What would be the appearv14u o25hk/prz kk9zwance of the Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fleet in the harbor dk,uqr+wf nf8tj; p,* of Syracuse by focusingqkftnwr,8+ j,p*;ufd the rays of the Sun with a huge spherical mirror. Is this reasonable?

Although a plane mirror appears to +sn zeu 0b8mtild6e,8d1(+ gvc2 ldi-oqv4jlreverse left and right, it doesn’t reverse up and dowimu8,i10v 2eq8bgjco d ddvt l4sellz6 +(+n-n. Explain.

If a concave mirror produces a real image, is the imagk 03on))ykkqpe necessarily inverted? Exp kq)yp no0kk3)lain.

An object is placed along the principal axis of a sphe8l +kf -+zob,nx;cd afo8rbb8rical 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 the image lob z-8or, c dfx ++8bbklafo;n8cated?

Using the rules for the three rays discussed with referen8.gzk1o 7ggo9jk j7 chce to (Fig. Below a), draw ray 2 for (g 1kgogjkzo7 hj9.c87Fig. Below b).
(a)
(b)

What is the focal length of a plane mirror? What is the magni,h g nn8)d/dzix 5(msvjyr/d*fication of a plane d h/v(ngy/di,z nm8jsd5r*)x mirror?

When you look at the Moon’s reflection from a ripply sea, it a.;am2ki lb po8ppears elongated . Expla;8ba okmp2 l.iin.

What is the angle of refraction 12+*meydokl)wucic(+w -j mdwhen a light ray meets the boundary between two matered c*jwul )m-2o+w i1 cym(d+kials perpendicularly?

How might you determine the speed of light in a solid, rectangular, transparen*h:p.zksja ;e 9n; szrt objs;;n*zrz jk a h.:p9seect?

When you look down into a swimming pool or a lake, are you likely to underestiv1g j4w(x:0n i qwe6gfmate or overestimate its depth? Explain. How does the apparent depth vary with the viewing a614j(we wf0:gig xnqv ngle? (Use ray diagrams.)

Draw a ray diagram to shotv:lrd8i9 n,zi.s9hu w why a stick looks bent when part of it is under water (Fig 9nzil8 uhvds:i, .tr9. Below).

Your eye looks into an aquarium and views a fish inside. ohyl46: sfbj-a qozyge14 i1 7One 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, indg: 14b6 7ohly o4z1faijsyq -eicate the approximate position of the actual fish. Briefly justify your answer.

How can you “see” a round drop of water on a taby 5dd)s (v6dtyle even though the water is transparent and colorl6vt5s)dy( d dyess?

When you look up at an objefb ;9qwpu+*s, hp1d ys:z.tu dct in air from beneath the surface in a swimming pool, does the object appear to be the same size as whedd;b,.u+qy w up9sz*s 1f :hptn you see it directly in air? Explain.

How can a spherical mirror have a nek1o9ii.op0a9na ipoz,p8 i; egative object distance?

Light rays from stars (including our Sun) adjvfbinp9 . 2uw.3w. jc6 f8iulways bend toward the vertical direction as they pass through theuci.wv. 6jnb3j 8pfw 2dif.u9 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 is to make a6ft fe yll6a+ez*9v 2nv9mv+f sharp image of an obj6yzf*tfl nfvl9e9a v 6 e2++mvect very far away?

What type of mirror ia6 66gl2yuz+p lz*hz*hx d-u ts shown in (Fig. Below)? Explain.

A photographer moves closer to his subject and then refocuses. Don(x61n t2- lp lcwf*twes the camera lens move farther from or closer to lfl(ww2x6 -c p1 tt*nnthe film? Explain.

Can a diverging lens form a real image under any j b (ym-6hg:ukcircumstances? Explain.

Use ray diagrams to show that a real image formed by a thin lens 9 r2eost0r 7vsis always inverted, whereas av ts7rr9o0s 2e virtual image is always upright if the object is real.

Light rays are said to be “reversible.” kysp 0t/ oul51i jj4 :0slwqw-Is this consistent with the thin lens equation? Ex qj0l41l5j t wk0:wpi /sy-uosplain.

Can real images be projected on a screen? Can virtual images? Can eitjc*jhlt (k ;k9her be photograp cj9(;lht*kkj hed? Discuss carefully.

A thin converging lens is moved closer to a nearby object. Does t,yk cv)mwn38fhe real image formm8yfn3c )w,kved change
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of reu1 vqwn16nef qf-kr, 2fraction n = 1.30 In air, it is a converging lens. Will it still be qre1 -nwu6vfq nf21k, a converging 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 converging lens. If the n ss 6s ,qyp43u; l;b1(f ahkex1iz+aetose and the tail are each focused on a screen in turn, which will have aa1 i+4xfhbuqkse6l e1 st3;;zs(py, the greater magnification? ----待选择----nosetail 

A cat with its tail in the ai)1c9h4w fc42bobrsf;jh a5tw5m.b p qr stands facing a converging lens. Under what circumstances (if any) would the image of the nose be virtuaqc)cw wo .;r5 hh2bf 41bj4mbsfa5pt9l 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 shorter focal length than tnk:d-lm2f(j2u7kc2tt z w sn :he diverging lens if the latter’s focal length is to be detenk sfnu(227wtc z:2d klm-:tjrmined by combining them?

Explain how you could have a v5c w3wrw7jc/epz+( yn irtual object.

  An unsymmetrical lens (say, planoconvexzowd-s (2g;tk9v-*a1iznh cs ) forms an image of a nearby object. Does the image n oshswi* z k--z9tg( a2v1c;dpoint change if the lens is turned around? ----待选择----yesno 

The thicker a double convebhby6)z1zh x9 fo 5+qhx lens is in the center as compared to its edges, the shorteh b9yxzf ) b+q5o61zhhr its focal length for a given lens diameter. Explain.

Consider two converging lenses separated b1m(,h vaw k*p;yj* klzrr/jl* y some distance. An object is placed so that the image from the first lens lies exactly at the focal point of the second lens. Will this combination produce an *j *v,lh jrl;(awk/1rp kmz*y image? If so, where? If not, why not?

  Suppose that you want to take a photograph ofz 3,n.lvs ;ubi0g, ytb yourself as you look at your image in a flat mirglsny bz30 ,i.;utbv,ror 2.5 m away. For what distance should the camera lens be focused?    m

When you look at yourself in a 60-cm-tall planp, nxog 6 n,f,ach4:7joj9mofe 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 diagrams to show why po,jg,,f67nfj4o :nxcmh9 a othis should be true.

  Two mirrors meet at a8b o4x9cyns,u 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 2.20 m in froec 9 er3,:trqiszijuyt0 )7/ tnt of a vertical plane mirror whose bottom edge is 43 cm above the floor, (Fig. Below) tt9j/i07y)er sq:i3,zturce . 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 d 7xlax1-xqv1s e+l( fis used to reflect the rays entering one eye from a point on the tip of your nose if your pupixev( - xl7dql1+1saf xl diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane 0 ;ze t96-g+qz5 emzxh: soegmmirrors 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 concave mirror pointed at the Sun, focuses the Sun’sqepr*zq-ec*w,l 7 f5v3 )bioo rays 18.0 cm in front of the mirror. What is the radius of the spherical surface fro 53*z bpr io *eqewlqc,ofv-)7m which the mirror was made?    cm

  How far from a concave mirr/e1wmz/ y +r/f umkj*tor (radius 23.0 cm) must an object be placed if its image is to be at infinit+//jmkuw1rzm y*e t f/y?    cm

  If you look at yourself in a shiny oojg76baec zm(y:d6 (Christmas tree ball with a diameter of 9.0 cm when your face is 30.0 cm away from it, wheraymo6 c (o:gd(b6e7 zje 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 2v6jtq hs+a0sm55t7+iskf m kimage of any person who stands 1.4 m in front of it.6t qks0m itv7jsfm5kh2a+ 5+s If the image 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 from a tooth, will pr.ccgv/ vj7j 6fxmn,l; y1cr9 5 xjil5ioduce 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 yo)y.rxyusyn9-poxq** z : p+yfu that are smaller than they would be if the mirror were flat. Arr y yu:yxsz- nx9p)py+*f*.q oe the mirrors concave or convex? What is a mirror’s radius of curvature if cars 20.0 m away appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is x i+r7r.3dj ttplaced 20.0 cm from a convex mirror of radius of curvature 20.0jx7 t3i+ tdr.r 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 + -qq(fx*wa tostore. You estimate the height of your image to be half of your x+qw (taq-* ofactual height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object be placed in front of a concave mirroqa0w9)jqipg g )8u2l(msm hi1 r so that it produces an image at the same location2 a1msp l0 igw)h8(9)m uqjiqg 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 viewed in rjfrleuaa6e) d 8/h gb8u,w.k-+/tmqvia6 b0a curved mirror. The image appears to be 18.0 cm behind the mirror. What kind of a muk8.v/i6q)lgt +ab eeh0r,6-d/j fau rwb 8mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniques,,wq76azf, e4f gfhlt. wih 9g0
(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 cots6tt4pwam,(9/ 2xm t yf b/ +.cik85rgfoefe nvex mirror is $m=-d_\mathrm{i}/d_\mathrm{o},$ just as for a concave mirror. [Hint: consider a ray from the top of the object that reflects at the center of the mirror.]

Use ray diagrams to show that the mirror equation, Eq. 23–2, is valid for a pm/ch.xb(yno5)5y en2 zmg 4econvex mirror as long as f is considereb g(xenmzh 5yme y .o)2p4/cn5d negative.

  The magnification of a;jz dx: 5ex7uc convex mirror 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 pla 78qca9 cmiaq r-1w9llced 28 cm in front of a spherical mirror. It is desired to produce a virtual image thalqrqwcm8i-1 9a7l9 cat 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 xkk wov57:f)c magnify your face by a factor of 1.33 whenf) w7kvo :5xck your 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 in;s y7f; h)a;-obabine
(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 isn u eel3ftm+,6 $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a ,jg 52isfxzm/z+z c, ccertain substance is 89% of its value in water. What is the index of refraction of this substan5m+ s,cf zz,jc 2i/zgxce? n =   

  A flashlight beam strikes the z- ox ua71jceii d1t:4surface of a pane of glass (n = 1.58) at a 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashlight upward from beneath the waterz,6w sgd4um wd8i.2pe 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 uipjm7xb*wi*/ -z,lu g nderwater spotlight exits the water at an angle of 66i -,i lxjgzw m*b/pu7*.0$^{\circ}\,$ to the vertical. At what angle of incidence does it hit the air–water interface from below the surface? $\theta_1$ =    $^{\circ}\,$

  Rays of the Sun are seen to make y:5)em a b;x qa;g5jlua 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 who6e:( cipmqqnkwgh/ 5 4se index of refraction is 1.52. A beam of light from outside the aquarium strikes the glass at a 43.5° angle to the perpend i(k:e wn/qq4 p6ch5mgicular (Fig. Below). What is the angle of this light ray when it enters
(a) the glass, $\theta_2$ =    $^{\circ}\,$
(b) the water? $\theta_3$ =    $^{\circ}\,$
(c) What would be the refracted angle if the ray entered the water directly? $\theta_3'$ =    $^{\circ}\,$

  In searching the bottom of a pool at night, a wlqol,,3x.u k catchman 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 bl .c,x,u3lk qoottom 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 prm5x fl mb5*h.gu.rluds2)i: n ism 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 = z:+xx9ncw(l6n c9e u4yqrv h8 s/sc 0f1.52) and is partially reflected and partially refracted. Find the angle of incidence y8c/w nqv(+: n9rx6zsh 4es0x9cflucif the angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam incident on a uniform layer of /dj ofox8v:*o transparent material, as in (Fig. Below), the direction of the emerging beam is paralle *o oo/:vxdfj8l to the incident beam, independent of the incident angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on a flat piece of glayg:c ) a7;cjrwy;ne)fss with index of refraction n as in (Fig. Below). Sf;en ;cy) :crg w)ayj7how 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 Lm(vdz38iivs 3ro 6u, s*a vqzbngv25v.f z4n2ucite? To be totally internally reflected, the light musun *z 2r2qgn 8bvvo5(,vv z343fvd6iz ismas.t start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certaine00e 22 az hi)kill-xs 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) bq/:gi t87( qxoafdt of water from a depth of 62.0 cm. Where must it strike the air–water interface, relative to the spot dirqxt):(o f/7qbgd ia 8tectly above it, in order that the light does not exit the water?    cm

  A beam of light is emitted 8.0 cm beneath the surface of a liquid and strikes jjl ;+r4z x)tu 5;zcoothe surface 7.0 cm from the point directly above the source. If total internr) ;zlczj x5u; t4jo+oal 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. Below) gl .m/o jl4zsr25wzo7at 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 fx :hgjs.:hn;ie7 ujvb;y uo(5 iber 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 w.:u g;hus(eo;yjn7jvb xh:5iords, 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 or plafp/3xtj4 h5n lstic prism to be used in binoculars (Fig. Below) so that total internal reflection occurs at hl4x5/jpf 3nt45$^{\circ}\,$? $n_1$ $\geq$   
(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 behflfn:wv/k 27yuyl8 4rind a 65.0-mm-focal-length converging lens. Find the o :l2vl yf8w yn4u/r7fkbject distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.5 cm behind a leg,io3s9t bt/tnf1i v* ns.
(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 fromv mjam. q6i(e , n0ybo1h)9/qsjf:lmm an object 2.75 m away as an image 48.3 cm on the other side of the lens. What type of lens is it and what is its focal length? Is the ima1v q:6b,lno mjem m(ya )i q.h/sj09fmge 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-fo9r.gl)i2 3g66qgj s;vqrdipf w/9 d gtcal-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 convergicsgj..t u+ /dcg/o q6kng lens with focal length 24 cm to view a stamp 18 cm in front ofd+qc./gt6 k/gujo s.c 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.t:-vuj6l eb8t5knru j zf3q5 60 mm high. What are the position, type, and k5-v:bj 5l6 unqze rt8f3ju6theight of the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to focus an image on the film of a c4,5mxr x9yx r(uqu1q camera. The maximum distance allowed between the lens and the film plane is4r( rqcux91,xmqxu5y 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 magnifx7dp 6lfj h()cy reading material by a factor of 2.5× when a book is placed 8.fx)hj 67d lpc(0 cm behind a lens.
(a) Draw a ray diagram and describe the type of image this would be.  ----待选择----realvirtual 
(b) What type of lens is needed?  ----待选择----converging lensdiverging lens 
(c) What is the power of the lens in diopters? P =    D

  An object is located 1.5 m from an 8.0-D lens. By how much does the image 94:5mncc3rxlndxd r 3move if the objecdcrcxm:9 n r45lx 3d3nt is moved
(a) 1.0 m closer to the lens,    cm away from the lens
(b) 1.0 m farther from the lens?    cm cm toward the lens

  How far from a converging lens with a focal length of 25 cm ss8bf h0- )ok dnna:+dyxyh+w+hould an object be placed to produce a real image which is the samef)ydhyb h xd+kan 8+s-wn+:o0 size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an objeec ,-hapwx,6 ,oue reo.g6 tv(ct be placed if its image is to be magni-e g x6hwve.up,,(tae o,o6rcfied 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 ok g ka4f4f(bb:g8 ofur/n4s, placed if its image is to be magnified o 8,o /kaff: ks gru4(g44nfbb2.00× 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 is 1.20 mq *dzju,k /qfy20 kqo( from a 135-mm-focal-length lens. Where is the image, howk,j0o qdfuyq*/(k 2zq high is it, and what type is it?
$d_i$ =    mm (real,behind the lens) $h_1$ =    cm (inverted)
(b) What if $f=-135\mathrm{~mm}$?
$d_i$ =    mm (virtual,in front of the lens)
$h_1$ =    cm (upright)

  How far apart are an object and an image form26v ot)luvhv +*vjb;dyey 88led by a 75-cm-focal-length converging lens if the image is 2.5× la* vle+26 oujvyd );lhv88ty vbrger than the object and is real?    m

  A bright object and a viewuno nc7i sz7/4ing screen are separated by a distance of 66.0 cm. At what location(s) between the object annc7 7/ inuszo4d 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.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length converging lendz2c7 p4i+;67ldvqc ac)v(to 1pjvel ses 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 lens be located? What is the total m277d4cv ip);qea j1+t co vllv6zd(pcagnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens wit m,ts/ dy)ls9zh $f=-31.5\mathrm{~cm}$ 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 leddy( bta *:kz3zx5;kpns is 21.0 cm behind a diverging lens. Parallel light strikes the d(tza ; k3 z:*bd5kpydxiverging lens. After passing through the converging lens, the light is again parallel. What is the focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Example 23–12 are now placed only 20.*osi, b2)de pl0 cm apart. The object i 2e,b)*osipl ds still 60.0 cm in front 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.c ;0*k60lrqgozlunh k xaf/53 The focal length of 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 left of the 15.0-cm-focal-length lens. A final image from both lenses is inverted and located halfway betk0log*rf k;c5h 3n 6z/0ulxqaween 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 foc7t pbbw./: zkmal length of is placed 12 cm to the right of a converging lens with a focal length of 18 cm. An object is placed 33 cm to the l:.p bt bmk7/zweft of the converging lens.
(a) Where will the final image be located?    cm to the left of the converging lens
(b) Where will the image be if the diverging lens is 38 cm from the converging lens?    cm to the right of the diverging lens

  Two lenses, one converging with focal length 20.0 cm and one di8i 7gekqjt/ j if,4z,ipw,v* iverging with focal length are,t,zi8ek,fv*iw jig 4i j7q/p 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 of fox -y is:zo:if: tibq32cal 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. Wop; 7t w;ps9lchat is the focal length if n = 1.52? o;cp wp9t ;ls7    cm

  Both surfaces of a double convex lens have radii of 31.0 cm.7gtzc fmc1 *5wcvi9 :d If the focal length is 28.9 cm, what is the index of refraction of the len5c:f g7i zw1ctv9m *dcs material?    cm

  A planoconcave lens (n=1.50) has a ynxa3 4t .gaf ge(d.:wimt:2g focal length of -23.4cm. What is the radius of the concave surface?4a2t :nd a3x tgg(:.fyw.igme    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat surface and the otheupvw*h 5u(8ueifh*z )r has R = -18.4 cm. What is the foc z*8ipuu*)uhv(fw5he al length?    cm

  A symmetric double convex lens with a 6odezl, u;x3y focal length of 25.0 cm is to be made from glass with an index of refraction of 1.52. What should be the radius of curvature for each su6 3dey;, oulxzrface?    cm

  A prescription for a corrective len .sl/ql8u9qa/ khyt7ks calls for +1.50D. The lensmaker grinds the lens from a “blank” with n=1.56 and a preformed convex front surface of radius of curvature of kl q.tql// uyh7as 8k940.0 cm. What should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each othevfzucwk;n.32 99 v *3dca*+xin zxeh fr 2.0 m apart as in (Fig. Below). You stand 1.5 m away from one of these mirrors and loda v+i nxz.cc* xzk*n fwh3u29f;ev39ok into it. You will see multiple images of yourself.
(a) How far away from you are the first three images in the mirror in front of you?
$d_1$ =    m
$d_2$ =    m
$d_3$ =    m
(b) Are these first three images facing toward you or away from you?
the first image is facing  ----待选择----toward youaway from you ;
the second image is facing  ----待选择----toward youaway from you ;
the third image is facing  ----待选择----toward youaway from you .

  We wish to determine the depth of a swimming pool filled with water. We meyjfoy;6 )xr9/z rs -deasure the width (x=5.50m) and then note that the bottom edge of the pool is just visible at an angle oyr/ s9)rjeod-yf xz6; f 14.0$^{\circ}\,$ above the horizontal as shown in (Fig. Below). Calculate the depth of the pool.    m

  The critical angle of a certasa -, ywom1+17.-mhwdpx uzjo in 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 considered a limiting case of a sp*b c2ea tqy*:jzmt6n8 herical mirror. Specify what this lim eb*q:t*n8 jyazt mc62it 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 mirrjm6l dh4+oc+ot56 *ljg /tq uiors so they form a 90$^{\circ}\,$ angle as in (Fig. Below). When you look into this double mirror, you see yourself as others see you, instead of reversed as in a single mirror. Make a careful ray diagram to show how this occurs.

Show analytically that a diverging lens can never fo t;8nqr*8.jtbk 4 pnhnrm a real image of a real object. Can you describe a situation in which a diverging lens can form a8ht8.jpb;4nk nnrt q* real image?

  Each student in a physip;/d4e, d yqmocs lab is assigned to find the location where a bright object may be placed in order that a concave mirror with radius of curvature r = 40 cm will produce an image three times the size ;qdy /,do4mep 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 2n vs atrqa.iy.8)ta(prism 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 cylindrbv.jv2n rpu(m* 4u2 ddical 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 3r2z: ftq ,i2tvwqr7ba 6. s/as3 cm in front of a converging lens of focal length $f_1=15\mathrm{~cm},$ which in turn is 55 cm in front of another converging lens of focal length $f_1=15\mathrm{~cm},$ (see Fig. Below).
(a) Draw a ray diagram and estimate the location and the relative size of the final image.
(b) Calculate the position and relative size of the final image.

A bright object is placed on one side of a converging wok 6taox;(z:7 1wwe6u 7s1h hyani:wlens of focal length f, an oikh:11 ww77sout aznx6;hew y( :w6ad a white screen for viewing the image is on the opposite side. The distance $d_T=d_i+d_o$ between the object and the screen is kept fixed, but the lens can be moved.
(a) Show that if $d_{\mathrm{T}}>4f,$ there will be two positions where the lens can be placed and a sharp image will be produced on the screen.$d_T$>4$f$
(b) If $d_{\mathrm{T}}>4f,$ show that there will be no lens position where a sharp image is formed.
(c) Determine a formula for the distance between the two lens positions in part (a), and the ratio of the image sizes.

  In a slide or movie projector, the film amij6el()v*2v) f vpj bk8ie )pcts as the object whose image is projected on a screen (Fig. Below). If a 105-mm-focal-length lens is to project an image on a screen 8.00 m away, how far from the lens should the slide be? If the slide is 36 mm wide, how wide will the picture be on e iv2)( pmkbij*)l68p ejv vf)the screen? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (picture size is actually ba uxa01h-;(9ois k i*ibber *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 ii9r(e1x a a0uih-i*;sk bb*b os to cover the screen?    cm

Show analytically that the image formed by a converging lens is real and invi ifa(n-) 0 r/v)74kk;xze 4gpfdimkgerted if the object is beyond the f;)eafzxim/ k 0d irgvn-4k(p)ig7k4 focal point $(d_0>f),$ and is virtual and upright if the object is within the focal point $(d_0>f),$ Describe the image if the object is itself an image, formed by another lens, so its position is beyond the lens, for which $-d_0>f$, and for which $0$<$-d_0$<$f$.

  A movie star catches a reporter shooting pictures of her at home. She c-pu92-6uh delwtzdlc 9 ue 2h:y(k)sdlaims the reporter was trespassing. To prove her point, she gives as evidence the film she seized. Her 1.75-m height is 8.25 mm high on the film, and the focal length of the camera lens was 210 mmpehcuh udedd9u( yk-z 2:s2 lwlt )69-. How far away from the subject was the reporter standing?    m

  How large is the image of the Sun on film unhfcrw,* oxn6/smb it/9*1 snsed 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.