What would be the appearaw71w/1 usucoznce 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 hr8 63oj5+vrbv spl+aazu0 m8warbor of Syracuse by focusing the rays of the Sun with a huge svbzopl 80ra3muv rj+8 + a6w5spherical mirror. Is this reasonable?

Although a plane mirror appears to reverse left and righm6s zu.w0-rck t, it doesn’t reverse up and dow6mrw z0 sk-c.un. Explain.

If a concave mirror pp,m dema 78ov;u9mk (eroduces a real image, is the image necessarily inverted? Expl;oe vad9m7p( k,memu8ain.

An object is placed along the principal axis of a sphebpmd1vjg2 knzng3u1w8 7)r bm.i*.i e rical 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 thegn7kjipd 1ug nr. ib8*mbv3zw .12m)e mirror is the image located?

Using the rules for the three rays dis zm6 zobeekrvc3f3 3xr1:3( y6j,fwg icussed with reference to (Fig. Below a), draw ray 2 for (Fig. Below b).z 1wj ekry:c6,3g3rez3m3b of(fiv x 6
(a)
(b)

What is the focal length of a plane mirror? xmz*0jro u,n njb9d.5 What is the magnification of a planej5z90j*m rd onu,x.b n mirror?

When you look at the Moon’s refvm93vsu0 5a etlection from a ripply sea, it appears elongated . Explainv9 0svm3eut5a.

What is the angle of refraction when a light ra eh+bc1 fphj s -dv78ceyf51e1y meets the boundary between two materials perpendicula-18se fc he+11jhypc f5 v7debrly?

How might you determine the speed of light in a solid, rec/tgrtq8(1d . kg3hfwb tangular, transparent 8d3g/bkq 1trg.ht(w fobject?

When you look down into a swimming pool or a.3zgt ze:p0o lerbm94 lake, are you likely to underestimate or overestimate its depth? Explain. How3r:.0e4zgm9ol e bpzt does the apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks bent wzd i/ 7lczl-vr.,px2ze75kj0yl jtc4hen part of it is under water ( 5lc0.zz lv4 zlk/ j2pe,- di7ry7txjcFig. Below).

Your eye looks into an aquarium and views a fish inside. One w(yc 8*k -v;6ycikf goray 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. Briefifc-v gk*6wy koy c;(8ly justify your answer.

How can you “see” a round drop of w xr83msq,f;d -cnenv24u,dk l aoj)m3 ater on a table even though the water is transqk 8o-r 2;d)m x,mjc3un al4sf v,ned3parent and colorless?

When you look up at an object in air from beneath the surf0ur 3 m9fbfuh z.qb5p: jn:y7 n-pr.nvace in a swimming pool, does the object appear to be the same size as when you see it directly in air? nnrnu0:pbbu .m3z9:pv7.q hy r5-ffjExplain.

How can a spherical mirror have a negative object distance0x 93vp3 oyr q,+gp)3s zduycp?

Light rays from stars (including our Sun) always bend toward the vu for,iz)kt 1dvt3. ok)3h2j kertical direction auv3oz)21fot i)hk d.tjk3k, rs 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 if a camera lens is to make a sharp image yij y, b;31iwpof an object very far away?1,wb;j ip3iyy

What type of mirror is shown in (Fi4j,d1r36i*qy k mxz kcg. Below)? Explain.

A photographer moves closer to his subject and th mqu*y8ixs:ur;ucp ,)en refocuses. Does the camera lens move fart,mycrq:p * u u;)uxis8her from or closer to the film? Explain.

Can a diverging lens form a real image under any circumstances? Exj5:ii;xp1ltx/,2 n y yvuxpa :plain.

Use ray diagrams to show that a real image formed by a thin l hcrstkm:07r b:8k4f gens is always inverrgr40 h:7kt fsm:c8bkted, whereas a virtual image is always upright if the object is real.

Light rays are said to be “reversible.” Is this consi5uwlp3 -tm - ud,phl5xstent with the thin lens equation? Explain.5uhl-,pm3t 5d- pxlu w

Can real images be projected on a screen? Can virtuagv,,pfrm(e--g ytc7 dazy* z9l images? Can either be photographedvta9 *f ,7yg,dygp e-rmz -c(z? Discuss carefully.

A thin converging lens tlpv;3ue .un2k 3ym,n is moved closer to a nearby object. Does the real image formed change my.3k2v3nt ,p euu ;nl
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of refractiou qf6toh 2 wig.jjl101mn+h.zn n = 1.30 In air, it is a converging lens. Will it still be a converging lens if placed in 6 12 .nzoifhut g.ljh 0qm1wj+water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in t-xeg3+f r ujb 8fa9eq2he air stands facing a converging lens. If the nose and the tail are each focused on a screen in turn, whichrj9 -8 ef3e qxgbfa+u2 will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stan/o q xzu2, azfce591tnds facing a converging lens. Under what circumstances (if any), e2zf/n5qat9u1o xcz would the image of the nose 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, musbow,h ub8dr, el3p5 4ht the converging lens have a shorter focal length than the divergieb r d34,h,upblwo8h5ng lens if the latter’s focal length is to be determined by combining them?

Explain how you could have a virtual object.ppcd;5 8fh2hk

  An unsymmetrical lens (say, planoconvex) forms an image of m rh7- t;mpj5n sb(6xp-xet*ya nearby object. Does the image point change if the ; mr5 -e y*j(xtnpbxtp s-h76mlens is turned around? ----待选择----yesno 

The thicker a double convex lens is in the center f6i wsh,1ho3 e.+zj31p m biljas compared to its edges, the shorter its fizohpw shjli1+ j, m3.bfe 136ocal length for a given lens diameter. Explain.

Consider two converging lenses separated by some distance. Anx qe,ie:iow 43 object is placed so that the image from the first lens lies exactly atxe,ow3e4 qii : 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 y0smcsks3ux 74s9b2rup :y )rf ourself as you look at your image in a flat mirror 2.5 m away. For what distance should the camera lens be focu0x)c 4fs:s 2rsbur s3kp9yu7 msed?    m

When you look at yourself in a 60-cm-tall plane mirror, you see the same a /)lqyxuod 7ngz. )7bjmount of your body whether you are close to the mirror or far away. (Try it and see.) Use ray dxn77o/ )gy)d ujqz l.biagrams to show why this should be true.

  Two mirrors meet at 6 -*vwr+ p(yvoacvs.s a 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 ;;tuacurg ;2v2.20 m in front of a vertical plane mirror whose bottom edge is 42;v ruat;gu;c 3 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 the mirror?    cm

  Suppose you are 90 cm from a plane mirror. xq*ui y.g7/ ot.i*wa yWhat area of the mirror is used to reflect the rays entering one eye from a point on the tip of your nose if your pupil diameter is 5u/x t 7o*gaq*.yiw.yi .5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors meet at an anfc *)uegl0x1 hbb2.jff zs +m8zpg-s6 gle $\phi$. 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 mirro1v6ph0),yikpolz8i ;5m wbsa- 62vn g b uzsu)r pointed at the Sun, focuses the Sun’s rays 18.0 cm in front of the mirror. What is the radius of the spherical ps hn06aoyu;l68vm5vzbk)p1, -s b2)izw u igsurface from which the mirror was made?    cm

  How far from a concave mirror (radius 23.0 cm) must an object bgp, w9vipz 1.qe placed if its image is to be at i. iq vw,1gpzp9nfinity?    cm

  If you look at yoursel1,qg)s0 4ggq z*vd xzof in a shiny Christmas tree ball with a diameter of 9.0 cm when your face is 30.0 cm away from it, where is your image? Is it real or virtual? Is it upright or invertsog *gq z 0gz,x1)4vdqed?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shows a4lvpt t .kvbn4hp*e :k83f(si n upright image of any person who stands 1.4 m in front of it. If the image is three times the person’s height, what in ( klb.:p83tphi*fv4t4sk ves the radius of curvature?    cm

  A dentist wants a small 3:p, g alfe x8s;uk9momirror that, when 2.20 cm 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 tha8djqvnn9h qej1 5q1 )wt are smaller than they 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 aw19 vwehqn1 d5qj)qnj8 ay appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high i6avzt- o ohxwdp 5(7)vs placed 20.0 cm from a convex mirror of radius of curvature tv7-opd65ah(w xzov )20.0 cm.
(a) Show by ray tracing that the image is virtual, and estimate the image distance.    cm
(b) Show that the (negative) image distance can be computed from Eq. 23–2 using a focal length of -10.0cm
(c) Compute the image size, using Eq. 23–3.    mm

  You are standing 3.0 m from a convex securbz ya:i )k2v7dity mirror in a store. You estimate the height of your image to be half of your actual height. Estimate the radius of c:2z )7iybadvkurvature of the mirror.    m

  (a) Where should an object be placed in front of a concavwh2a0h2 jdan/e mirror so that it produces an image at the same location as the0dnja wa22h/ h 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 viewo 67wq3oym0fiqbq4 )lc k nl7(ed in a curved mirror. The image appears to be 18.0 cm behind the mirror. What kind of mirror is it, 4qqwi) y3m7nlf7 o l(bck60 oqand what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different technvxy4g/.yc.dt)q5 ajm 4xy bg4iques,
(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,8bz30bn 8hjfr98 ( mo5mv6erxoc6t iv that the magnification m of a convex mirror is $m=-d_\mathrm{i}/d_\mathrm{o},$ just as for a concave mirror. [Hint: consider a ray from the top of the object that reflects at the center of the mirror.]

Use ray diagrams to show that the mi4) hz* jl1zok)oy am-vrror equation, Eq. 23–2, is valid for a convemkz -v)aho oyz)4lj*1x mirror as long as f is considered negative.

  The magnification of a convex mirror 4k6 b8db uv2gnis $+0.65\times$ 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. *yi wqr 1u0v2qIt is desired to produce a virtual image that is upright and 3.5 cm tall. 2 w0iqv*1yur q
(a) What type of mirror should be used?  ----待选择----convex mirrorconcave mirror 
(b) Where is the image located?    cm behind the surface
(c) What is the focal length of the mirror? $f$ =    cm
(d) What is the radius of curvature of the mirror? r =    cm

  A shaving/makeup mirror is designed to magnify your face by a fn.hex;m9 - 5p bv zbdx1d3ao5aactor of 1.33 when your face is pla3do1xpd a m-n5.hxzeb;ba v5 9ced 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 u1-ndd9wy); ( ogudg) dkl3wm(cc gs7
(a) crown glass,    $ \times10^{8 }\;m/s$
(b) Lucite,    $ \times10^{8 }\;m/s$
(c) ethyl alcohol?    $ \times10^{8 }\;m/s$

  The speed of light in ice is u2 wzd,w-dmz4$2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain substance is 89% of its value in water. What ij 2zkmczv/: m(4 kbn0ns the index of refraction of this 20vm zk:(bc /n zjnmk4substance? n =   

  A flashlight beam strikes the surfwyjxc /b a nzvtz/gu900(0*da ace 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 bb:urw r-0ji5nqp/ fe) eneath 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 shak)s-sdzd.l+ zej*+: .l mmwater at an angle of 66 z*ml s ez.ddlk:sm+).j+- sha.0$^{\circ}\,$ to the vertical. At what angle of incidence does it hit the air–water interface from below the surface? $\theta_1$ =    $^{\circ}\,$

  Rays of the Sun are seen to make a 8ewan9nnz ga0oq58c b79t4a t31.0$^{\circ}\,$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?    $^{\circ}\,$

  An aquarium filled with water has flat glass sides whose index of refractio1r z/ .zdlxzn1n is 1.52. A beam of light from outside the aquarium1/l z1 .zndrxz strikes the glass at a 43.5° angle to the perpendicular (Fig. Below). What is the angle of this light ray when it enters
(a) the glass, $\theta_2$ =    $^{\circ}\,$
(b) the water? $\theta_3$ =    $^{\circ}\,$
(c) What would be the refracted angle if the ray entered the water directly? $\theta_3'$ =    $^{\circ}\,$

  In searching the bottom of a pool at night, a watchmaf27: -oy 4qj8jorxzv rn 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 thy 28jrr7qz of:vjo- 4xe 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 equilaterald(,xur u +om(jakp7q03k eiu5 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 strikesgzy-l d+32y9fhc s5 ieh1jti . a slab of glass (n = 1.52) and is partially reflected and partially refracted. Find the angle of incidence if the angle of reflection is twice the angle of redj- 5elstyhh+g1izi3 f9y2 c.fraction.    $^{\circ}\,$

Prove in general that for a light beam incident on a 53d 096xncxv9 sf ntk65erecluniform layer of transparent material, as in (Fig. Below), the directi93dc5 xx6nt5cn ve0fe96klsron of the emerging beam is parallel to the incident beam, independent of the incident angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on chdjt4,h1ior9+ k ) yoa flat piece of glass with index of refraction n as in (Fig.) h9i tko4r1oj+ hc,yd 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 b ;b ( eb jkxcnltj;g9b.,.javp wq.,5e5 fr0hinterface between water and Lucite? To be totally internally refla xhbfjvk5be, lq,.0rp9w. (bj ngt5;cbe; .jected, the light must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–lbg4 rc 1.rlm3air 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 fromx. m x7)a4vda(tk/bo(m1ouuj 1vgye / a depth of 62.0 cm. Where must it strike j (b71 v. kuaemvut4/xao/mdgoxy)1(the air–water 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 surface of a liquid an ,tv ao+7lvn z+irij,)d 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 refraction or7j ,v +il,v)a+nzo tif the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face of the prism in (Fig. Below) at 45ai(coyg z 7h74.0$^{\circ}\,$ as shown, but is totally internally reflected at the opposite side. If the prism apex angle (at the top) is $\phi=75.0^\circ,$ what can you say about the index of refraction of the prism? $n \geq$    (retain three decimal places)

A beam of light enters the end of an optic fiber as shown in (Fig. Belo(,jpynxudt6ig 2 9x b5w). Show that we can guarantee total internal reflection at the side surface of the material (at point a), ifd ,9npbg6 5xxy2t(uij 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 glx+xpvd-22vo nass or plastic prism to be used in binoculars (Fig. Below) so that total internal reflection occurv+x-vpx2odn 2s 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 61/ vezmmwkm .e) n5 jx(t.emlyj3/ rm85.0-mm-focal-length converging lens. Find the objec5r ynm..ej/ l mxzm) jme(kt1m8 3e/wvt distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to f uri2w- cc;5iaocus at a point 18.5 cm behind a lens.
(a) What kind of lens is it?  ----待选择----converging lensdiverging lens 
(b) What is its power in diopters? P =    D

  A certain lens focuses light from an object 2.75 m away as an image 48.3 ; ) *pj+jg, tka5aahstcm on thesg)jtk*aja5 +aht ,;p other side of the 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 powera v:j-nj,o iq q7z.0sd of a 20.5-cm-focal-length lens? P =    D  ----待选择----converging diverging 
(b) What is the focal length of a lens? $f$ =    cm  ----待选择----converging diverging 
(c) Are these lenses converging or diverging?

  A stamp collector uses a converging lens with ;ayos1 yw,gil *xl6)s focal length 24 cm to view a stamp 18 cm iy gs, wl)6 y*axi;l1osn 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 14.0u-n 8:(;v qxby;ise ii cm from an object 4.0 mm high. What are the position, type, and height of the image? ivxuebsn;8i-;q (yi :
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to focus an image d; gyphg87h5wp,)y 2 crovo h*on the film of a camera. The maximum distance allowed between the lens and the film planh,p5;o28y 7ghyw gr)ovcp*dhe 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 m0et v2x m-n88ili kl7katerial by a factor of 2.5× when a book is placed 8.0 cm behind a lekl280l xn- ikvtm 87eins.
(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 imttisc g2 v911iage move if the object is sctiit112gv9 moved
(a) 1.0 m closer to the lens,    cm away from the lens
(b) 1.0 m farther from the lens?    cm cm toward the lens

  How far from a converging lens with a focal length of 25 cm should an8m6w fftmxb .yet(s,yx1a z62 object be placed to produce a real image(x zea,8 62 myt1syfw fbxm6t. which is the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an object be placed ifi1av1nd j)t 4f its image is to be magnified 2.1 aivfjnd1t )400× 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-lengttuswb0f-c6:5eyj w,u h lens must an object be placed if its image is to be magneu w5j:y,- wt6fsu0c bified 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 i8h .ypf 1mj7yzr-ffr)s 1.20 m from a 135-mm-focal-length lens. Where is the image, how high is it,ff81mh jrfy.) zy7-r p 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 g 2b dre(ha728cph5axan image formed by a 75-cm-focal-length converging lens if the image is 2.5× larger than 2 h5rc8xga pb2a(e7hdthe object and is real?    m

  A bright object and a viewing screen are separated by a dista7jbn 8+mdfk o*nce of 66.0 cm. At what location(s) between the object and the screen should a lens of focal length 12.5 cm be placejd+k b8nofm7 *d 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 convergi+a h*nir6j*ar8 4y 5 iv(ntq zeryir.2ng lenses are placed 16.5 cm apart. An object is placed 36.0 cm in front of one lens. Where will the final image formed hi(yi2r6 8vz.j*r re5irat4naq yn *+by the second lens be located? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens with awqql rnwb( (pri:tk362 -uc8$f=-31.5\mathrm{~cm}$ 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 lenypfopqc:x*-4ip 0s 7d s is 21.0 cm behind a diverging lens. Parallel light strikes the diverging lens. After passing through the converging lens, the ligh q:sd-c4xiof 0py7 pp*t 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 plr/* o xc2;s4gftc+rp( yn f0mnaced only 20.0 cm apart. The object is still 60.0 cm in front of the first lens as in (Fig. Below). In t+/c gfo*mfr;tc r4(nyxns0p 2his 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 lensknr4f9c6 wk u; on the right is 20.0 cm, and the focal length ofkrn;c 6 4wuk9f the lens on the left is 15.0 cm. An object is placed to the left of the 15.0-cm-focal-length lens. A final image from both lenses is inverted and located halfway between the two lenses. How far to the left of the 15.0-cm-focal-length lens is the original object?    cm

  A diverging lens with a focal lengtdslpd)1t-;jc xji 5fb; a11efh of is placed 12 cm to the right of a converging lens with a focal length of 18 cm. An object is placed 33 cm to the left of the converging lens. ci t1;5jlbf;f)jd1dp1x es a-
(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 diverging w,y xjc mjl5(2aith focal length are placed 25.0 cm apart. aj cx2y (lmj5,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 focal length tfe: o p8paoy-vv22d. $f_C$ 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 surfx6kq69wi k4 6p 9s)o zgu0nvhface radii of 34.2 cm and 23.8 cm. What is the focal length if n = 1.529 x iszg0n)kwvh6o6pf64 u9 qk?    cm

  Both surfaces of a double convex lens have radii of 31.0 cm. If the focal lengt y0)5ewj e1hwb,x 4goah is 28.9 cm, what is the index of refraction of the ljwy 50)xb eea1wo,4hgens material?    cm

  A planoconcave lens (n=1.50) has a focal length of7 qrzcnqby4j/nsro1 i6/mg 7+ -23.4cm. What is the radius of the cobjcrzg//7 1m+rn ns67yio4q qncave surface?    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat surface and the ot*sz)u zo f7ri8ffy.e+ lqw 1z*her has R = -18.4 cm. W8o*7r*zf +i.ezf fl )yzw uqs1hat is the focal length?    cm

  A symmetric double convex lens with a focnm)lz+1tu. l36qn*u)v /tk9 ivekk kpal 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 fvu/z1p3k m* eln )ktk6. t9+vlnuiqk )or each surface?    cm

  A prescription for a correct 5hr* crx: td4r,g, ubd6nk: 0hya.upwive lens 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 40.0 cm. bctru5n dgd ::whr0.,u6*pkrx,4yah What should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face eachy og84 qr wg)48lma89rjtp * ct7ljmj. other 2.0 m apart as in (Fig. Below). You stand 1.5 m away from one of these mirrors and l.9 g jrm48ltcgq4j8*a)jw7rm y8tpolook 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 wa2xy6, fv4y bdmter. We measure the width (x=5.50m) and then note that the bottom edge of the pool is just viydy4m bf6v 2x,sible 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 )h43rnhjz h34xz 0vx tair 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 casp s+f+ao8ie+ e51unvkrr:4iw e of a spherical mirror. Specify what p5o re wk 4fe: r+v8+iin1+asuthis 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 8y u5glk;qerp7x9n3t 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 6g k cl+x;.cchcan never form a real image of a real object. Can you describe a situation in which a diverging lens can form a real image?6gck.h;+ xcl c

  Each student in a physics lab is assi8a9z;tss h-myk ru m16gned to find the location where a bright object may be placed in order that a concave mirror with radius of curvature r = 40 cm will produce an image three times the size of the objecs yhku6z1sr-9m; 8amtt. 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 /uf /wriy/pym)r t7 b0a 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 cylindricalv. e w,nupd/5wu z2k/y 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 of 5iluig6 jp(/ 9, fxyuffocal 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 ofl: 4m5 d,nl 9yv.xve25guacs m focal length f, and a white screen.2gv4y5m c5d vnl emxa9u,:sl for viewing the image is on the opposite side. The distance $d_T=d_i+d_o$ between the object and the screen is kept fixed, but the lens can be moved.
(a) Show that if $d_{\mathrm{T}}>4f,$ there will be two positions where the lens can be placed and a sharp image will be produced on the screen.$d_T$>4$f$
(b) If $d_{\mathrm{T}}>4f,$ show that there will be no lens position where a sharp image is formed.
(c) Determine a formula for the distance between the two lens positions in part (a), and the ratio of the image sizes.

  In a slide or movie projector, the film acts as the object whose imb d6k+6 osr jv3.oi+wfage 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 picturejdr6 io6swk.v f3bo ++ be on the screen? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (pictud))nzzwo*j c4sbi gi6 ;.,nrpre size is actually 24 by 36 mm) is to be projected on a screen 1.80 m by 2.70 m placed 7.50 m from the projectoroig6s)b .cz* np zdrji;4 nw,). What focal-length lens should be used if the image is to cover the screen?    cm

Show analytically that the image formed byasx6g 0rf8ycp0 ou9; c a converging lens is real and inverted ifxg a6fc;ys0rco 80 up9 the object is beyond 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 pictures of her at home. She6iub5u5q20gr;rq fii- 3seh c claims 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 lenr 5 63b qce5iuigf2qh0-r;usis 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 aan2oe,r;2 a t9px 34gklfqo7p camera with
(a) a 28-mm-focal-length lens,    mm
(b) a 50-mm-focal-length lens,    mm
(c) a 135-mm-focal-length lens?    mm
(d) If the 50-mm lens is considered normal for this camera, what relative magnification does each of the other two lenses provide? The Sun has diameter $1.4\times10^6\mathrm{~km},$ and it is $1.5\times10^8\mathrm{~km}$ away.    for the 28 mm lens    for the 135 mm lens.

  (a) An object 34.5 cm in front of a certain lens is imaged 8.2c:+e/t y n/l/w 76 aqxobinqg30 cm in front of that lens (on the same side as the object). What type of lens isqb yclgt// 6qi7an:on w 3+xe/ 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)

  When an object is placed 60.0 cm from a certain converging lens, it form(42w5h+awz x6 y /tkrbr8bcl zs a real image. When the object is moz a2w+6zlrkb/w( x5brtcy h84ved 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