What would be the appearance of the Moon if it hb*1r0hv; oopspey1/kad
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fleet in the harbor of Sy15sp9txedr fqg3s: y1 racuse by focusing the rays of the Sun with a huge sphericfsxpd 5ty seg:1r9q 13al mirror. Is this reasonable?

Although a plane mirror appears to reverse left and right, i7ry yqep 7),mkc1pbsi/ra0g6t doesn’t reverse up and down. Explk)6ep aimybr,qr1/ sy7gc7p0 ain.

If a concave mirror produces a real image, is the image necessarymjy6rx x9c2tycy8;ar;a -e3 ily inverted? Expeja2y a8 9cy -6try;yxmrx3;clain.

An object is placed along tv2r0b3bz fv/hhe principal 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 mirror is zh3/ f2br0bvv the image located?

Using the rules for the kz6c,0 8rp na*pll8n hthree rays discussed with reference to (Fig. Below a), draw ray 0plackhl*,6n8zp rn8 2 for (Fig. Below b).
(a)
(b)

What is the focal length of a plane mirror? What is tal y6p .m3o4zi,f.djh:t c3o46paidd he magnification of a plane mirro4 omi t6j33a,da 4ipf: 6lph.coz. dydr?

When you look at the Moon’st w t,qs.a107xgq/py tg)aon9 reflection from a ripply sea, it appears elongated . Exq9 7g/.xys q,t1awtopa gt) 0nplain.

What is the angle of refraction when a light *(zwehg12op6 kicvfn64c:p m ray meets the boundary between two materials pemchizk 2 npf*16:g vpe o6(cw4rpendicularly?

How might you determine the speed of light in a solid, rectangular, r drp:j x4a:,kyfo5j6transparent obje jro,5fax 6p: dky4r:jct?

When you look down into a swimming pool or a lake, are you5ycco1a *vm8y likely to underestimatecy* cayom8v15 or overestimate its depth? Explain. How does the apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks bent when part of it is unflseo+ e-rw,7der water (Fig. oel,r7ws+ fe- Below).

Your eye looks into an aquarium and views a fish inside. One ray of ln( ye7uj 0xe9u2si/vuight that emerges from the tank is shown in (Fig. Below), as well as the apparent position of the fish. In the drawing, indicate the approximate position of the actual fish. Briefly justi92x(j7ie/ue vs0yu un fy your answer.

How can you “see” a ro uyg .jrh)hq/-xo-x0 pund drop of water on a table even though the water is transparent an0g hrxxj h)/uo.yqp-- d colorless?

When you look up at an object in air from beneath the surface i(u(fnq0njn7j tr d/m)l cbi.ky/**van a swimming pool, /t0(di 7njn/um f*.)rjb(yvnq k la*cdoes the object appear to be the same size as when you see it directly in air? Explain.

How can a spherical mirror have a negative object distanq 0az.v1gvs+a(fzhv 4 ce?

Light rays from stars (including our Sun) always bend toward the 5z33j krupz- hvertical direction as they pass through the Earth’spuh 3zkj35r- z 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 cmzn30 33bdcsfamera lens is to make a sharp image of an object very 3b3 dnf30 mszcfar away?

What type of mirror is shown in (Fi( i ix2ty:)vnmg. Below)? Explain.

A photographer moves closer tv/ z456m:ygxcvk9+got5jrt os . lo9ho his subject and then refocuses. Does the camera lens mo.4r 5:vz msot59ytgkhgl6cx+ jv oo/9ve farther from or closer to the film? Explain.

Can a diverging lens form a real imak +vm8rjc)p q(ge under any circumstances? Explain.

Use ray diagrams to show that a real image formed by a thin lens is cbgb z7 i(vc;i+m8xv3always invertec;g 87 vzm3(+ivxbcibd, whereas a virtual image is always upright if the object is real.

Light rays are said to be “n *,z- j)q6ivxci6mtx reversible.” Is this consistent with the thin lens equation? Expxiv6ci*jz,t6 n q )-xmlain.

Can real images be projected on a screen? Can virtu .vdkxq7j d m.(mnoe91al images? Can either be phot. d(m.j9deomv1 knx 7qographed? Discuss carefully.

A thin converging lens is moved closer to a nearby object.t*32m 0y6.djyu o urkh Does the real image formed chang3u .odmyk hr6*0juy t2e
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material wr k sr1, cth3e)md05qvith an index of refraction n = 1.30 In air, it is a converging lens. Will it still be a converging lens if placec0er)rm5vq,k3 ds 1th d in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands facing a converging 2x0 px v*e0xharb :uh;lens. If the nose and the tail are each focused on a screen in turn, which will h0: axx;bhh0r2* upxe vave the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stf85e/dznupg/ ands facing a converging lens. Under what circumstances (if any) would the image of the nose be virtual and the image of the tail du5 f e/g/pz8nbe real? Where would the image of the rest of the cat be?

Why, in Example 13, must the converging lens have a shorter focal -p0k 4ybk98k9j dlgti6 5i hc(v4tmce length than the diverging lens if the latter’s focal length is to be determ t c9pk6k5-kiv(bim4yde0jgh8 4 tl9 cined by combining them?

Explain how you could have a virtual object.g,)dbns3 bx ;bdza)8wu- 0aeg

  An unsymmetrical lens (say, planoconvex) forms an image of a n8pt )n sawe+ep 9bw-3pearby object. Does the image point chw +wap)tsp9 3 be-nep8ange if the lens is turned around? ----待选择----yesno 

The thicker a double convex lens rpqfwtss dv 4 . mhp:+ /j8oknb,fi5t+n 8ot:0is in the center as compared to its edges, the shor /df w+,bmsvht :q sn:otpt80p 84f+.5njr kioter its focal length for a given lens diameter. Explain.

Consider two converging lenses separated by some du.)qj s2pvk,u;f9o opistance. An object is placed so that the image from the first lens lies exactly at the focal point of the second p;jus,)ouf9q. v2o kp lens. Will this combination produce an image? If so, where? If not, why not?

  Suppose that you want to take a phownbk(90 -oxn hoqff* rs6x5a7am q:/ltograph of yourself as you look at your image in a flat mirror 2.5 m away. For what distance should the csbln:7(a*xrqx6mw -/o okfn fah509q amera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mirror, you see the same amount zz7s nys w *z.k.u:ds8of your body whether you are close to the mirror or far away. (Try it and see.) Use ray diagrams to8 udz 7*ks.wyszn:zs. show why this should be true.

  Two mirrors meet at a -;x ) lpte;x4v.5j jj2sivqvj 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.*fb )yswtt(z xj2fp3)20 m in front of a vertical plane mirror whose bottom edge is 43 cm above the x)3tjf )bz*p(w2 y stffloor, (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 the mirror is us+h8tr pa6y en6ed to reflect the rays enterin+ra86ythn p 6eg one eye from a point on the tip of your nose if your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors me) siebfw h)6f)4 b5ftjet 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, realkvlaru *0b;x 6xu5bs .ly a concave mirror pointed at the Sun, focuses the Sun’s rays 18.0 cm in front of the mirror. What is the radius of the spherical surface from which the mirro* b .6bxvarx5k0;ulu sr was made?    cm

  How far from a concave mirror (radius 23.0 cm) must an object.n0 tkuejd; efpxb+9: be placed if its image is to be atjkexetu; b+f0n :.pd9 infinity?    cm

  If you look at yourself in a shiny Christmas treerocu-3 *,1oiyl w8me z,zsa8 y ball with a diameter of 9.0 cm when your face is 30.0 cm away from it, where is your iaou* -z1y y8mis,3ow z8, crlemage? 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 imaqi3(q -cltd1 b(ekcw9ge of any person who stands 1.4 m in front of it. If the imabwe3q ld1k-9t c(qc(ige is three times the person’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror that, when 2.20 cm froczn4p dg 6b: g9t, bs 02w:odtra5tv3im 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 mirror2g3nj97-tf fap /p dxys produce images of cars behind you that are smaller than they would be if the mirror were flat. Are the mirrors concave or convex? What is a mirror’s radius of curvatureff3atp7p x d92nj yg-/ 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 pqka0/wu96gzd4p ; 95jg yy qua convex mirror of radius of cuaq9d;yzjqy4 pw6g/k 5u09 pgurvature 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 store. You estim-o*s7bb y3n,gjxf+oc, 2e zxyate the height of your image to be half of your actual height. Estimate the radius of curvature of the mirro,3ycx+b* x2,7g zse ofonb j-yr.    m

  (a) Where should an object be placed in front of a concave m6w +k:y1,v pkb.5yblpht g1nutw1ia( irror so that it produces an image at the same loc1y5pbb pu:+,1v6t yh nwg1w(k.ai tklation 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 viewoh k r042p*xrcp3 lv7) hi:iyied in a curved mirror. The image appears to be 18.0 cm behind the mirrcylhi:3oi0hr 7vp4* x2 pir k)or. What kind of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different tecdb 0b6gnkq,b+yg d7 vdpb3* c1hniques,
(a) a ray diagram,
(b) the mirror equation, to show that the magnitude of the magnification of a concave mirror is less than 1 if the object is beyond the center of curvature $C\left(d_0>r\right),$ and is greater than 1 if the object is within $ C (d_0 < r) $.

Show, using a ray diagram, that the magnification zv-l;(cn b*/cenmp z5 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 m,cr ,h s9ja.x1lqbe4s,ap 9(xm5i yjthat the mirror equation, Eq. 23–2, is valid for a convex mirror as long as f is considered ne bmhil,4j1,rs(s ycpqx, xe 95aa.9jmgative.

  The magnification of a convex mirrzk(opsavb,)y k:(8ka qdwp)5f 9et h/or 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,9 l4vvyvlot :3sj q3 fkuk-*w in front of a spherical mirror. It is desired to produceusk33 vljlvq:-49 w*v y tfk,o 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 fa/c o*wdp(b3mbn( fr7oce by a factor of 1.33 when 7 (( d p3bnbo*worcf/myour 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 ligndq5n*mgifzp3j-mv bw:k7/-qoo0 +gx) 2fy bht in
(a) crown glass,    $ \times10^{8 }\;m/s$
(b) Lucite,    $ \times10^{8 }\;m/s$
(c) ethyl alcohol?    $ \times10^{8 }\;m/s$

  The speed of light in ice is sv k t):ps5)wgzp37wr$2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain substance is 89% of its value in watnqoj,.b, k3r2s w4xs aer. What is the index of refraction of this sub ,nabs43sxk.,w ojq2rstance? n =   

  A flashlight beam strikes the surface of a pane of glass (n = 1.58) atz 0bfby6wf.eh 038sg h a 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashlight up f3o0z jh)d0zpward 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 anv 5frf p(t*uf/ underwater spotlight exits the water at an angle of 6 f(uf*t f/5rpv6.0$^{\circ}\,$ 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 ma2wlua) v,kzn+ nq0 h6 jh1:tuhke 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 refraction is;k/npj sk7ppn +*u 788sf.6g o ejixb1gxua)n 1.52. A beam of light from outsidk 71 a)u8nsex n;k. uopxp+ ijbp86*jfn/g7sg e 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,.0kj(xen, brbpe,,b q 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 p,jbq,bnep0 kx r.e( ,bool (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 a 45ne6koiwb5 jzqg8x6 /2.0$^{\circ}\,$ 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 = 1.52c)-9lvj zj *nyj6vbcx a7j5 7z) and is partially reflected and partially refracted. Fizxv)lzc57 n*j-a9jjy cb76v jnd the angle of incidence if the angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam incident on a uniform layep;4 o fno wb5gcbj644tr of transparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the incident beam, og tnj5 op;64c4wbb4f independent of the incident angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on a flat piece oa(9dd8.c tr m)m* baccf glass with index of refraction n as in (Fig. Below). Sha dcda9 m(bm)8t* c.crow 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 criticalyflebi;ol 3 5j*oa(wgkms0 (l7 ,in5l angle for the interface between water and Lucite? To be totally internally reflected, tws egl ao( lyjk0l75*( ;5,onmi3lfibhe light must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–air surface vkyra v(agt:;j 5tb,2is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in a poolv 8 j/5ay( b zq*mqi/;qjdaruo*wz3c 2 of water from a depth of 62.0 cm. Where must it strike the air–water zv2wc y*/ad qqjm;b(q a or3zuj*/i58interface, 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 ngeo 84etk8y5e, e)muh0n 4khcm beneath the surface of a liquid and strikes the surface 7.0 cm fr8ye)k h 8h50egkeu4tnmn,o4 eom the point directly above the source. If total internal reflection occurs, what can you say about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face of the prism lfjux a+zc,62in (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 shown i +run lvh-, a;2pnibs2n (Fig. Below). Show that we can guarantee total inter,sp n+l vhnua;2-2 ibrnal 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 glasfaff i; (ts(1v*j b;xes or plastic prism to be used in binoculars (Fig. Below) so that total int fj v1x; ab(t(e*;fsifernal 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 beh a o6r93w1aj9tyna+mmpp:w 3w ind a 65.0-mm-focal-length converging lens. Find the objet p:waawam6+ wmy3139on9j pr ct distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.5 cm behind x ga aw+(ju ku0e2 ao;zm*;uwh.y/qa8a 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 away as an image 48.3 cm on ko,o:nye; ;f tthe other side of the lens. What type o :;o,ky;onteff lens is it and what is its focal length? Is the image real or virtual?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the power of a 20.5-cm-f)8 ojpzl1ryp 5ocal-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 co3cfne q 52vef6nverging lens with focal length 24 cm to view a stamp 18 cm in front of the lens. c6e2 5q3envff
(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 pn :*kbhxa k wl3m4)o;0lhfx. xjet3s7osition, type, and height of the imj:sex xh)oat;lblwkf33n k*0m.x7h4age?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to focus an imag 5ttat) pvu75zu cy vg6a/v3)xe on the film of a camera. The maximum distance allowed between the lens and the film plane is 120 mm.5)vt/ucu3t5vg6 p x7)tzaav y
(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 magniaysuubb/ *;vs3y 3 3srfy reading material by a factor of 2.5× when a book is placed 8.0 cm behind a lensa/ byubsv3s 3ryu3s;*.
(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 7ck4qonyu65d(ip2g w .5 m from an 8.0-D lens. By how much does the image move if the object isw2i u6 k7qpyno4dcg(5 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 ano tv1(s-o,l xn object be placed to produ-,t1xlns(ov o ce a real image which is the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an object be placed*-h:o frmvs+ g)deiimfj(: s) if its image is to be magmig(:d+or )e:fmvs) *s-ij h fnified 2.00× and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm

  (a) How far from a 50.0-mm-focal-length lens must an object be placeogu x3im6; :r*juuc.o alv/t6d if its image is to be magnified 2.00× and u ;6/ctujr vuxa.om:*ol ig6 3be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm (formed by some other piece of optics).]

  (a) A 2.00-cm-high insect is 1.20 m from a 135-mm-focal-length r/8ika*f 0c nylens. Where is the image, how high is it, and what typei0*f a nr/yck8 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 hhku8og1 nhffm3 h;o*ve a0;. -6 xtbza 75-cm-focal-length converging lens if the image is 2.5×-k3h ma.8fzthuobfng;*1h h6;xev0 o larger than the object and is real?    m

  A bright object and a viewing screen are separated by a distance of 6*6zdgebcu 4m w,b6;ep 6.0 cm. At what location(s) between the object and the screen should a lens of focal length 12.5 cm be placed in order to produce a crisp image on the screen? [Hint: first draw a diagram.] lg,6bd cwzee64 ubm*p ;ens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length convergint01 *fgod/:bq6 ctdleg lenses are placed 16.5 cm apart. An object is placed 36.0 cm in front of one lens. Where will the final image formed by the second le6:01qbtd*fl ed/cog tns be located? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens withty8fu+b+mn r:lo/:2rr sz 9 xa $f=-31.5\mathrm{~cm}$ 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 convergif,*/*qjq b dugv* eks):ic.j ing lens is 21.0 cm behind a diverging lens. Parallel light strikes the diverging lens. After passing through the converging lens, the light is again parallel. What is the focal length of the diverging lens? [Hint: first drais)q.*u i, f*jj/q vgek* bd:cw a ray diagram.]    cm

  The two converging lenses of Example 23–12 are now placed only 20.0 cm apart. Thsb *deqy6;uvu9a- lt 5e object is still 60.0 cm in front of the dltv -b es9 5ay*u6;uqfirst lens 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 are placed 30.0 cm apart. The focal length of the lens ogjpv2g(e;d rt9+pn5 kn the right is 20.0 cm, and the focal length of the lens on the left is 15.0 cm. An object is placed to 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 rg2pkvn+9;t (edgj5 p far to the left of the 15.0-cm-focal-length lens is the original object?    cm

  A diverging lens with a focal length of is placed ud w:9u, sukhfr,2e4fnib4 )msd;;g d12 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 converging lensd 9: ,,sne uwg) 2f4umibd rd4;;fkush.
(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 diverginak9eld1vey+w0 8le 5 hg with focal length are placed 25.0 cm apart. An object is placed 60.0 cm in front o 5v1 eall0hwk89+ deeyf 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 hmm0f;yk 3(q*tdn ob3placed next 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 cm and 23.8yi-jt47 fj1nwq6cdu7 cm. What is the focal lecd 77juqj wiftn4y1 -6ngth if n = 1.52?    cm

  Both surfaces of a double convex lens have radii of 31.0 cm. If the focal l ,2egxm3kqs /dength isq 3ek/mgsx,d2 28.9 cm, what is the index of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm. What is thcaz .n:ftai7 j1 -tf:thwh m:6e radius of the con: t: fatft:-ni.jwh zcm 6h17acave surface?    cm

  A Lucite planoconcave lens (see Fig.nwv700twj+pnlje 5( w Below) has one flat surface and the other has R = -18.4wj+v wlp 7(en tn50jw0 cm. What is the focal length?    cm

  A symmetric double convex lens with a focan atm9 ea68x/u.t5n dgl length of 25.0 cm is to be made from glass with an index of refraction of 1.52. What should be the radius ttma.d 8u5/ex 6gnan9of curvature for each surface?    cm

  A prescription for a corrective lens calls for +1.50D. The lensmaker grindsi/+mojeo)s(d1 n,3e yq vss+j 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 of t 1sjsev+y)+o, q3(n sie/modjhe other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (F2;3t umq9h, fka2 thskh d5uf.ig. Below). You stand 1.5 m away from one of thes53t,h dka9u hq;.k2 uhmf2sfte 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 ld0qq7 d l,i5hdepth 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 visibl7q5l q0dlh ,die 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 cetz -v:,;urqtg )w;ql3piaz0 o9sel u4rtain piece of plastic in air is $\theta_{\mathrm{C}}=37.3^\circ.$ What is the critical angle of the same plastic if it is immersed in water?    $^{\circ}\,$

(a) A plane mirror can be cons d9by0n ,a0pjck2jd3kidered a limiting case of a spherical mirror. Specify what this liajbd09np 3j2k, ky0c dmit 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 so0s j/i+4wk. v0xsdng,3ag qah 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 dive/m3j 1dc1k h:wlw4 jdwrging lens can never form a real image of a real object. Can you describe a situation in which a w4l:1md jw3wc k jh1/ddiverging lens can form a real image?

  Each student in a physics lab is assigned to find t et)kxre(9duv zf(93 dhe location where a bright object may be placed in ord vz (9d fu)exktr(d93eer 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 justify your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of a prwvf4 ehz,p;bdp+p 87gism 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 glass rr vxn1)3u t6jgx/zd +yvw2b7 cod $(n=1.54)$ 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 ql)ptg*x .j*h0l ktel ;xse37a 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 convelxvbq(dkr * +*jxuj6 .pyf 9;drging lens of focal length f, and a white screen for viewing the image is on the oppob.dpjdy+frk q ux6*9;vjx*(l site 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 yi(:arngd 4s o6, s6tras 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 le:o s(4asntgr y66i ,rdns 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 is actually 00x qe p8apl)nxfm77t3f- m3,vzbgwm 24 by 36 mm) is to be projected on a screen 1.80 m by 2.70 m placed 7.50 m from the projector. What focal-length lens should be used if the image is m3lx3 w0am0zpvegb7nf7tp m8)fq-x,to cover the screen?    cm

Show analytically that the ima *taxg-*nzge,59l svtge formed by a converging lens is real and inverted if the object is beyond the focal 5,ts9g *eax-t gz*lvn 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 78v-4xkm xdyj(,;j t2m ok+cljk4s swat home. She claims the reporter was trespassing. To prove her point, s4,+xjs7xwtc (o48 ykjjk;lmmvk - 2dshe 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 - -x)jey+j zj ok22- ksn,*s lmd(cjl1q3t dkxfilm 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 fron,z w8/yubh:k7gf(c,y yvp9 tclhb pbf215du2t of that lens (on the same side as the object). What type of lens is this, andb5 y c/tzy:cbd2bvlp87fp gwh(u uf9 1 k2yh,, 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 60.0 cm fcn 5hwiuzj (6bu9u: ,;xwnscb/ j9kc;rom a certain converging lens, it forms a real image. When the object is moved to bjw uc,i/69un;;:cbux nw (s h5z j9ck40.0 cm from the lens, the image moves 10.0 cm farther from the lens. Find the focal length of this lens.    cm