What would be the appearance of tp5uv4xr5nrsa35 9.uzue wwc 6 he Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fleet in the harbort8(t x+0r2 lyi/ vqpscg9;txf)qb4v y of Syracuse by focusing the rays of the Sun with a huge spherical mirror. Is thi ti;9vvq(glt4yy8 t cx2x+q rb/0f sp)s reasonable?

Although a plane mirror appears to reverse left and rig5q :5feo9ntf9 ubyyb:ak(a 8t4l *wxuht, it doesn’t reverse up and down. Explai bw5*4 axatk8:l bf(n of5yy99q:eutu n.

If a concave mirror produces a real image, is the image necessarinvu.+lt 5 o zb sh5d.trvs)7:ely inverted? Exp zour 7 v).+nt.:ts55dbhevsllain.

An object is placed along the principal axis fj, fjw )* 0j,n*uwc,o+ wbgwhof a spherical mirror. The magnification of the fj,*hf n bw ,wujw,+cw0g jo*)object is -3.0 Is the image real or virtual, inverted or upright? Is the mirror concave or convex? On which side of the mirror is the image located?

Using the rules for the three rays discussed with referenx9(i :s.b j.r)kpsfeu ce to (Fig. Below a), draw ray 2 for (Fig. Belowbp9k.(si jer fx)u s.: b).
(a)
(b)

What is the focal leiwob6e 5db(s2r i-g 6hngth of a plane mirror? What is the magnification of a plane mirroi he6bro gbdw(6-s2i5r?

When you look at the Moon’s reflection from a ripply sea, it appears eloel8snajmqqz2darh l2 / /0rqx y;)55ungated . Eyl2eusn2lq85hazj/q 50)aq dm/rxr ;xplain.

What is the angle of refraction when a li 5eh,8 ;opoj95pskbtk/x xif5ght ray meets the boundary between two materials perpendoex,9 p8k fsithx;p55j / 5okbicularly?

How might you determine the speed of light inxbt zb(tz013 o a solid, rectangular, transparent objectb3tz1 xo zb0(t?

When you look down into a swimming pool or a lake, are you likelyqist(e y9)9lv to underestimate or overestimate its depth? Explain. How does the apparent depth vary with t(iq9st ly )9vehe viewing angle? (Use ray diagrams.)

Draw a ray diagram to shoc ,8 dy1velsr3uhh4 2m;2:r(sze iwzow why a stick looks bent when part of it is under water (Fig. Below;y:c ohe(rz2 2, emwrlhz38ui4 d1ssv).

Your eye looks into an aquarium and views a fish inside. One ray of light bub8 wcqt4s 6bxr(;8j n-oc3 r;,ofkxthat emerges from the tank is shown in (Fig. Below), abr (,xbt rkbu688;x -joos;ncfc w3q4s 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 tabl 9wd9coq j y- j57yceie5pfw+2e even though the water is transparent y w+9j-q7wo55i cpd2jyc f9eeand colorless?

When you look up at an object in air from benea+wfnsm+n q hz0uqx.(it*z0(w th the surface in a swimming pool, does the object appear to be the same size as when you see it directly in air? wxsqqn+ztz+mn(0u( h w *i0f .Explain.

How can a spherical mirror have a negatig af5zrnoh 2e;8xf(b/m l3ka)ve object distance?

Light rays from stars (including xvq9l1pg0 bbm4 ez0-jour Sun) always bend toward the vertical direction as they pass through the Earth’s atmosphermpbqjxe z094 - bl1v0ge.
(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 a3wzgrp -( m3ee sharp image of an object very fae-3rp (wm3gezr away?

What type of mirror is shown in (F5tq v/cspqd7 ef-:nr 7ig. Below)? Explain.

A photographer moves closer to his subject and then refocuses. Dosh8kw0mg1*h1 )a dd4qr,u j u(zc7viw6k9ozles the camera lens move farther from or closer to thed uhk 8u mwdk qz49lwsj(vr6chozi*g 7,a10)1 film? Explain.

Can a diverging lens form a real image under any chrxjd q +zu8vw /vs0,*ircumstances? Explain.

Use ray diagrams to show that a reeac ycr19aj xk 5ll5rzp-*2ml5 k* ax2al image formed by a thin lens is always inverted, whereas a virtual image is alc mlk r*5x9aeyj 2x p5az* clk1-5r2always upright if the object is real.

Light rays are said to be “reversible.” Izio 5o .r 5mww.6t- -.xqm*agot5polk s this consistent with the thin lens equ- 5 xltao6.wrt og.-mo.zwk 5om*5pqi ation? Explain.

Can real images be projected on a screen? Can h;ood6 th.mpgwv*e.mv+-wm u i;*m4 rvirtual images? Can either be photographed? Discuss;v-t*4uiow vdh+mre6*wmmp.; o h. m g carefully.

A thin converging lens is moved closer to a nv o+w-)jaxo g-earby object. Does the real image formed change jvoxag - +)ow-
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material witr2vwp /sy va)9u/y:mlh an index of refraction n = 1.30 In air, it is a converging lens. Will it still be a converging lens y2swl:r/yvmp/ ua )v9 if placed in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands facing a c9r yf ,f)1jqejonverging lens. If the nose and th91 yrqe, jf)jfe tail are 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 **9;gize cfefconverging lens. Under what circumstances (if any) would the image of the nose be virtual and the image of the tail be real? Where would the imafcz* f9eeg *i;ge of the rest of the cat be?

Why, in Example 13, must the converging lens have a shorter focal length lz1h+9 anfmz 2than the diverging lens if the latter’s focal length is to + l2z1 nahmf9zbe determined by combining them?

Explain how you could have a viay9f bi0+zbse8u3zd9qs *5fqwv9m 0 yrtual object.

  An unsymmetrical lens (say, planoconvex) forms an imagw/j5crx5-ay5mqei-3 ,tr ji oe of a nearby object. Does the image point change if the lens is turnermjoj,t/xr3 55 i5ycq ai-we -d around? ----待选择----yesno 

The thicker a double convex luuapl ;9y-+ob ens is in the center as compared to its edges, the shorter its focal length for a given lens diameter. 9+pl o;byuu- aExplain.

Consider two converging lenses separated bb( v)a6 )knmrgy some distance. An object is placed so that the image from the first lens lies exactly at the focal point of the second l nkb)r 6a)gv(mens. Will this combination produce an image? If so, where? If not, why not?

  Suppose that you want to take a photograph of yourself as you8o akyy8gp+lnf wa:/. look at your image in a flat mirr agky./yfp n:+8aow8lor 2.5 m away. For what distance should the camera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mirror, you see the same,wo(w zpyqm+n/ao/ 4f0o,m1zqok,jb amount of your body whether you areawbzm0q,(mo nkzjf1p oq/4 + ,w,yo/o 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 ysqw l ojlf 0u-3nqx.8tr6*,gbqu7 f3a 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.)wqy +w z+r*-,* qlujcmxp;kht;( ifg 68 m above the floor stands 2.20 m 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 of the wall supporting the mirror of the nearest point on the floor that can be seen rei)l,qw + pyjr(t+*fg;k h- uqm zwx;c*flected in the mirror?    cm

  Suppose you are 90 cm from a plane mirror. Whal 2vpuhdcl-an7 ta1z9c+3 1yvt area of the mirror is used to reflect the rays entering one eye from a point on the tip y7zn a 39cht+-vldc l2pu1va 1of your nose if your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors mee n,a,za;pj/qbal:/f s t 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 poingwjcvea;d52a u+ u,h 95u2y v 5wmcc6cted at the Sun, focuses the Sun’s rays 18.0 cm in front of the mirror. What is the radiushc d;55c6w2c2 veuc+m wg5a9yu ,vuaj of the spherical surface from which the mirror was made?    cm

  How far from a concave mirror (radius 23.0 cm) must an objecn(/t y(0qjl, amab/wq t be placed if its image is/ a( /yjl(tnwb0 q,amq to be at infinity?    cm

  If you look at yourself in a shiny Chrisq+t6kagffsyr4 23wx el.zn/.tmas 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 virtual? Is it upr+q/a643.zlx2n ywr .ftkegsf ight or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shows an uprrwp;q xy :s7d1zp-* j3bibok* -nasv7 ight image of any person who stands 1.4 m in front of it. If the image is three times the person’s height, what is the radius of curvy1 w7 zbs -3*pk;vnb-do j7rq:asp*i xature?    cm

  A dentist wants a small mirror that, when 2.20 cm from a tooth, will produce a fa lho33o*avd -enu,tk-q-o 3$\text{4.5×upright}$ 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 p5u;rzbcupp9l97 f n*qroduce images of cars behind you that are smaller than they would be if the mirror were flat. 9q prp9 b lzu;5*cf7nuAre the mirrors concave or convex? What is a mirror’s radius of curvature if cars 20.0 m away appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is placed 20.0 cm fromd2nw3 xem(get,dag 8fn:d t7 2 a convex mirror of radius of curw,gdxe2gme78ndn(t dt :32favature 20.0 cm.
(a) Show by ray tracing that the image is virtual, and estimate the image distance.    cm
(b) Show that the (negative) image distance can be computed from Eq. 23–2 using a focal length of -10.0cm
(c) Compute the image size, using Eq. 23–3.    mm

  You are standing 3.0 m from a convex security mirror in a stozxy9f.7a ls:bre. You estimate the height of your imaglf.9b xyas 7z:e to be half of your actual height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an obje)dq6asxci- k- ct be placed in front of a concave mirror so that it produc iqd-x)k -acs6es an image at the same location as the object?
(b) Is the image real or virtual?  ----待选择----realvirtual 
(c) Is the image inverted or upright?  ----待选择----invertedupright 
(d) What is the magnification of the image?   

  The image of a distant tr4i m2xnyg nx;/+str/cee is virtual and very small when viewed in a curved mirror. The image ap+ gn mx24 srixt/y/nc;pears to be 18.0 cm behind the mirror. What kind of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different tec 98i cfyty9lcqadwhs m0 /7(c;hniques,
(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 (vt0hvex* o+ut 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 equation, Eq. 2 k-* aja5f9g/uoh)hqf 3–2, is valid for a convex mioj k 9)uh/a*5agh- fqfrror as long as f is considered negative.

  The magnification of a convex mirror 9cdmnj )ozgh2i7yy) )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 mirro mx j-+7hzip*gr. It is desired to pro+zjx* 7p gi-hmduce a virtual image that is upright and 3.5 cm tall.
(a) What type of mirror should be used?  ----待选择----convex mirrorconcave mirror 
(b) Where is the image located?    cm behind the surface
(c) What is the focal length of the mirror? $f$ =    cm
(d) What is the radius of curvature of the mirror? r =    cm

  A shaving/makeup mirror is designed to magnify your face by a 7; r9gw tmnei klsth.5f7hj .7factor of 1.33 when y9t7;.h s5njre.l7 mk f it7hwgour face 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 in1gw/r x scc;p8 m7a;cy
(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(ty mur xaevl9m,*m,g7q1f:4 esmj4c is $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a c3 38glmdal:wxj ca9w ;ertain substance is 89% of its value in water. What is the index of refraction of this ag jw;3ldaxmc3 l :98wsubstance? n =   

  A flashlight beam strikes the surface of a pane of cr;sc6 ob*t be 4/gy;pglass (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 fr 3k b21+xarthpom 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 + a+ +qpdszaa33ysz r-an underwater spotlight exits the water at an angle of ps++- a3+z yq3 arszad66.0$^{\circ}\,$ 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 seen to make a 31.0y pfmnc9ktjqkvn5/k9. 6/ m(1-m oghq$^{\circ}\,$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?    $^{\circ}\,$

  An aquarium filled with water has fl:j/paokg1mdl ,j2 p- fop) l 8of7b7wi-sq-gxat glass sides whose index of refraction is 1blipa-f/dq,8omf-7j2go1 jpw: xk)- pgos7 l.52. A beam of light from 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 wagkik1ol*rp*t1 x/l 6o tchman shines a narrow beam of light from his flashlight, 1.3 m above the water level, onto txrllkog/ *p1k o6* i1the surface of the water at a point 2.7 m from the edge of the pool (Fig. Below). Where does the spot of light hit the bottom of the pool, measured from the wall beneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equilateral glass prism at ihetc.m9kghj7i h,*l g v*-7h 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 bfk sworn.19;i-s/vfglass (n = 1.52) and is partially reflected and partially refracted. Find the angle of incidence if the angle of reflection is twice 9s/.s n;k fifv o1-rbwthe angle of refraction.    $^{\circ}\,$

Prove in general that for a light beamzko n ab.33fh3 incident on a uniform layer of transparent material, as in (Fig. Below), the direction of the emerging beam is parallel to .oan3 h3z3kfb 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 n as ibcpzn-(tf,k* 7y +*z,0emadym 9o nn ln (Fig. Below). Show that iz7ef*z 0+byn, *dl pcky -(aonmntm,9 f 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 water and Lucite? Tocyi10l 2wk;m fb b5hr, be totally internally reflected, the light mh 51wil,m;02bc b kfyrust start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquu jii7( ks ).ifu6 uttgyu,:+bid–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 oyo :d0-xlm9 m-qdg4pm gn,+kxf 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 exi mg9ln--0:qdgxkom4+ x py,dmt the water?    cm

  A beam of light is emitted 8.0 cm beneath the surfacwlfpxcj aa35uq /r4)8w w :jdurb 6(8ke 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 say5 pjrwj 3qlk:(ux/ad)c8b f4a 6rw8wu about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left fac norcphshfjl0d2vd;r8q 847. e 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 enters the end of an optic fiber as sho+v f0(tar/ q mceqxp5-y0vkp /wn in (Fig. Below). Show that we can guarantee total internal reflection at the side surface of the material (at point a), if the index of refraction is greater than about 1.42. In other words, regardless of the angle the light beam reflects back into the material artp +-apqx f y/q05/v0 vc(kemt point a.

  (a) What is the minimum index of refraction for a glass or plastic prism to bl1 ik;gs(ukv7 10 rquc1x7kiwe us q ;i0 s17vixkk1gu kc1(rl7wued in binoculars (Fig. Below) so that total internal reflection occurs at 45$^{\circ}\,$? $n_1$ $\geq$   
(b) Will binoculars work if its prisms (assume n=1.50) are immersed in water?  ----待选择----totally reflectingtotally transmitting 
(c) What minimum n is needed if the prisms are immersed in water? $n_1$ $\geq$   

  A sharp image is located 78.0 mm behind a 65.0-m7p efw9 ydx*x9s54il cm-focal-length converging lens. Find x*s7xc5fy l4p9 iwed 9the object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.5 yrg)27sn* x rrcm behind a lens.
(a) What kind of lens is it?  ----待选择----converging lensdiverging lens 
(b) What is its power in diopters? P =    D

  A certain lens focuses light from an object 2.75 m awq dtlu5 cb;e 6bw/t yjll4*7,way as an image 48.3 cm on the other side of the lens. What type of llt;4ubdyl*5tb w, wec6 lj /q7ens is it and what is its focal length? Is the image real or virtual?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the powe kfib.h 8 kh3dkr4w5,q d)9rj3 foww)zr of a 20.5-cm-focal-length lens? P =    D  ----待选择----converging diverging 
(b) What is the focal length of a lens? $f$ =    cm  ----待选择----converging diverging 
(c) Are these lenses converging or diverging?

  A stamp collector uses a converging lens with focale6rqudl 5e (jmk:fq60 length 24 cm to view a stamp(06rj:u dqke f5 meql6 18 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 from an object 4.0 mm high. What are the position,g n2l9bbq,z*jn3 b w-mvr)5mb type, and bqb)9v,g-rn 2 zmwn35lb*mjbheight 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(as iv(- mz)af camera. The maximum distance allowed between the lens i(fa() msa -vzand 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 read wr5zy/./ ng mgzy:7sming material by a factor of 2.5× when a book is placed 8.05s.gmg/zy: n/w7zy mr cm 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 lenwl.r iet 8lwk+p 3w,0vs. By how much does the image move if the object isw evlrt,lw308.+ik wp 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 d/,bu6q1o1u/hl+tj:y ui wrcan object be placed to produceuj/+ht:6 yru11 w/q dcl,uobi a real image which is the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an object be yy(z2k l e943 gll;pc,qxt n0wa k*z/pplaced if its image is to be magnified y;lyaxwl/k tne,pk z* z02l3pc(q 9g42.00× 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-le n 4 pngl+v3;thj m3q5m*vj)jnngth lens must an object be placed if its image is to be magnified 2.00× and be real?)3mlqvjp3 ;jn m*gjvh nt+4n5    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 fromh5g8/r gkme (r ts+w,db,he/w a 135-mm-focal-length lens. Where is the iwbe,wm,+5 8sh ed(r/gr/htk gmage, 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 75-cm-vf zaihh:lfy*c + * pcvcj)34-focal-length converging lens if the image is 2.5×p*j-h fccy*z 43flvh v a+)c:i larger than the object and is real?    m

  A bright object and a viewing screen are sepx i wcfp 5*kw.yvwjx4l6-d 4*warated by a distance of 66.0 cm. At what location(s) between the object and the wwvcwxf- .wp*4 li x6y*4j kd5screen 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 diagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length converging lenses are wob.mfw u,v/2placed 16.5 cm apart. An object is placed 36.0 cm in front of onb w.vfuo wm,/2e 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 wit*2,.4- q1fvbedp1sll agt wyeh $f=-31.5\mathrm{~cm}$ 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. o(jlkhf -*lnd4h im84Parallel light strikes the diverging lens. After passing l4fmhlko4 nhdj-*(8i through the converging lens, the light is again parallel. What is the focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Example 23–12 are now placed only 20.0 cm apart.y g2cy v1;+y* msjafb; The object is still 60.0 cm in front of the first lens am ;jf g1a+by;ycvs2y*s 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 are placed 30.0 cm apart. The fzvo5tyl 8 9ro+ocal length of the lens on the right is lt+vo5 9ozyr820.0 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 le9k.c, n snnsu*n2:avf7 8yy focal length of is placed 12 cm to the right of a converging lens with a focal length of 18 cm. An object is placed 33 cm to the left of the co :c9uy78e f,lk2vy*snn san.n nverging 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 ono- ;0uv +t u )nc:1dfw4: wbwuujqzc:be diverging with focal length are placed 25.0 cm apart. An object is placed 60.0 cm in front of the conver +czubo wu-w14j;d ):0 vcu: :bqwutfnging lens. Determine
(a) the position    cm to the right of the diverging lens
(b) the magnification of the final image formed.   
(c) Sketch a ray diagram for this system.

A diverging lens is placed next to a converging lens of focal le(w k:q zd7xao(ngth $f_C$ 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 suuzea+pamv53y723 v hhrface radii of 34.2 cm and 23.8 cm. What is the focal leng732a zvaphv+y 3em5h uth if n = 1.52?    cm

  Both surfaces of a double convex lvu*7:9i(uq oblpivm8ens have radii of 31.0 cm. If the focal length is 28.9 cm, what is l:9 u*bp8u v7(ivm iqothe index of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a f1f ;7u qoziho(ocal length of -23.4cm. What is the radius of the concave surface? o7oi1q(z f uh;    cm

  A Lucite planoconcave lens (see Fig.ksu 9dfk)dxs34a cf/sf;2fz * Below) has one flat surface and the other has Rdsdfku *c 3f9 sx42fz f)/;aks = -18.4 cm. What is the focal length?    cm

  A symmetric double convex lens with a focal length of 25.0 cm is to be made fr)pqwh l86s8enom glass with an index of refraction of 1.s pne8lqh8w)652. What should be the radius of curvature for each surface?    cm

  A prescription for a corrective lens calls for +1.50D. The ovm0iie)e)tajd .h 3-lensmaker grinds the lens from a “blank” with n=1.56 and a preforma)3. ieh0toi-v) ej dmed convex front surface of radius of curvature of 40.0 cm. What should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face s9;5arv5e rmx:mu ys, each other 2.0 m apart as in (Fig. Below). You stand 1.5 m a: rrsuy5; v 5,maexm9sway from one of these 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 poo)v. e2m,*p )lkzgmp okl filled with water. We measure the width (x=5.50m) and then note that the bottom edge of the pool is just visible at an angle oz. *gvo) ke,pml2m)kpf 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.2vsg oau7:qnv;ss n5 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 limitin0 w0bmcl8 z9qyuy,qu )g case of a spherical mirror. Specifyucl08y,wz )b0 u9qq my 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 mkty7kerly9a x c6js33a5 /y x5irrors 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 nevejdhs ibyk:m;/o kek;*) k3i r)r form a real image of a real object. Can you d*oi)s:k kr ek ;kh/;)jdbmy3iescribe a situation in which a diverging lens can form a real image?

  Each student in a physics lab .y8tajd w(w5his assigned 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. Explain why thej(w5h a.dtyw8y 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 pris9fn **gjc3 sziyckn3*m 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 fznbkts)0: m 3glass 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 .-w 3ct ftc1sbg96lmr .ekwl8of 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 converging lens of focal lb/r faesxw.qe8(yi365*t ys (y9m noaength f, and a white screen/a ante 9 mf* sq.yr(68yi(woxs5e yb3 for viewing the image is on the opposite side. The distance $d_T=d_i+d_o$ between the object and the screen is kept fixed, but the lens can be moved.
(a) Show that if $d_{\mathrm{T}}>4f,$ there will be two positions where the lens can be placed and a sharp image will be produced on the screen.$d_T$>4$f$
(b) If $d_{\mathrm{T}}>4f,$ show that there will be no lens position where a sharp image is formed.
(c) Determine a formula for the distance between the two lens positions in part (a), and the ratio of the image sizes.

  In a slide or movie projector, the film acts as the object whose imfs9+ xqaz;9/ z4t rnfwage 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, h +ffrwnz;a9q/4t zs9xow far from the lens should the slide be? If the slide is 36 mm wide, how wide will the picture be on the screen? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (picture size ish3qc4/r. v7z5: aww(f deawrb actually 24 by 36 mm) is to be projected on a screen 1.80 m by 2.70 m phc.adaq 4:zv 7/fbwrer53(w w laced 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 convergin t:tf)8j /-*amzafresbno f ./g lens is real and inverted if the object is beyond the foc*t-zab)o/f.s/arjtmef nf 8 :al 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. She clais g7- 69ttcrci 7/sjmtms the reporter was trespassing. To prove her pointits 9g6trm-7j7c sc/t, 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 film used in a 8a;2vx1 z5detf-anl p 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 le x9 b)/i5nmrywns is imaged 8.20 cm in front of that lens (on the same side as the objbi/ )m yx9n5wrect). 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)