands 2.20 m in front of a veujtf2k(; si,7uj, dg krtical plane mirror whose bottom edge is 43 cm above the floor, j;, k7k(, jifsu2tgdu(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 a plane mirror. What area of .f 0q hk-h4,yugmptebm/dz 5+ the mirror is used to reflect the rays entering one eye from a point on the tip of your nose if yo4equ0, - .d gk+/tb zhypmfm5hur pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors meet at an angle7 on 2t eb s4zdbo gcdr,7w;1d-v2/ens $\phi$. a single ray reflected successively from both mirrors is deflected through an angle of $2\phi$ independent of the incident angle. Assume $\phi<90^{\circ}$ and that only two reflections, one from each mirror, take place.

  A solar cooker, really a concave mirror pointed at the Sun, fo ch v(pfjms 1so,i)y/6cuses the Sun’s rays 18.0 cm in front om(vis p, c6jfy/h)so1 f the mirror. What is the radius of the spherical surface from which the mirror was made?    cm

  How far from a concave mirror (radk rgb5g;re qab9d-w4 b;aj19b ius 23.0 cm) must an object be placed if its image is to be at infa bbbr9r1g-9wqe kgb;5;da j4inity?    cm

  If you look at yourself in a s s11i+ec (wl/.pm cznyhiny Christmas tree ball 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 virtpwce+/(iz1lsm.c n y1ual? Is it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shows a*-cb/ u iq.l2gu 7igp tcu))ion upright image of any person who stands 1.4 m in front of it. If the image is three times the person’s height, what is the r* ii2)iccgoblt /)ug pu-u7 q.adius of curvature?    cm

  A dentist wants a small mirror that, when 2.2w 15x yix xwbw(zl/4ia3 y0(yy0 cm from a tooth, will produce a $\text{4.5×upright}$ image. What kind of mirror must be used and what must its radius of curvature be?
 ----待选择----convexconcave 
r =    m

  Some rearview mirrors produce images of cars +zj rqi1,fv4 gp+ ea0 hjrk; z6h,hfki.r/fo +behind you that are smaller than they would be if the mirror were flat. Are the mirrors concave or convex? What +h / z+i1q4k6if.jh fjrgz0kpoh+f r,;rv ,aeis 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 mirrox:a1iy8 cc/5nnx-2ao; xj l ifwey *5zr of radius of curvatur;/nl51x -x xeoc iy*zf ic8na2a5:y wje 20.0 cm.
(a) Show by ray tracing that the image is virtual, and estimate the image distance.    cm
(b) Show that the (negative) image distance can be computed from Eq. 23–2 using a focal length of -10.0cm
(c) Compute the image size, using Eq. 23–3.    mm

  You are standing 3.0 m from a convex security miy nlnvow5u q,6qr1d-n4r mf01rror in a store. You estimate the height of your image to be half of your actual height. Estimate the r1d-r1wmqv yn ,n60 nf4 lqo5uradius of curvature of the mirror.    m

  (a) Where should an object be placed in front of a concave mirror so that it prqg/a 1zfs o04,th nlm0oduces an image at the samt0gfmh/ 0snl q1z,o4a e 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 w2e *ahxob n,v1 ke-)twhen viewed in a curved mirror. The image appears to be 18.0 cm behind the mirror. What kind knbe,2t1 hexow- )av*of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniques, bnxm*ih-65o. (fqye o
(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, tha/3mkir*o9e8 *)a rhgh ji sxj3t the magnification m of a convex mirror is $m=-d_\mathrm{i}/d_\mathrm{o},$ just as for a concave mirror. [Hint: consider a ray from the top of the object that reflects at the center of the mirror.]

Use ray diagrams to show that the mirror e j0 mj.eed)/q w+6drehquation, Eq. 23–2, is valid for a convex mirror as long as f is considered negative).6mdd re j0qje/e+hw .

  The magnification of a convex mi:ce4 sh3e6z cyrror 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 mirf47zfi o xjd4oio i9,72e2lsym:c e3sror. It is desired to produce a virtual image tha2y7m 7joxzdie9f 3 2of 4si4o: selci,t 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 fa (b xd dq+*a1q6wch*r.h ibc:ice by a factor of 1.33 when your face is plac+i i: (6q*cb.r1bddwqc*axhhed 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 x 99h uuvbgj;.
(a) crown glass,    $ \times10^{8 }\;m/s$
(b) Lucite,    $ \times10^{8 }\;m/s$
(c) ethyl alcohol?    $ \times10^{8 }\;m/s$

  The speed of light i qgn8rsv( /d*adem+jzz*l .s8n 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 r)lhgvp-i 4m.substance is 89% of its value in water. What is the index of refraction ovgl4p rm-)hi. f this substance? n =   

  A flashlight beam strikes t/yj6k f8(icno he surface of a pane of glass (n = 1.58) at a 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashlight upwa-zk -xbwiwss8f- tq:/be v(fhp8; 1o brd 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 tdyccscvlg ,l9l02y9+xp z-u : he water at an angle of 66. vcxyllpu-:cd 9c, s9+2l0 zgy0$^{\circ}\,$ 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 make;aqt 7t(yc2lyziey*;aje0. tu8 - m bg 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 i tkcpnh7;4bkse.84e whose index of refraction is 1.52. A beam of light from o c pb nih.ks7;8k44eetutside 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 watchman shines a narrow beam of l( quy8f26;pv 1 iwwa ghqn:r/night 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). n fugy16qa q rniw/hvw:;2(p8 Where does 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 equilateral glass prism sz/3)ho mp lfud/at:a2qtr-)8;ztrg 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) and is partially reflaiw ;lbn-72d- )box faected and partially refr-a27fwbal x) od- i;nbacted. Find the angle of incidence if the angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a 5e; pw-gkai8)cgca(7d/ h,d)vlu l vzlight beam incident on a uniform layer of transparent material, as in (Fig. Below), the direction of the emergingw g7huc liz)d5kd-av8/p( e) ;val cg, 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 c3ax c.6l c0voindex of refraction n as in (Fig. Belowc.3coaxc06 v l). 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 between wate7osfst :)k9cdr and Lucite? To be totally internally reflected, the light muko:) t9sfcs7dst start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for bgaxio:3zi,l :u 3t v(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 desff77n.wf d.9tr y5gg pth of 62.0 cm. Where musw 95f.fnyf .7dr ts7ggt it 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 yobk58ye06 zb and strikes the surface 7.0 cm from the point directly above the source. If total internal reflection occurs, what can you s60zo byykeb58ay about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face of the prism in (Fig. Below) aqka5kr*;1dl z2s rh9g t 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 thb-48k g3kvq hb9zbvarxe n.31e end of an optic fiber as shown in (Fig. Below). Show that we can guarantee total intekr3g1 v- 8aqb. 3kh4eb 9bznxvrnal 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 rewgp 5z2gp//z qxm1p3ifraction for a glass or plastic prism to be used in binoculars (Fig. Below) so that total iwpgzipx z/ /5q13m2pgnternal 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-length co m *o+xh)mzqj:nverging lens. Findmqm*zxh:jo + ) the object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to fovzc73zyh)fh):bgk l7pnj 8* rcus at a point 18.5 cm behind a lens.
(a) What kind of lens is it?  ----待选择----converging lensdiverging lens 
(b) What is its power in diopters? P =    D

  A certain lens focuses ligh x2 2urr0 *jmj.h f(ntx4w/beywto4; mt from an object 2.75 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 length? Is the image real or vt* x m4yh0/o(nwx4f mr;.rw2e jbt 2ujirtual?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the power of a 20.5-cm-focal-length cl 9d 6, x(cbz6b; ds)lbs;jsolens? 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 ; x)eq6exegds6hz68mqshp*9lens with focal length 24 cm to view a stamp 18 cm)esq sd9mhz686h ;6e e*pgxxq in front of the lens.
(a) Where is the image located?    cm behind the lens (virtual)
(b) What is the magnification? m =   

  A -5.5-D lens is held 14.0 cm from an objel)))xfx ft6 f-9d( k7dwd el(gz.x obnct 4.0 mm high. What are the position,bl()9dxfk -( 7tgn)dfwf. xol6)dz ex type, 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 cam )e*x1l27tlig5rbk2s y og0arera. The maximum disr1bo ik0ge2l)sr g7 yxal*t25tance 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 material by a factor of 2.5× when a book isjn/6x)z ykoy r 02 ;xx,rq06x /mgiybh placed 8.0 cm b b0qryirhxmnxz0 xgyo/;/ j)k y2, x66ehind 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 m e/-in0;/qdh1ouok f rove if the urn eq/h d;-f/ok01io 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 25 cm should an objdtvcmbs 5e; 4i5uwbk8 y83,ou ect be placed to produce a realcoy84mst5,; 3wbvbi duu e85 k image which is the same size as the object?    cm

  (a) How far from a 50.0-mm-focjfksy 0 oedk4rfn(q8 r 1dx 5(1s,qxe3al-length lens must an object be placed if its image is to be magnified 2qnsf0ek(4d8krrxy 35,efxod1 sj1 ( q.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-lee8v4 9t8ly isql3xa- cngth lens must an object be placed if its image is to be magnified 2.00×y3-qle8i a cl4tx8 v9s 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 r;hyz03 hv;le135-mm-focal-length lens. Where is the0r3vey hl hz;; image, how high is it, and what type is it?
$d_i$ =    mm (real,behind the lens) $h_1$ =    cm (inverted)
(b) What if $f=-135\mathrm{~mm}$?
$d_i$ =    mm (virtual,in front of the lens)
$h_1$ =    cm (upright)

  How far apart are an object and an image formed by a 75qt 2u4x(* u(k annzr8j-cm-focal-length converging lens if the image is 2.5×(natqr 4uk(8jx* 2nuz larger than the object and is real?    m

  A bright object and a viewing screen are separated by a d7*;):m*nn8w )lfs flh pwwx ilistance of 66.0 cm. At what location(s) between the object and the screen should a lens of focal length 12.5 cm be placed in order to produce a crisp imap8fl )si nnl;7mfh* wl xw*):wge on the screen? [Hint: first draw a diagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-lengtela0)fq( a .wxh converging lenses are placed 16.5 cm apart. An object is placed 36.0 cm in front of one lens. Where will the final image formela eq().0a wxfd 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 3y0bk6sl4wl g $f=-31.5\mathrm{~cm}$ is placed 14.0 cm behind a converging lens with $f=20.0\mathrm{~cm.}$ Where will an object at infinity be focused?  ----待选择----realvirtual ,    cm beyond second lens.

  A 31.0-cm-focal-length converging lens is 21.0 cm behind a diverging lens. Paralw lv1s(w.kt5 kkak+ +alel light strikes the diverging lens. After passing through the converging lens, the light is again parallel. Whatk5w1 k (v aa.wksl++tk is the focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Example 23–12 apiohpj vb vh)oj6a+n .q j/*i54gtkzs-;ii+6 re now placed only 20.0 cm apart. The object is still 60.0 cm in front of the first lens as in (Fig. Bel.j6jqh6) z;-b*sk oiitv p+pjhi4o+ g/a 5ivnow). 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 ardkh 1:iz 9,(ac +bvsjie placed 30.0 cm apart. The focal length of the lens on the right is 20.0 cm, an:1(ivi9cz bsjh+d ,akd 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 5 bm39ieqzi;n is placed 12 cm to the right of a converging lens with a b; 5i9zm3inqefocal 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 4mvt8g 17bs, oxymej5with focal length 20.0 cm and one diverging with focal length are placed 25.0 cm apart. An object is placed 60.0 cm in front of the converging lens. De84xm b 5yet1s7,vgojm termine
(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 ne/poegzu30 p8x2j 1m epxt to a converging 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 34.2 cmv 5nu/ld97 fvh and 23.8 cm. What is the focal length if n = ufh7n5dl/ v9 v1.52?    cm

  Both surfaces of a double convex lens hyb ki:1 sf4:j(owyq11 3peau xave radii of 31.0 cm. If the focal length is 28.9 cm, what is the index of refraction of the q :p s w1au3ix(jkb4yyf:1e1olens material?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm. Whatr8 7f t5uhu1a 04mptfc6znf.e is the radius of the conzch0.ua8fn57ur4 fftp 1t6e m cave surface?    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat sp ,8wx8nvpqfik0x 1; aurface and the other has R = -18.4 cm. What is the focal length?ppn aqv 1, w8fk80i;xx    cm

  A symmetric double convex lens with a focofzj,zxc -2xk/r;t+f nnj,wq3x fl 06 al 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 curvature for eac,3kzojwnfzfn fr jt,lq-+x6 /x2x;c0h surface?    cm

  A prescription for a corrective lens n4j)pl 4x3xik1tyhil q7tt,2 calls for +1.50D. The lensmaker grinds the lens from a “blank” with n=1.56 and a preformed convex front surface of radius of curvature of 40.0 cm. Wh j 7lp4 xinxq4tkt2ytl3 h)i,1at should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each t6v7s 0b-az u*/s,b7ls;lu,jerr1 tu7pbue a other 2.0 m apart as in (Fig. Below). You stand 1.5 m away from one of thes6- j*ur0,er zblbsa,tt 71us b ;l7ap/7usuvee mirrors and look into it. You will see multiple images of yourself.
(a) How far away from you are the first three images in the mirror in front of you?
$d_1$ =    m
$d_2$ =    m
$d_3$ =    m
(b) Are these first three images facing toward you or away from you?
the first image is facing  ----待选择----toward youaway from you ;
the second image is facing  ----待选择----toward youaway from you ;
the third image is facing  ----待选择----toward youaway from you .

  We wish to determine the depth of a swimming pool filled with watkngv.t/dwrgj ,) 2;ug hff7b*er. We measure the width (x=5.50 vr,bd/ ;*k thjng.7 fwg2)ugfm) 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 certain piece of plastic in air s/iby4y/ya: 10gl f; rcpszk:p)c sy.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 con7 3 2peuwsh ,ssgj4wr1r8mzx4sidered a limiting case of a spherical mirror. Specify4 8m21esrgsp w hurj4xzw,3s7 what this limit is.
(b) Determine an equation that relates the image and object distances in this limit of a plane mirror.
(c) Determine the magnification of a plane mirror in this same limit.
(d) Are your results in parts (b) and (c) consistent with the discussion of Section 23–2 on plane mirrors?

Stand up two plane mirror.f3 gc+c trz-as so they form a 90$^{\circ}\,$ angle as in (Fig. Below). When you look into this double mirror, you see yourself as others see you, instead of reversed as in a single mirror. Make a careful ray diagram to show how this occurs.

Show analytically that a diverging lens can never form a real image of a real obp b )2q7izp-mdmivots,7( 8mtwn 67jcur1p +fject. Can you describe a situation in which a diverging lens can form a rea6tpc7fdt77 )1s mbpj-pi+m n vmz8iu,q(wo2r l image?

  Each student in a physics lab is assigned to find the location w :-xydhl t iq19gp5ku7here 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, bu5 9gi -qhluxydt7p:k1 t 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 is 06qd jnze 4jvo 5e0w1d$\phi=72^\circ$ see (Fig. Below), what is the minimum incident angle for a ray if it is to emerge from the opposite side (i.e., not be totally internally reflected), given $\mathrm{n=1.50~?}$ $\theta_1$$\geq$    $^{\circ}\,$

The end faces of a cylind*+sjblqb y x63rical 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 offnnexz/eu ( 5p)9fas*cye94j 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 conveu62okv 9rlnf4+g(af x z18 xoxrging lens of focal length f, and a white screen for vo r9xu (8nlgo 12x4a+xffzkv6iewing 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,oe lx,1 w clsi+0al3(b0gxi,p 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 mmlxp , 3a0oicies0(+bx1w, llg wide, how wide will the picture be on the screen? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (picture size is axnl gat/:jj57sd3do* ctually 24 by 36 mm) is to be projected on a scree jls7gn3jd: *ta do/x5n 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 cover the screen?    cm

Show analytically that the image formed by a conzpne n (z3 ddhfuv59t.es; 0:qverging lens is real and inverted if tvn z(eh3d q;u5ed9tf :z 0.spnhe object 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 homeylus 33: nk0gq. She claims 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 lens was 210 mm. How far away from the subject was the reporter 3gsnkq:l3 y u0standing?    m

  How large is the image of the Su*p;wlae q.s ,fgfck 3 k2llyxbh: c41(n on film used in a camera with
(a) a 28-mm-focal-length lens,    mm
(b) a 50-mm-focal-length lens,    mm
(c) a 135-mm-focal-length lens?    mm
(d) If the 50-mm lens is considered normal for this camera, what relative magnification does each of the other two lenses provide? The Sun has diameter $1.4\times10^6\mathrm{~km},$ and it is $1.5\times10^8\mathrm{~km}$ away.    for the 28 mm lens    for the 135 mm lens.

  (a) An object 34.5 cm in front of a certain lens is imaged 8.20 cm in fro*. zujza, hu;ent of that lezeah* u;. ,zujns (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 placed 60xt 9vlb xsm8nr:c(9p5 q-d. vsla /,dn.0 cm from a certain converging lens, it forms a real image. bxa9 5xc.lsq-8 nd9ms/p tvnv(d,rl: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