What would be the appearance of the Moon ifsuxz; s2pb77t it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to hu(q/ 4 3h;t 6,fjbrut4nu wlltave burned the whole Roman fleet in the harbor of Syracuse fj b6ultnqhw4( t lu, t43/;ruby focusing the rays of the Sun with a huge spherical mirror. Is this reasonable?

Although a plane mirror appears to reverse left al;zu0h;eczp(l ph63uue0 r w3 nd right, it doesn’t reverse up a el0 ;u3(hphc zu6p0 ;3ruzlwend down. Explain.

If a concave mirror produu4 xljxltic94x. n:fc/a kj;9 ces a real image, is the image necessarily inverted? Expl9jtc4ukcxllf .9 i4j nx;/: axain.

An object is placed along the bqb k*;uil)hy/ p2aon7j zl;jc)g0g0 principal axis of a spherical mirror. The magnification of the object is -3.0 Is the image real or virtual, inverted oryug)) lqbjab2h0g p; k /zi7nojc0*;l 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 reference to (Fig. Below a),jho.r* :i n fnn;e2gv.32r poo draw ray 2n2ghrei2.p. : f3or onj*n;vo for (Fig. Below b).
(a)
(b)

What is the focal length of a plane 77;b*r (pqi nkan) okamirror? What is the magnification of a plane mirroi*(aq 7k );n7knr poabr?

When you look at the Moon’s reflection from a rqipqa2t.d gu)d5 rk (6ipply sea, it appears elongated . Explak5 2.ard)ugpqt6qi (d in.

What is the angle of refraction when a light ray meets the h1 ;gf.dkj;js ;;z9wt tzzrf3boundary between two materiats 1fzr.f;jdh;kj tz39g; w;zls perpendicularly?

How might you determine the speed of light in a solid, rew:ydr6uvjy u *7 au8dy h94c(yctangular, transparent objeyjy hvr48(7uda*y9d y uuwc: 6ct?

When you look down into a swimming pool or a lake, are you likely to underestim:4ti3n.iswapi lw d 23yr.d 5p ,eqfmsr 2-ud2ate or overestimate its depth? Explain. How does the apparent depth vary with the viewing angls riar3s4 m tiu:2.3 qd,e wd. iy-f252ppldwne? (Use ray diagrams.)

Draw a ray diagram to show why a sn 8t25vsz6zd ttick looks bent when part of it is under water (Fi t2 sd86tvz5zng. Below).

Your eye looks into an aquarium andk9u +50 lcfezocu5ic1 views a fish inside. One ray of light that emerges from the tank is shown in (Fig. Below), as well as the apparent position of the fish. In the drawing, indicate the approximate position of the actual fishf+uc o9z1lck50uic e 5. Briefly justify your answer.

How can you “see” a round drop of wate9wn 5u. scctev ny(9ju -eg2d34mk1yrr on a table even though the water is transparent and coymk9(5 t us1eru3 4jny.c -9ewn gcd2vlorless?

When you look up at an object in air from benea7r zmdj*mjq)i 9 29rne52rf xcth the surface in a swimming pool, does the object appear to i2e)j9 mc9rrq *m5 2xzn7jrdfbe the same size as when you see it directly in air? Explain.

How can a spherical mirror have a negative obj*)5x+ig q2d5uzqig.*vlnge kect distance?

Light rays from stars (including our Sun) always bend t:i yfd3;,e7 zb .ix8x6kkjcjyoward the vertical direction as the 7yxjexki,y;b: 63j.8idkzcf y pass through the Earth’s atmosphere.
(a) Why does this make sense?
(b) What can you conclude about the apparent positions of stars as viewed from Earth?

Where must the film be placed if a camera lens isqlq3shb ;z,*pml0o1c to make a sharp image of an object very far 3zc,*pq bs1m;q lo0 lhaway?

What type of mirror is shown in (Fig. Belodioewd f ukb;9 9sc-,3w)? Explain.

A photographer moves closer to his subject and then refoc)qeme9 6qt -*st(b- am ;f pg2mb,mzjeuses. Does the camera lens move farther from or closer to the film? Explain.t- bfmq,pmaz qtm -gmseb;) ej*2(96e

Can a diverging lens fo1j7j8q r*zo wn1m. wsirm a real image under any circumstances? Explain.

Use ray diagrams to show that a real image formed by a thin (1iyoo8dr ,o(po,t.eig qwd1. l tr a3lens is always inverted, whereas a virtual image is always uprig(yeidro38plw ,1 1ad .togt ro(oq.i,ht if the object is real.

Light rays are said to be “reversible3l*upo8w q op ).hkms;qzh65 d.” Is this consistent with the thin lens equation?psk h3hpz.qou; d5 l w8o*q)6m Explain.

Can real images be projected on a screen? Can virtual images? Can either be pho:qrdy6kc- *yk )irot;hfzxc+ em9 tq99psm8-tyt cx c9o 9d8r)+zyqfi*ht kkm ;m9 :-q6-esprographed? Discuss carefully.

A thin converging lens is moved closer to a nearby object. Dotao7)1;j+/b*v 46pbek i;jeo cxnstnes the real image formed c ;o);s ncbove at*+/i1b e476tnkjjpxhange
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an indexvd.p/x+l cxb: )b uk:b+dbz4c of refraction n = 1.30 In air, it is a convek/) d4lcpv.+u:xbx b:cb+z dbrging lens. Will it still be a converging lens if placed in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air sta6udk18z 1q udvnds facing a converging lens. If the nose and the tail are each focused on a screen in turn, which will have the greater magnification?1u 6qv1 k8uddz ----待选择----nosetail 

A cat with its tail in the air stands facing a hg73yq4,w zed converging lens. Under what circumstances (if any) would the image of the nose be virtual and the imagq4wh de7,zg 3ye of the tail be real? Where would the image of the rest of the cat be?

Why, in Example 13, smz)* ql 2 zl(ii4abj;q/k6 pimust the converging lens have a shorter focal length than the diverging lens if the latter’s fo ;i/ aj)i*qlbzlpz(4s2m6ki qcal length is to be determined by combining them?

Explain how you could hdmay(zoaxwdn e601 / npda03zhh2t29 ave a virtual object.

  An unsymmetrical lens (say, planoconvex) fore*d / n42tlrhxms an image of a nearby object. Does the image point change if the lens is tured42l xntr/* hned around? ----待选择----yesno 

The thicker a double convex lens is in the center as compared to its edgev cw 48cd1w8ies, the shorter its iw48ccv8d we1 focal length for a given lens diameter. Explain.

Consider two converging lenses separated by some distance. An object is plac g) n2rw/rbw9vu46iwzed so that the image from the fir4rbzr/uvi)9 n6ww2w gst lens lies exactly at the focal point of the second lens. Will this combination produce an image? If so, where? If not, why not?

  Suppose that you want to take a photograph of yourself as you look at your i;zhnbu r8urs 4 -idvqb1aw++2mage in a flat mirror 2.5 m away. For what distance should the camera lens b4 vwr+ ud;+b12r8 -hzaubnisq e focused?    m

When you look at yourself in a 60-cm-tall plane u lh93fll +q7jmirror, you see the same amount of your body whether you are closllj 7+u9hlf3q e to the mirror or far away. (Try it and see.) Use ray diagrams to show why this should be true.

  Two mirrors meet at a 13an e9v-4(5;;yzj c0 udxgmlf z5$^{\circ}\,$ 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 9m0esc v-fx)hthe 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 distancevs-) h9me0 cxf 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 mirror52.an+r dvxtoq)c1 +,y fs lnjl ;d9xh. What area of the mirror is used to reflect the rays entering one eye frar xsvy.on1j c+hn t l9d)dx5;f+ l,q2om 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 meet at an a ;h1zk)bkp 3+ zpzg5gvngle $\phi$. 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 ark 4l 9w4dyu.d2x/qqv concave mirror pointed at the Sun, focuses the Sun’s rays 18.0 cm in front of the mirroddl.9uk x 24qy rv4wq/r. What is the radius of the spherical surface from which the mirror was made?    cm

  How far from a concave mirror (radius 23.0 cm) musvop:oboa3 3-nsc 3rs3t an object be placed if its image is to be :3 spo oobcra3nv 33-sat infinity?    cm

  If you look at yourself in a shiny Christmas tree bs3 ,/575cokgq6 x)c4nmc ksg*hdnwmf all with a diameter of 9.0 cm when your face is 30.0 cm a5c)cgq* ksx 3mcgm, nfn5ko d w/6sh74way from it, where is your image? Is it real or virtual? Is it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shows an upright imagejfh6q q 6,mlk7 of any person who stands 1.4 m in front of it. If the image is three times thhmq,6l fjq6k7 e person’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror that, when 2.20 cm from a toot1j;oth*x 5w-tgau0(7 ncr vwhh, will produce a $\text{4.5×upright}$ image. What kind of mirror must be used and what must its radius of curvature be?
 ----待选择----convexconcave 
r =    m

  Some rearview mirrors produce images of cars behind you that are smaller than thp:ie /g0xor,t 4bh x9eey would be if the mirror were flat. Are the mirrors concave or convex? What is a mirror’s radius of curvature if cars 20.0 m away appear 0.33× their 0rpix4b9t exge/o :,hnormal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is placed 20.0 cm from a con8zu10msrv/7 s.cmip fq; ah8 jvex mirror of radius of cufz scjs7iph;08 .m va1mr 8u/qrvature 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 conve.fsu 3bb0igvi(lm7 h9cu01x i z+j0td x security mirror in a store. You estimate the height of your image t(ijx dihfb+ zu0. 1 9 70mulbgvctsi03o be half of your actual height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object be placed in front of a concave mirror so thaim2ym fx/2 c+p +xx/jvs(ew e6t it produces an image at the same location as the o+/2ex6pisx+ j(2 mwf vmcx/eybject?
(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 whel2lyyw8c:t -u7p*vc3qy f9 sxn-ap +j n viewed in a curved mirror. The image appeaj qfys3nlp7x *yuwtc lp+-:y2-c9a8 vrs 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 techniques2v-g;u tkd9 es,
(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 magnificj 3mrz27oc a+sation 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 mmfw/ krfxs 494hjh.2pac(mwck 70 m j2irror equation, Eq. 23–2, is valid for a convex mirro.j7mxjkhw0fswfh mr9(44c m c 2/p2 kar as long as f is considered negative.

  The magnification of a convex bgzv-1 k6ep(pmirror 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 frx.4 l 3sa,shieont of a spherical mirror. It is desired to preshal.3sx 4i ,oduce 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 zaic3 72 57lgdpqr(harch,y 3 magnify your face by a factor of 1.33 when your face is placed 20.0 cm in front of itr75zy i3plg qd23 ac, hrh7ac(.
(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 1 ib/q-qvef*kkyi2x +w2 7u -olhd+iw
(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 i nh4sce* 7b448.bv u7wbczxtzs $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain substance is 89% of its valuek6 nn1b l67ipg in water. What is the index of refraction of this substance? n = l61n b6ik7 png  

  A flashlight beam strikes the surface of a pane of glass (n = 1.58) at a 6b75f;ib 2tdvxn z1 -vz3$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashligh :t1cfdib5l9gt upward from beneath the water at a 42.5$^{\circ}\,$ angle to the vertical. At what angle does the light leave the water? $\theta_2$ =    $^{\circ}\,$

  A light beam coming from an underwater spotlight exits the water at *, g3 lzvjffh/an angle of 66. h3v ,lg*/fzfj0$^{\circ}\,$ 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 t13(k4jhkyqu n8/ub7m rpw0j so make a 31.0$^{\circ}\,$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?    $^{\circ}\,$

  An aquarium filled with water has flat glass sides whose inijl4 ef2 fp3drvd x+-*dex of refraction is 1.52. A beam of light from outside the aquarium strikes the glass at a 43.5° angle to the perpejxvl- 4dp3r+2ff * deindicular (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 nig co dzc cod.p4b3k d0s7.e;/mmht, a watchman shines a narrow beam of light from his flashlight, 1.3 m above the water level, onto the surface of the water at a point 2.7 m from the edge of the pool (Fig. Below). Where does the spot of light hit the bottom o7d;p czkb.d4cmosed o 3.mc0/f the pool, measured from the wall beneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equi6exm ysw1-4 ;wau-kxclateral glass prism at a 45.0$^{\circ}\,$ angle to one face, (Fig. Below). Calculate the angle at which light emerges from the opposite face. Assume that n = 1.58.    $^{\circ}\,$ from the normal

  A beam of light in air strikes a slab nq hm,o5y0agv;y 296 hb,p givof glass (n = 1.52) and is partially reflected and pv,gahhygp2 6q9y05 ;ovimnb , artially refracted. Find 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 layer u;bzy2ip i9bpt4n xs411qt8eof transparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the incident beam, independent of the tb z29qxet;48n b iu4s1pi1p yincident angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on a flat piece o-ii51xzbm (6 c;ctwjyf glass with index of refraction n as in 1 i6zm;y5 t(jxiwccb-(Fig. Below). 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 water and Luciav-hly ; /pi 4r+ou*ldte? To be totally internally reflected, the light must start in whichypr*hli o4u;lad v +-/ material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle foel, : q3dvgv8my bc:n4r 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 wkc169n h8d8d6 -tog,op gyuew ater from a depth of 62.0 cm. Where must it strike the air–water interface, relative to the spot directly above it, in order th88dy1egw,gnhoctu 6k dpo96- at the light does not exit the water?    cm

  A beam of light is emitted 8.0 cm beneatx zs/5rzay 4,vh the surface of a liquid and strikes the surface 7.0 cm from the point directly rzzs,ay5 4xv/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 in (Fig. u 5yp)bx v(i tma.u6(rs.a0psBelow) 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 the7j9)3ljqd x9uyx n mc:y* y(hb end of an optic fiber as shown in (Fig. Below). Show that we can guarantee total internal reflection at the side surface of the material (at point a), if the index of refraction is greater than about 1.42. In other words, regardless of the anglejc7qhn*j9)d :byxu( m yx yl93 the light beam reflects back into the material at point a.

  (a) What is the minim hc m9r-b xi2sg-ev7 r)z)xd-mum index of refraction for a glass or plastic prism to be used in bi72 -s zmer r-v))hmx-gdb 9ixcnoculars (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-mm-focal-length converging lz 7z(nsd.ay:kx+p 7x lsr-2u nens. Find the object d.7-s yn7 (:n u 2dzsxrlakpz+xistance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.5 cm behind a lencg5)f fgoaj8 (s.
(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 as3o )qk/e4hno z an image 48.3 cm on the other side of th oz oh/)enq43ke lens. What type of lens is it and what is its focal length? Is the image real or virtual?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the power of a 20.5-cm-focazb b a/venr;8(l-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 0xsi(l+ e2cumdy+h/ o 5k-wqbconverging lens with focal length 24 cm to view a stamp 18 cm in front of the lenhw0coqbexsd u++(m -k/l52yis.
(a) Where is the image located?    cm behind the lens (virtual)
(b) What is the magnification? m =   

  A -5.5-D lens is held 14.0c /l.gq,o*g kqji:+cf cm from an object 4.0 mm high. What are the position, type, and height i,f+l:qckojg/. g*cqof 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 fieqb0*9tw(c ,zlrxgq-0 zwb a5lm of a camera. The maximum distanbqq e-*a005,rbwwc xl 9zz( gtce 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 atip9rf d*u6j qa:4.i r book is placed 8.0 cm u fd:r.*6ti i4qj9 arpbehind 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. B61 d+quyt3ge6pjq2v er6g qv ,y how much does the image move if the object is 2+g eqdpt16jgv 63rvqe6 qy u,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 22xe5e :prrb-pxl2hc-5 cm should an object be placed to produce a real image which is the same sir-25h pl2 pc-x eebrx:ze as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an objecpuk(jj zu *o)6t be placed if its image is to be magnified 2.00× an6jp) uu(*okz jd be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm

  (a) How far from a 50.0-mmrcyhafqv). 778lt;- u vh0tln-focal-length lens must an object be placed if its image is to be magnified 2.00× and bl7tc78.u; lhr- vq nv)tfh ya0e 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-f*e-bp 5,,xyb +e0bt jtgsxd2 zocal-length lens. Where is the image, how high is it,e b2tjxdygz +b5 -xep*,bst0, 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-focal-length conver y:m /alfxh2n,zj 96qtging lens if the image is 2.5× larger than the object and itqznf:xa /mh ,6j92 lys real?    m

  A bright object and a viewing screen are separated by3. byz z5pauhsl1 d79a a distance of 66.0 cm. At what location(s) between the object and the psy.93 zald 7b 5u1zhascreen 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 placed 16.5 cm apart. An objeck)ig 6bq;sjs3t is placed 36.0 cm in front of one lens. Where will the final image formed bkg;)jssbi3q 6 y the second lens be located? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens with-8a 9gv52j s jgqte* 3hl6ilxo7 bx5xn $f=-31.5\mathrm{~cm}$ 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 cmsys -v*0yc5l d 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 *dycvsly 0 -s5the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Example 23–12 are nowbyvsz6g , ok4 jk1fd-6 placed only 20.0 cm apart. The object is still 60.0 cm in front o,v6g fzjbks o 4yk6-d1f the first 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 on 1q oo:aak la8+,q/+fvzszwj76fz )htthe 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 invertedl+azzkf v8 aq ,1htf6+) wa:sjz/ o7qo and located halfway between the two lenses. How far to the left of the 15.0-cm-focal-length lens is the original object?    cm

  A diverging lens with a focal length of is placed 12 cm to egp q8yy5u.h,the right of a converging lens with a focal length of 18 cm. An object is placed 33 cm to the left ofgyhpeq ,8.u5 y the converging lens.
(a) Where will the final image be located?    cm to the left of the converging lens
(b) Where will the image be if the diverging lens is 38 cm from the converging lens?    cm to the right of the diverging lens

  Two lenses, one converging with *ad7nv j/ge0nfocal length 20.0 cm and one diverging with focal length are placed 2dj0*v7/en ga n5.0 cm apart. An object is placed 60.0 cm in front of the converging lens. Determine
(a) the position    cm to the right of the diverging lens
(b) the magnification of the final image formed.   
(c) Sketch a ray diagram for this system.

A diverging lens is placed next to a conve (s+ a f5n9jxpx/dsm8xpe0fe(rging 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 34.2z:./i5-;nrje y7 racd q z)cdq cm and 23.8 cm. What is the focal length if n = 1.52?cay 7: dciz5 rz;rn.q )edj-q/    cm

  Both surfaces of a double convex lens have radii of 31.0 c:v 667jo92ps wek ehlhm. If the focal length is 28.9 cm, whahs 7j6hk:p9 ee v6lw2ot is the index of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm. What 1caw; q; dja1cis the radius of the concave surf;1ajq ccw;da1ace?    cm

  A Lucite planoconcave lens (see Fig. Below) has one fl.n3a. duyh/ c)nnq2ulat surface and the other has h .d2 n qncu.aynl3)u/R = -18.4 cm. What is the focal length?    cm

  A symmetric double convex lens with a focal length of 25.0 ctql8x4y h o3,mt0v zn ab)(iz9m is to be made from glass wi0h(zat9q y3oit8mzvb, nx l4)th an index of refraction of 1.52. What should be the radius of curvature for each surface?    cm

  A prescription for a corrective lens calls for +1.50D. The lensmaken.p;opuv whr,)r fas+p9g7mg l)-wv* r grinds the lens from a “blank” with n=1.56 and a preformed convex front surface of radius of curvature of 40.0 cm. What should be the radius of cur-wmrpp9v p+sa)u* gnvgh;r. l ) 7fo,wvature of the other surface?    m (convex)

  Two plane mirrors farn+5t +k v gyh,em,0gja:bqx :ce each other 2.0 m apart as in (Fig. Below). You stand 1.5 m away from one of these mirrors and look into it. You will se,q5hbjx, vm:y:r en0 g+k+gate 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 o2w2kuzj h):so5 gds-r;,ezd tfam s1)f a swimming pool filled with water. We measure the width (x=5.50m) and then n2;sd-f,hu)z)d5r amjtg k1 s2esz:owote 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 plast6.b wyq8t8 albty vf (++j-1 m to4l+hu3lcrpgic 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 consifbvcsp0cb /8n8 qvxq0u 8*+oqdered a limiting case of a spherical mirror. Specify what this nbc 0qf p cvqs*u0o8xv8/ 8+qblimit is.
(b) Determine an equation that relates the image and object distances in this limit of a plane mirror.
(c) Determine the magnification of a plane mirror in this same limit.
(d) Are your results in parts (b) and (c) consistent with the discussion of Section 23–2 on plane mirrors?

Stand up two plane mirrors so they form a7w0lsv (3ct3d4pxu,xq gc -aokxz:.l 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 r9 )c;/nvbr4fo/l sx breal image of a real object. Can you /;)n /bflxo9rsrbcv4describe a situation in which a diverging lens can form a real image?

  Each student in a physics lab is assigned to find the lxp d.zv1g :7e(fapkax9jpa:(ocation 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 theda7g1 (pe9(v::pfpx .jkxaaz 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 priodw5.zv s:j*, bid2xksm 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 cylindriu.bb5z 1v 3sxiikn5dj; sb7+acal 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 ofsn-km au+br*ccmcy )(x u/c*4 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 on fh1czh9z9; h wn5(6kh-khcnge side of a converging lens of focal length f, and a white screen for viewhh c5;c96 hkn9zhz (wnh k1f-ging 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 obje3)fi. h5dz*0m znjpaict whose image is projecteanj 3.0iz)5 hzdp*mfid on a screen (Fig. Below). If a 105-mm-focal-length lens is to project an image on a screen 8.00 m away, how far from the lens should the slide be? If the slide is 36 mm wide, how wide will the picture be on the screen? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (picture size is actually 24 byg1yxl+m9lt1b *a:; qccqv6 *kzep k3c 36 mm) is to be projected on a screen 1.80 m by 2.70 m placed 7.50k+ *c*x9vc3:k61z eylablq mtqg1c; p m from the projector. What focal-length lens should be used if the image is to cover the screen?    cm

Show analytically that the imoli i7(ng387clt .qt hage formed by a converging lens is real and inverted if the object is bent lth8go il.ic77q3( yond 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 pictu*c g3o ktpy v(w.u5gh dz6q0u5res of her at home. She claims the reporter was trespassing. To prove her point, she gives as evidence the film she seized. Hw*0quyzcgop6 tu35( 5vhd.kg er 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 filyi 1k: -ca 3rgkol1n.v8oq-(xnp;zh em 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 ceyw82x 1+hc;o(amvzziu+ r jzo9k eo7,rtain lens is imaged 8.20 cm in front of that lens (on the same side as the ov27 wheo,mz koy+9u z8ix+a;zr( o1cj bject). 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)