What would be the appearance of the Moon i345 7q7a rdfpj71uyxinqoja8f it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fleet in the harbor of Syracmc;sz+c luj 4lqx/z :*hz(t+kuse by focusing the rays ofkc cxjtq lz++hs4*/:z ; l(umz the Sun with a huge spherical mirror. Is this reasonable?

Although a plane mirror appears to reverse left and b*vo-3d ph8nz right, it doesn’t reverse up and down. zvnpo83hb *-d Explain.

If a concave mirror produces a real image,p9e 3wl: -bdny is the image necessarily inverted? Explaine :nlbd w9-3yp.

An object is placed along the principal axis of a spherical mirror. The magnificdf+fztl7dpp7 g65 d4e ation 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 the image locat4l7z 5p6pedf7ft+g dd ed?

Using the rules for the three rays discussed w h 8dbd vs0lw,fd,(7rfith reference to (Fig. Below a), draw ray 2 sr,,ddv0hw fbfl78d(for (Fig. Below b).
(a)
(b)

What is the focal length of a plane mirror? What is the malp ) 9v;f 9vqk;v2n-ytucrrfe 9 kw62)znsf8qgnification of a plane mirrkpqe2lf-f9r2tc z n;f8vsk9rw)6n; uv 9 y)qvor?

When you look at the Moon’s reflection from a ripply sea, it app-l+rldsl) vd/ ears elongated . Expv)l+ldl -rs/ dlain.

What is the angle of refraction when a lightq86 )pvxg *oic ray meets the boundary between two matercx g8p v6qoi*)ials perpendicularly?

How might you determine the speed of light inzd 917 oihv+wo a solid, rectangular, transparent obz1o+ dhv9wi 7oject?

When you look down into a swimming pool or a lake, are you likely ty1swpgu o z705o underestimate or overestimate its dept0wszgu 7 yp1o5h? Explain. How does the apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stimk ::h6 eg(exuck looks bent when part of it is under water (Fig. Be(x6u: g:emkeh low).

Your eye looks into an aquarium6ps77v hjjy ro2/t vr:8 vr0im and 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 fish. Briefly justify your answerm2o tvi6 0:s77 v j8h/rrryjvp.

How can you “see” a round drop of watuy oyeetzg94 nrln70(e / v5g 2.s8ekker on a table even though the water is transparel(9e0k4 rn k25uvyg.ntoes8/y e 7ze gnt and colorless?

When you look up at an object in air from beneath the surface in a swimming poodd)/ ai ij:2j5xw9p7 ju+ aja37iieme/lj h6pl, does the object appear to be the same size as when you see it dia/j ii5w9e :3 7+du2pa m e7dphx6ia)jlji/jj rectly in air? Explain.

How can a spherical mirror hav+w3-peekh)cs y3s:a n e a negative object distance?

Light rays from stars (including our Sun) always bend t ctr vtcmfx.); 7px8isxq9;q8oward the vertical direction ;8m8 xictcx.)rqq x9 t;7fvpsas they 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 b4 goduo6r(hf3- :jwmif a camera lens is to make a sharp image of an object very far away6j( uf -g4omb:whd3 or?

What type of mirror is shown in (Fig. Below)? Explain m3eotu:8t5tkpf3: hep ;lmb3.

A photographer moves closer to his subject and then refocusesemh498v9idmx1 qpb:d3t px e,. Does the camera lens9mx1d 849xpp: teed3q,vhmbi move farther from or closer to the film? Explain.

Can a diverging lens form a real image under any circumstd * h9n5tx+sbhances? Explain.

Use ray diagrams to show that a 92 sj q;yg6g pxp2iru 5r3o/dtreal image formed by a thin lens is always inverted, whspdig;q rgtpyuj3/26529r o xereas a virtual image is always upright if the object is real.

Light rays are said to be “reversible.” Is this consistent wityu4n 4,rzu).mertdl 9r(u ,oth the thin lens equat4nlotuu) z dmrut9, (4.e ry,rion? Explain.

Can real images be projected on a screen? Can virtual images? Can either m *j*s4d 5j9a q/hxmwbbe photographed? Discuss carej bqwhx5*m9/a4sd*jm fully.

A thin converging lens is moved closer t;4, z 9 ,0lwdr+cd,pxpskpwf so a nearby object. Does the real image formed csp0 s,p,wfl ;,rc k9d4+pwzxdhange
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of refraction n = 1.30 In nsx sv-fl 4/ *m6qn9 mfkyn6t;air, it is a converging lens. Will it still be a ckln t n4m9v /6y6s fn*sfmq;-xonverging lens if placed in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands facing a convergi /xwklx*or7 5dng lens. If the nose and the taild*x wr/l ok57x 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 converging lens. Under what ciu4*. 4ajwreb kbzs5s1x/.xzx rcumstances (if any) would the image of the s*j.zz ax 5r e/4s14kbxbxw.unose be virtual and the image of the tail be real? Where would the image of the rest of the cat be?

Why, in Example 13, must the converging lens have a shcxilnf2q. k4*6i: uzuorter focal length than the divergin4lxiz2fuc:u6in . *k qg lens if the latter’s focal length is to be determined by combining them?

Explain how you could have a virtual ob6e9h +kdp0u vhject.

  An unsymmetrical lens (say, planoconvex) forms an image of a nearby object. Do3m0l .fb j/looes the image point chan.fob3om/ ll 0jge if the lens is turned around? ----待选择----yesno 

The thicker a double convex lens is in the center as comi 7+g txhrr *,xz+q+snpared to its edges, the shorter its focal length for a given l n+rizx 7x s,rh++gqt*ens diameter. Explain.

Consider two converging lenses separated by some distance. An object is pl1yf.(;b homkcve7y:b8 uwt v ,aced so that the image f8 m,(ek:y1b.vbc t hyu;fv7 owrom the first lens lies exactly at the focal point of the second lens. Will this combination produce an image? If so, where? If not, why not?

  Suppose that you want to tarou9*kfk,:c rk;k y9qke a photograph of yourself as you look at your image in a flat mirror 2.5 m away. For what distance should the camera c,fk k9oq9;ru:rk yk* lens be focused?    m

When you look at youzc50b bkx*tr( rself in a 60-cm-tall plane mirror, you see the same amount of your body whether you are close to the mirror or far away. (Try it and see.) Use ray diagramxz*0bckb 5tr (s to show why this should be true.

  Two mirrors meet at a 13:f,s 4vni o+ c:ihspw,5$^{\circ}\,$ angle, (Fig. Below). If light rays strike one mirror at 40$^{\circ}\,$ as shown, at what angle $\phi$ do they leave the second mirror?    $^{\circ}\,$

  A person whose eyes are 1.68 m above the floor stands 2.20 m in front of a verpe)-d 1 qld6vvtical 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 reflected in th-evd) 1vpdl6 qe mirror?    cm

  Suppose you are 90 cm from a plane mirror. What ++f.7r*.lxdlkpl uwdzr2y 5farea of the mirror is used to reflect the rays entering one eye frf25 7lrr.+d.l xup z y*wkld+fom 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 mirroryt2/7g;mn* i yr)l ipys meet at an angle $\phi$. a single ray reflected successively from both mirrors is deflected through an angle of $2\phi$ independent of the incident angle. Assume $\phi<90^{\circ}$ and that only two reflections, one from each mirror, take place.

  A solar cooker, really a concaf ;fw2 u5w7l .douqdj9rcle,crj 9 1q-ve mirror pointed at the Sun, focuses the Sun’s rays 18.0 cm in front of the mirror. What is the radius of the spherica fdjcod r-wqw92 u;uel 5r1.fq, 9jcl7l surface from which the mirror was made?    cm

  How far from a concave t **it p3vie5o u43xaomirror (radius 23.0 cm) must an object be placed if its image is to be at iux 4 *5ivai3t3*ooptenfinity?    cm

  If you look at yourself in a shiny Chriso o pbs99p*( my (s:4lm.wazzutmas tree ball with a diameter of 9.0 cm when your face is 30.0 cm away from it, where is your image? Is .9 (wz9u *aomspz(4sp:yoblm it real or virtual? Is it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shoucv ,hr.i.bji 9z*0b ows an upright image of any person who stands 1.4 m in front of it. If the imag. r9* zjo0vbi ,.uchibe is three times the person’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror that, when 2.20 h:7 wv3afidkn0ads 2ok b 6 z3+fro./pcm from a tooth, will produce a $\text{4.5×upright}$ image. What kind of mirror must be used and what must its radius of curvature be?
 ----待选择----convexconcave 
r =    m

  Some rearview mirrors produce images of cars behind you that are smaller than th: f2rz5 q1fgcaey would be if the mirror were flat. Are the mirrors concave or convex? What is a mirror’s radius of curvature if carqag:1cf f5r z2s 20.0 m away appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is ppvi.aru ) : zm)g4/vfglaced 20.0 cm from a convex mirror of radius of curvature m)vfgugri/):ap v 4. z20.0 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 estimate t 5ivd4w:n8 2qdc,ouuau n:+zthe height tv 2q8 i,do5uc wa+unnd:zu4 :of your image to be half of your actual height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object be placed in t3l dw kb:i23qms0 4xkfront of a concave mirror so that it produces an image at the same locaxm 3 :bt40d3isklqkw2 tion 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 v4 -yxn5v5uc)a qsuo2k ery small when viewed in a curved mirror. The image appears to be 18.0 cm behind the mirror. What kind of mirror is it, and what is its radius of curvature2a4 u)-c5nuqvys x5ko?
 ----待选择----convexconcave 
r =    cm

Use two different techniques, 9f2f-+d/3say .shdupninh - zciij4 1
(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 m of a convex mir9+u)mx*gviki 2z 6tft0 amy y/t7l0u xror 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. 23–2, is valid for a covum03/fys-sy 1 xmgd) nvex mirrfym v)gs-d3 x/us0y m1or as long as f is considered negative.

  The magnification of a convex mirror ispaey2n ,(5hdj v5xzef5 (guf8 $+0.65\times$ 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 mirror. It is d4gq ayd9m (zj+esired to produce a virtual image that is upright and 3.5 cm tall. d +ag94q(j yzm
(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 yo j f,ffyb*fm(0ur face by a factor of 1.33 when yo(ffmj ybf 0*f,ur 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 inex ;p v85ku9va
(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 m* wqj-pbwrj:*rkl5+is $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a cer y2ir09gt :nhutain substance is 89% of its value in water. What is the index of refraction0hntri :g9y2u of this substance? n =   

  A flashlight beam strikes the surface of a pane of glass9:m8z6qgjoveu5 -8p sue3-o moo ,bq g (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 from beneath the water4x3y),u)iv ml8 dwkhug(p .3y-net mq 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 e3-9xfgft:u ra *:dkqs xits the water at an angle of 66*q:kfras gtd-xu f:39.0$^{\circ}\,$ 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 mz))wk v+qtcgh(2l ) grake 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 txe,fkem+ -vp,m: bfhl.2)fknq i +) csides whose index of refraction is 1.52. A beam of light from outside the aquarium strikes the glass at a 43.5° angle to the perpendicular (Fig. l f.,hi kmexpe +)n)-ftc2,fqb:k+vmBelow). What is the angle of this light ray when it enters
(a) the glass, $\theta_2$ =    $^{\circ}\,$
(b) the water? $\theta_3$ =    $^{\circ}\,$
(c) What would be the refracted angle if the ray entered the water directly? $\theta_3'$ =    $^{\circ}\,$

  In searching the bottom of a pool at night, a watchman shines af ):e-dmak;fd d 04jhkdg m/h0 narrow beam of light from his flashl-fa dg:e4jh dh /0 ;0dkf)kmdmight, 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 of the pool, measured from the wall beneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an 64n2d yn m,d1/wnzhf0ak l: zhequilateral 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 of glass (n = 1 ovqgo6 2lkl li14-1sy.52) and is partially reflected and partially refracted. o2yg4lqilkv o6ls 1-1 Find the angle of incidence if the angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for ;t*bt trd641taza 0 eha light beam incident on a uniform layer of transparent material, as in (Fig. Below), the direction of the emerging beam is parallelrt 1 a ze*dt4;6abtht0 to the incident beam, independent of the incident angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on a flafwco dbic tk8c98+;qdva;07tf bpl;4t piece of glass with index of refraction n as in (Figq4 clabd+ 9bt87ckt ;dwofpc;i08f;v. 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 bq d.zru(f,(b hetween water and Lucite? To be totally internally reflected, the light must strdz uh ,f((.bqart in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certqow:l l0y5d0k zh32lh; zu 2bnain liquid–air surface is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in a pool of water from a depth of 62.0 cmu:qhmo 4 (m4 :cb4wmuc. Where must it strike the air–watmh u4qm: uw mcb(4o4:cer interface, relative to the spot directly above it, in order that the light does not exit the water?    cm

  A beam of light is emitted 8.0 cm beneath the su;0pjv ip y,3evu3be8g rface of a liquid and strikes the surface 7.0 cm from the point directly above the source. If total internal reflection occurs, what can you say about the index of refractiog ,ej;vb3i 0v 8upyep3n of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left far9aov)d 76faz)qz/rjce 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 opticlvizb:bd :t y4,1f1-d*xe xso fiber as shown in (Fig. Below). Show thazt-b14 vedyx1b*siod :,xlf:t 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 at point a.

  (a) What is the minimum index of refraction for a glass sb1jz tr6z,: ( slkvx9or plastic prism to be used in binoculars (Fig. Below) so that total internal ref,vsjzl :sb9k z6(1r txlection 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 npn2 th m *v;3wm;jed-mm behind a 65.0-mm-focal-length converging lens. Find the object dinhdv pmen;;2m-t*w 3jstance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.5 cm behindf*9ydv+ r6or du aj0-8bgg,yq 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 frov/m-cw2c y d3ym an object 2.75 m away as an image 48.3 cm on the other side of the lens. What type of lens is it anm-cydv cwy/23 d 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 ofk 1 oppbfi6 8ng.h:dm2 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 focal lengt+zv: fee5u, oeh 24 cm to view a stamp 1e5 ezefvou,+: 8 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 mmz )iakkj x39g( high. What are the position, type, and height of thek gjixzk 3)(9a image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is2:opc1i n ej)lh4f wq7n a;n9egc48 nd used to focus an image on the film of a camera. The maximum distance allowed betweenonc ea44 l hefpi;qj9nn1gwcd2n8 ): 7 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 2l04rw cl doa9af8e15ok,htw* .5× when a book is placed 8.0 cm behind a dwc,8kw a *o1a9oflhrl04t e5lens.
(a) Draw a ray diagram and describe the type of image this would be.  ----待选择----realvirtual 
(b) What type of lens is needed?  ----待选择----converging lensdiverging lens 
(c) What is the power of the lens in diopters? P =    D

  An object is located 1.5 m from an 8.0-D lens. By how much does the image move fzfa bas9+m: 4if the oaf ma:fs 4zb+9bject is moved
(a) 1.0 m closer to the lens,    cm away from the lens
(b) 1.0 m farther from the lens?    cm cm toward the lens

  How far from a converging lens with a focal length t)s*q8nw* es0 3pk dpnof 25 cm should an object be placed to produce a real image which is the same size as t ep8 03*np*w)kqssntd he object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an object be plafi0c.(+4fjdmcx cbk4ced if its image is to be magn mjfc+4dkx.bi c(4f0cified 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 a m;mn qsy3wv)ka(co0 .z/qt2 un object be placed if its image i(osn k2c u;.qw azmytvm)3/0qs to be magnified 2.00× and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm (formed by some other piece of optics).]

  (a) A 2.00-cm-high insect isr(yf+wdop7,pqi1 oxjp *2 1mk 1.20 m from a 135-mm-focal-length lens. Where is the image, how high7pk1ox qdprj 1 ow*2+ip( ,yfm 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-focal-l263/ .aa plrhgxfo, 8xi ai:kvength converging lens if the image is 2.5× larger thani2a3x hg ,i/:l k x6rf8va.opa the object and is real?    m

  A bright object and a viewing screen are separated by a distance of 66.0 cm. At *1u m udvh2/8)tttd tqwhat 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: t)u*hvutd/ dtt qm281first 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 o,fn2xuv*v 8m is:u5bhv+lb6h bject is placed 36.0 c528uh blf:b+ vnsv m*,h6viuxm in front of one lens. Where will the final image formed by the second lens be located? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens withqz5 (nl nsbpmk8 00k3+*uryaa $f=-31.5\mathrm{~cm}$ 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 convergin;3qy-vd -v old0 -yqclg lens is 21.0 cm behind a diverging lens. Parallel light strikes the diverging lens. After passing through the converging lens, the light isyc0;-dqd- -l lqy vvo3 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. 48r/abdfmr -u The object is still 60.0 cm in fm 4rb/ a-ufdr8ront of 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 o75gia 124c qkt urpzx+f the lens on 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 li+uq xrp5gt472 kz1 caeft of the 15.0-cm-focal-length lens. A final image from both lenses is inverted and located halfway between the two lenses. How far to the left of the 15.0-cm-focal-length lens is the original object?    cm

  A diverging lens with a focal length + drg/6b9 r: beiwe.b3 pt;bgcof 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 op;dbe 9b.w/b+e 3:tricg6g brf the converging lens.
(a) Where will the final image be located?    cm to the left of the converging lens
(b) Where will the image be if the diverging lens is 38 cm from the converging lens?    cm to the right of the diverging lens

  Two lenses, one converging with focal length 20.0 cm and one divergs/li1r,rjeh ks- ;vg /ing with focal length a/sr1hrvekli/ -j ,;sg re placed 25.0 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 converging lens 8zgpik+u y 3/br:1og8bj8 fl.jo)duf 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 23.8 cm.lr ui((x*78 ukes 6opy What is the focal length if n = 7u8or*iu ekls(x6(p y 1.52?    cm

  Both surfaces of a double covl 1 fkyw7xvgk3khiu ,8(st 86nvex lens have radii of 31.0 cm. If the focal length is 28.9 cm, what is the index of refraction of the lens 1i8,v6kk lv y f8g7h(3stxkwu material?    cm

  A planoconcave lens (n=1.50) has a f8uj).,xeu x:n q-extg/s q3ei ocal length of -23.4cm. What is the radius of the cjst x,.-e e8 qu)i3xuq /negx:oncave surface?    cm

  A Lucite planoconcave lens (see Fig. Below) hadxx l;6hs/0, l0dhq;d-hhndq s one flat surface and the other has R = -18.4 cm. What is the focal lengd/hnhhdll d s;, qq; -xd600hxth?    cm

  A symmetric double convex lens with a focal length of 25.0 d( -zk+v1nmpif;yt 6 ncm is to be made from glass with antdzi+6; pn-f (m1ykvn 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 3rgo0q*z + jhrlensmaker 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*3h0rq z+ogjr the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fig. Below). You lw4 uf-am xg4ux)zz -+zd-sa9q7xw i :stand 1.5 m away from one of these mirrors and look into it. You will see multip wgaxl4s9ua 4wumi+zx7 q-:)z-zf-xdle 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 ktlov;z-e 8i hy :,)thdepth of a swimming pool filled with water. We measure the width (x=5.50m) and then note that the bottom edge of the pool voh);k ,tilyhz-t e :8is just visible at an angle of 14.0$^{\circ}\,$ above the horizontal as shown in (Fig. Below). Calculate the depth of the pool.    m

  The critical angle of a certain piece of plastic in air kxn.i o13-nova3z6 ,tlmncs( nyem()is $\theta_{\mathrm{C}}=37.3^\circ.$ What is the critical angle of the same plastic if it is immersed in water?    $^{\circ}\,$

(a) A plane mirror can be considered a limiting case of a spheo(8d;.obj2aga mu 5ml rical mirror. Specify what t5 au;2d jgomo.b(lm8ahis limit is.
(b) Determine an equation that relates the image and object distances in this limit of a plane mirror.
(c) Determine the magnification of a plane mirror in this same limit.
(d) Are your results in parts (b) and (c) consistent with the discussion of Section 23–2 on plane mirrors?

Stand up two plane mirrors so tq da4g*9ht hwiy.r/g 4hey 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 nevery;;u hk /wc r(*iqoei8 form a real image of a real object. Can you describe a situation in which a di/ ;y; w(oikru qci8e*hverging lens can form a real image?

  Each student in a physics lab is assigned to find the locnjoxxmp+d 1(r+ls.g),b ml q9ation where a bright object may be placed in order that a concave mirror with radius of curvature r = 40 cm will produce an image three times the size of the object. Two students complete the assignment at different times using identical equipment, but when they compare notes later, they discover that their answers for the object distance are not the same. Explain why they do not necessa r() xmmo jd. bnlq,gs1+px9+lrily need to repeat the lab, and justify your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of a prism .h4ptna6 re,- 8j( iyltlyv ffsi+e(/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 cylindri hhkzdb*- y9hj; pu9)bcal 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 conb :n9q-j u1jg-v s6krbverging 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 lengt ma((2ompbwy) 2ha gie 2n)n;oh f, and a white screen for viewing the image is on the opposite side. The distanco2ah)(no wb)iyp ;2 m e2mg(ane $d_T=d_i+d_o$ 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 image)6qm gd3m xz8h is projected on a screen (Fig. Below). If a 105-mhgxzmq6)38m dm-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 by 36 mm) is to be projected c 5eb,yhlj7w yne-r:, on a screen 1.80 m by 2.70 m placed 7.50 m from therlewb, yhn,c 7-j:y e5 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 converging lensv(4wmzvbu lng + 1gsc+apt l3c( 1 +zr*tnvz/5 is real and inverted if the object is beyond the focc+ v(utl5rnp*vz/cg zt 1vz a1nmsw+4 g+l3b(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 rfbj7h / w3bfjyaq7r89eporter shooting pictures of her at home. She claims the reporter was trespassing. To prove her point, she gives as ev jb rbaf/wyjh78q93 f7idence 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 camera withqev. wec0 h3/ih3mxt0
(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(e sgf1mjd:86wpt/v m 8.20 cm in front of that lens (on the same side as the object). What type of lens is this, and what is its1d (gte8pvmf6 m/sw j: 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 from a certain )1 51kh lgwnab 2,yhqfconverging lens, it forms a realnhykq2g a5wh)1, fb1l image. When the object is moved to 40.0 cm from the lens, the image moves 10.0 cm farther from the lens. Find the focal length of this lens.    cm