What would be the appearance of the Moon if it had r4i7 f,l6ct/lkg, e n nwpz+j.
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole ys3wq6hksu,mew)3d 3Roman fleet in the harbor of Syracuse by focusing the rays of the Sun with a huge spherical mirror., emwwh6skq)3 3u d3sy Is this reasonable?

Although a plane mirror appears to reverse left and right, it doesn’t 34zfup7tl ss 2reverse up and dowsslt 4 fz72pu3n. Explain.

If a concave mirror produces a real image, is thipix : dzd8w5z:+svy0e image necessarily inverted? Explain.s+w v 85i :dixpzy:z0d

An object is placed along the principal axis of a spherical 2z- 2q xmt7jp sku3v-d j+hlg8mirror. The magnification of the object is -3.0 Is the image real or virtual, inverted mzhjq -2uj-p+dxv7gk8 stl23or upright? Is the mirror concave or convex? On which side of the mirror is the image located?

Using the rules for the three rays discmw-o g f lf:0-wu.dn3nussed with reference to (Fig. Below a), draw ray 2 for (Fig. Below budlf:3 g nfmw w0n.-o-).
(a)
(b)

What is the focal length of a plane mirror? What is the magnification of a pla8bd 3rhvs 5x8bne mirror3bs8 8xbhdr 5v?

When you look at the Moon’y24xjjkr bc4 /s reflection from a ripply sea, it appears elongated . Eyb2cj4 j/ xr4kxplain.

What is the angle of refraction when a light ray meets the boundaram dyke9 p5;:ny between two materials perpendicularap;5d en:9km yly?

How might you determine the speed of light in a solid, recq+o: v ,-a n8hwgkye7etangular, transparent object?+o yh 7-qwve:gnea,8k

When you look down intoudlz:sfy o3. , a swimming pool or a lake, are you likely to underestimate or overestimate its depth? Explain. How does the ap:zs3.dl oy ,fuparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks bent when part of it is utj gs*3yu- b*utjp/n)nder water (Fig.)*gb-ut3tjyp j*snu / Below).

Your eye looks into an aquarium and views a fqvp u;9:ks o*.kt*b s *fioymi(,iqg5ish inside. One ray of light that emerges(5suyspoit*iv k* f.;kqmgo ,*qb i :9 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 answer.

How can you “see” a round drop of water on a tab,b 6jcqbo qb6 o:8ew1kle even though the water is transparent an8b6cq61ebjq:k o,bowd colorless?

When you look up at ai6kc1 /5e4xf)vxr kf i6t+rlnn object in air from beneath the surface in a swimming pool, does the object appear to be the same size as when you see it directly in airk5r4)itx fr/k +ncf6 i6lex1v? Explain.

How can a spherical mirror have a negative obje .3qfl-dp;asfb7 yre6ct distance?

Light rays from stars (includin.gvx /peeo+9k 54 inlg2ee(s xg our Sun) always bend toward the vertical direction as they pass 9+v xox( ke 5se2l .png/geei4through 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 sha5vj/k/axylm +:3 ap kxrp image of an object very /a+ :mxjak/ vxy3l k5pfar away?

What type of mirror is u9b 923p0g0pf //dxwgw :srwi.hshrg shown in (Fig. Below)? Explain.

A photographer moves closer m0 e;. 0poig/l8,u(dlr enwue to his subject and then refocuses. Does the camera lens move farm8.l/(ue deg no0lrpi; u, ew0ther from or closer to the film? Explain.

Can a diverging lens form a real image under any circumstanszp*5xr1sq0gzh6 t exk) .m5ov-zc8 t ces? Explain.

Use ray diagrams to show that a real image formed by a thin lens ks7sx4 b7tm , ech4m4jis always inverted, whem77h4j sxmb4 ck,t4s ereas a virtual image is always upright if the object is real.

Light rays are said to be “reversible.” Is this consistent witybcw+.bg c 020zxx dc/owk0/ ek)af/eh the thin lens equation/c +20 wkwogcd. /yk bbzxe ac/)fx00e? Explain.

Can real images be projected on a screen? Can virtual hbt qf;segc 5,/ 6)wrnimages? Can either be photogrq6s nrc5bt/)f gwh,;eaphed? Discuss carefully.

A thin converging lens is moved closer to a nearby object. Does the real imag5rrkoua dgjau;v7 ys /( 39pq gg+7)qce formed5/y9(gk+qa s3 p7r)jguocrg;7ud q av change
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of refractivge-g1mi dhgfg z;k f0* xha/6hfif.jn547 l/on n = 1.30 In air, it is a converging lens. Will ig*a0f ./ z hdhk54ng e hf7lxf1ivjfi/g6g- ;mt still be a converging lens if placed in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail i janzh-nx8dr7,)v+ x nn the air stands facing a converging lens. If the nose and the tail are each focused on a snnxzx+nd7j)r v,8ah- creen in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in n5;r yy7(qynj(s- dwi the air stands facing a converging lens. Under what circumstances (if any) would the image of the ny n7nyqw;i5(d syr-j( ose 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 convergii 3d( m 3u7l4; jhuujs1;bjbjing lens have a shorter focal length than the diverging lens if the latter’s focbu;j3hs7b4 u ji ljj(i1d; 3mual length is to be determined by combining them?

Explain how you could2w3l;x a -n epvf(1fxx have a virtual object.

  An unsymmetrical lens (say, planoconvex) foj, vu+ tj9gsw+ cu:3amrms an image of a nearby object. Does the image point change ifv cm t:uju9gj+was+,3 the lens is turned around? ----待选择----yesno 

The thicker a double convex lens ikfr:5yjeb( 8-mr:3cupw rx 0qs in the center as compared to its edges, the shorter itsq05:m wp :e (r-brufr xckyj83 focal length for a given lens diameter. Explain.

Consider two converging lenses separated by some distance. An object is placedo9 ndhjs07 dqo1, h*g d+np0tg so that0j,psq *ghn d 1gdoto70+dhn9 the image from 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 take a photograph of yourself as you look at yo xv)nl0hzc q5f+v(.nyur image in a flat mirror 2.5 m away. 5)cv0 lqv+nf .z( xyhnFor what distance should the camera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mirn.-o3fpyku,4is.ve f.ltlj : 1 h g)gnror, you see the same amount of your body whether f3llgn.p1t.,en :4ihg fsy vu)kj.-oyou are close to the mirror or far away. (Try it and see.) Use ray diagrams to show why this should be true.

  Two mirrors meet at a 135 tb.f7) xfkn1 f/emrf5$^{\circ}\,$ 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 floori. z04zfl7554 biplymnxb j i, stands 2.20 m in front of a vertical plane mirror whose bottom edge is 43 cm xz, n5bz5p4m jbly i0if l7.4iabove 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. What area of th -c 6stx(o/fg0ffi1.x/ps nxce mirror is used to reflect the rays efxn p1/x/ctsoc-i f0sfx 6.( gntering one eye from a point on the tip of your nose if your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors6ls ;fen oa/+v 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 conca7h:b y: v:5 gco,xvpfr:cf3a sve mirror pointed at the Sun, focuses the Sun’s rayy :v:fs7:v carpo:5,h bfgc3xs 18.0 cm in front of the mirror. What is the radius of the spherical surface from which the mirror was made?    cm

  How far from a concave mibm tn 1:;de)hnrror (radius 23.0 cm) must an object be placed if its image is to be at infinityd;1mhen t:bn)?    cm

  If you look at yourself in a shiny Chris2*o0 ekkcsgt9 dy 5bs3tmas tree ball with a diameter of 9.0 cm whe0e3ktkg* b952scoy dsn your face is 30.0 cm away from it, where is your image? Is it real or virtual? Is it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shows an upright image of (qcqtis7 n03 f/nv3.gb r (ul9dpdj l0any person who stands 1.4 m in front of it. If the image is thri9(q3 .nl (cfudb0/ qjdr0l svt7g3npee times the person’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror thats7n8yk1i*nwfw 8 wg i:l eww4,uz+jl-, 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 that are smaller than+ -,zs j ea4zyxwg9s6c. oi,so they would be if the mirror were flat. Are thesassz6gzi9.yj -o 4c, ,+eow x 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 placed 20.0 cm from a convex mirr 81 y6i )tgsmb ik5);dqldje3-,iouagor of radius of curvato bi))i,m6tegy-8gj k;liadqd 5 3us1ure 20.0 cm.
(a) Show by ray tracing that the image is virtual, and estimate the image distance.    cm
(b) Show that the (negative) image distance can be computed from Eq. 23–2 using a focal length of -10.0cm
(c) Compute the image size, using Eq. 23–3.    mm

  You are standing 3.0 m from a convex security rjkiy 6t8) ekgbb 6/m-lrf4 :tmirror in a store. You estimate the height of your image to be half of your actual kbbmi/gtjr lfky :-r46e)68 t height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an obrr+gd8,fh2;)kkq4ns gk 8iz8 q6jcy xject be placed in front of a concave mirror so that it produces )sf6 qr8+8xk28 gygn;zqrihk c4j ,d kan image at the same location 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 4-myavrcz5l j(kreq * z2w.,osmall when viewed in a curved mirror. The image appears to be 18.0 cm behind the mirror. Whalrwz(y r 2v5q*.4mkzjoeac, -t kind of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different tech(9ho bn* 2il.v+nh-zsdst q+y niques,
(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, thaer rf/g;f)y1d :m,a zat 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 mirror equatio:u-zq(gc o(pkpt62 7qtv;4wtcgo 9 gsn, Eq. 23–2, is valid for a convex mirror as long as f is considered negatiqpop :t-w4(us gqtvcgc( 6g9;z ok2t7 ve.

  The magnification of a convex mirror iip y8hgjq9:uutse a37odewa9. b /11ps $+0.65\times$ 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 at:x6nm1 fvk v* n0mhaxk41m0w spherical mirror. It is desired to produce a virtual image that is upright40f*m mnnx 610wkv k vxm:tha1 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 mirroro7uz)*q.g x lq is designed to magnify your face by a factor of 1.33 when your f 7qogux .qz*l)ace 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*)1bg iy*5tf)spx vc3jn, isg in
(a) crown glass,    $ \times10^{8 }\;m/s$
(b) Lucite,    $ \times10^{8 }\;m/s$
(c) ethyl alcohol?    $ \times10^{8 }\;m/s$

  The speed of light ibiq7pgrm a*htey(fgy; 28:0 bn ice is $2.29\times10^8\mathrm{~m/s}.$ 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 i 7,f+k1mh adpqs the index of rem,q fk+7dhpa1fraction of this substance? n =   

  A flashlight beam strikes the surface of a pane of glass ( dkh to:* jqh,2ms9s(un = 1.58) at a 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flasphql) gq.o/ko*-4p(sp4saku hlight upward from beneath the water at a 42.5$^{\circ}\,$ angle to the vertical. At what angle does the light leave the water? $\theta_2$ =    $^{\circ}\,$

  A light beam coming from an underwateri 57dvxz- bjh2av,7gg spotlight exits the water at an angle of 66gzg7ji- vxvh d 527b,a.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 31.0rh/lj+v7e95 sr,gcg ek l) l/f$^{\circ}\,$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?    $^{\circ}\,$

  An aquarium filled with water y2tydll ueal(8m 5) j5jds74 yhas flat glass sides 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 (F(yu 2ly ejl)l 5dtj8d54y7masig. 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 atfu )do+l 6pojn*d87 /l nusc6v night, a watchman shines a narrow beam of light from his flashlight, 1.3 m above the waterljdn68vs+u l )fc o/d6 o7pn*u 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 a *gl av z74ruro2q;2x:vf) kmkn equilateral 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 l*k)ym3x, 4l2wipswcr1vp: z(n = 1.52) and is partially reflected and partially k4c,lp m3i wsl):w*zx2pv y1r refracted. Find the angle of incidence if the angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam incid j 9)rc6ema 0nfyh0gst u;di+/ent on a uniform layer of transparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the incident beam, ine rg)n t; cm0d/j9uhsfai0y6+dependent of the incident angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on a flat piea:d4 t; be7opxce of glass with index of refraction n as in b;p4de: a oxt7(Fig. Below). Show that if the incident angle $\theta$ is small, the emerging ray is displaced a distance $d=t\theta(n-1)/n$ from the incident ray, where t is the thickness of the glass and $\theta$ is in radians. [Hint: for small $\theta,\sin\theta\approx\tan\theta\approx\theta$ in radians.]

  What is the critical anglinc7 vnc46-ihatq* :c0bgqk) e for the interface between water and Lucite? To be totally internally reflected, the light must start in which material?va0c-*g:tqk h7qbn)c4 n 6ii c
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid 7(/9xgr w+ u/olrja0dfuy.xeros , (z–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 cm. Where-x+ qzn7l)inl must it strike the air–water interface, relative to the spot directly above it, in order -) nl7 nqxl+zithat the light does not exit the water?    cm

  A beam of light is emitted 8.0 cm*/q5ii mu4tuu beneath the surface 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 inq4uiu* imtu5 /dex of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left f /a;z4tkcqpmyf ew6+6 ace 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 optic fiber ade,g 5t:eo5tn ro83 f/sno x,ys shown in (Fig. Below). Show that we can guarantee total internal reflection at the side surface of the material (at point a), if the index of refraction is greater than about 1.42. In other words, regardless of t5ygo:t otde x/3 8fse 5ornn,,he angle the light beam reflects back into the material at point a.

  (a) What is the minimum index of rkzn,mn0nb2v b):at+ n gn21 -rw/oj uqefraction for a glass or plastic prism to be used in binoculars (Fig. Below) so that total internal reflection occurs at 422otrvbz,b0 mn n+1nw/aqu:) kj -ngn5$^{\circ}\,$? $n_1$ $\geq$   
(b) Will binoculars work if its prisms (assume n=1.50) are immersed in water?  ----待选择----totally reflectingtotally transmitting 
(c) What minimum n is needed if the prisms are immersed in water? $n_1$ $\geq$   

  A sharp image is located 78.0 mm behind a 65.0-mm-focalyomi9 whahc+ y206toz a)0/ wl-length converging lens. Find the object d i) tay02o ahymc/zhwwo l96+0istance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point3-q0vt/fsgy1u i emb2 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 48.3lc8 32r8so5g5gm bnpi cm on the other side of the lens. What type of lens is it and what is its focal length? Io2cri85gn m8l s gbp35s the image real or virtual?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the power of a 20.5-cm-fo6pkkx8jg y1gg0s :pudbm9k ,-)reia- cal-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 usesg 1gvbyo)5wx-nu . gn: a converging lens with focal length 24 cm to view a stamp 18 cm in front of the lg vng 1bxygu )ow-:5.nens.
(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 4.0hlu6a kxm,n98 mm high. What are the position, type, and height of the89hkn6a,xu l m 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 camera. Thchw 6aw,q((l-jtqdfl p (h9 ,ye maximum distance allowed between the len6 -,q cq( fdhlt, (l(jya9hwpws and the film plane is 120 mm.
(a) How far ahead of the film should the lens be if the object to be photographed is 10.0 m away?    mm
(b) 3.0 m away?    mm
(c) 1.0 m away?    mm
(d) What is the closest object this lens could photograph sharply?    mm

  It is desired to magnify reading material by a factor of 2.5× 4 to:wz6u8r,c7.g:ecs(mxy2jdae br when a book is placed 8.0 cm behind a lens. 6amd: eroz(sy b.:j,w7t4 rc8xg2ceu
(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 8g 1tx5 zw)yv,r zzhr,;.0-D lens. By how much does the image move if the object is moz5 gyrx vt,),whzr;z1ved
(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 anrts f.4.x, 7,rh qkv3 kwp+sxj object be placed tox7rxktq.s 3 pj ,,swrk4h+.vf produce a real image which is the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lensub5c gz6l +)ts must an object be placed if its image is to be magnified 2.00× and be realstb+ 6 zuc5g)l?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm

  (a) How far from a 50.0-mm-focal-le 4 j g-pl3h.lo9ynce5hngth lens must an object be placed if its image is to be mag4g hco e9.jhlpn53ly-nified 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 is 1.20 m from v4aqh63pvm9ql)m q q6a 135-mm-focal-length lens. Where is the imageqvav )6h3ql64q9mmp q, how 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 im3n vo)1y et7anage formed by a 75-cm-focal-length converging len1ytoav)n7ne3 s if the image is 2.5× larger than the object and is real?    m

  A bright object and a viewing screen are separated by a distance of 66.0 cm. Atdocl7c 1(0 yyz8s5uz p what location(s) between the object and the screen should a lens of focal length 12.5 cm be placed in order to produce a crisp image on the screen? [Hint: first draw 0(1 o zlzypdcs8u y75ca diagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length converging lenses are s; 0rg ,lncnqclim:(.placed 16.5 cm apart. An object is placed 36.0 cm in front of one lens. Where will th; qs:imr0n(cgnl,c.l e 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 with so )g8do4j*kp$f=-31.5\mathrm{~cm}$ is placed 14.0 cm behind a converging lens with $f=20.0\mathrm{~cm.}$ Where will an object at infinity be focused?  ----待选择----realvirtual ,    cm beyond second lens.

  A 31.0-cm-focal-length converging lens is 21.0 cm behind a diverging lens. Parax4-k uy8 d3k kjfisj46llel light strikes the diverging lens. After passing through the converging lens, the light is again parallel. js u4k83dyj kfxk-i64What 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 placeocy7s cor eyv9nxg 6f;-v0 0d9i+pqr/ d only 20.0 cm apart. The object is still 60.0 cm in front of the first lens as in (Fig. Below). In this case, determine o0iog er6vp cf;9yvq7nd0s9cx- y+/r
(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 foqy;h77y3:g /iby4y nywee- vucal length of the lens on the right is 20.0 cm, and the focal length of the ln/yyy ;gyue 7-:ieqvh47 b3wy ens 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 length of is placed 12 cm to9pm3scyw wl,4r m es,g4on+m,6irq f7 the right of a converging lens wgy4smm7se+6wrq, i94 f l3omc n p,,rwith a focal length of 18 cm. An object is placed 33 cm to the left 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 divergj41uade /16h c8siy4pli;dgh e itp /:ing with focal length are placed 25.0 cm apart. An obj/hicy;djsd:4ghup 4 e/e1i t1la6p8iect 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 oho1qb9/0bjnp al( n7 $f_C$ 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. q8vndp )gw0 hgr. n;2pWhat is the focal length if n = 1.)qdnn rpg8.pvw2 0g;h52?    cm

  Both surfaces of a double convex lens have radii of 31.0 cm. If the focal lrlx1q7i:ht 6 length is 28.9 cm, whax:17li r ht6lqt is the index of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.41xyc582ee6ia fqm eyt,+ dy;ocm. What is the radius of the concave me56yy ,adye2;cxfoie+ t 8q 1surface?    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat surface avj ws77ur7()onf zjnbuh jfhxws n*g6d96929nd the other has R = -18.4 cm. Wha6sw9jz(w9ju) x n6d7bhnhr9ufo 7 fs*j g7n2vt is the focal length?    cm

  A symmetric double convex lens with a focal length of 25.0 c1 qwa15s4:u9y kjnudvm is to be made from glass with an index of refraction of 1.52. What should be the ru1wk9y 1qa4 nu:5svdjadius of curvature for each surface?    cm

  A prescription for a corrective lens calls for +1.50D. The lensmakep9i+pygs ft c:7zic34r grinds the lens from a “blank” with n=1.56 and a preformed convex front surfiz cy3 s4 +7p:pcigf9tace of radius of curvature of 40.0 cm. What should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as (39u7jkmwf 5sh /iw8pyo km5s in (Fig. Below). You stand 1.5 m away from one of these mirrors and look into it. You will see multiple images of yourself. u jwmo(kik9fwps/78h 3 s 5y5m
(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 swimmid hn *gkq6zzk6u6f23:p gok )zng pool filled with water. We measure the width (x=5.50m) and then note that the bottom edge of the pool gh 2*gfk o3unkpz qdz:kz66)6is 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(yksttzz*npw qd1 - it)*w 2l4 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 spherical mirror. Sphc i /n sco;+u(zv+-ix1eqc-h ecc in;c-/ (ohu-c1+es vixzqh+ ify what this 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 mirrors4ozs-qqi d2pk* yqu kv/z 8t (s*nr8n9 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 divergingo .1whrfc:z r+ lens can never form a real image of a real object. Can you describe a situation in which a diverging lens can form a real imag c.fhwo+r :r1ze?

  Each student in a physics lab is assigned to find th) fbi(edka yxm1b10v41d h.h h+tw1ine 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 thb0 (k+11yba m.)hw1ift4hdhi1nve xde size of the object. Two students complete the assignment at different times using identical equipment, but when they compare notes later, they discover that their answers for the object distance are not the same. Explain why they do not necessarily need to repeat the lab, and justify your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of a prism ;c7vp2 ekl+9t yw d-sz *gf6rmrm4i; jis $\phi=72^\circ$ see (Fig. Below), what is the minimum incident angle for a ray if it is to emerge from the opposite side (i.e., not be totally internally reflected), given $\mathrm{n=1.50~?}$ $\theta_1$$\geq$    $^{\circ}\,$

The end faces of a cylindrical glass roqx 1h+ve9ju e:d $(n=1.54)$ 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 q5ry s9o6u3 yqy7csp) 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 leng,/i zpvak) oa.+dnb /9ho5 zmm)ov a)mth f, and a wmd +v boma)v ,a/zkom.npi/)) 5zo9hahite 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 acts as the object whose imagqd0djc1yqy8n)z t .( /rypaz:e is projected on a screen (Fig. Below). If a 105-d jp/yr :.q)q8zd(at 1ny0zycmm-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) o ro.9cax4 kz9is to be projected on a screen 1.80 m by 2.70 m placed 7.50 m from the projector. What focxk9r oa4ozc .9al-length lens should be used if the image is to cover the screen?    cm

Show analytically that the image formed by a ckcv 08vsk b4;i. kd2mlonverging lens is real and inverted if the objekvc.s ;kbdvm82k04 lict 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. She clampb7 7bx1 ,q-b6ns0 bs fs(tjgims 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 mm. How far away from the subjec,x6j bgsb1fb7sb(q0 -7nsp t mt was the reporter standing?    m

  How large is the image of the Sun on fiq. s3+jyr r:no8.qlts lm used in a camera with
(a) a 28-mm-focal-length lens,    mm
(b) a 50-mm-focal-length lens,    mm
(c) a 135-mm-focal-length lens?    mm
(d) If the 50-mm lens is considered normal for this camera, what relative magnification does each of the other two lenses provide? The Sun has diameter $1.4\times10^6\mathrm{~km},$ and it is $1.5\times10^8\mathrm{~km}$ away.    for the 28 mm lens    for the 135 mm lens.

  (a) An object 34.5 cm in front of a certain lens is imaged 8.2ld+xdvsa0gf..h 8d z8 fikj).0 cm in front of that lens (on the same side as the object). What type of lens is this, and what is its focal length? Is the imagedikxhsgv8)ad.fj 0+l.zfd 8 . 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 c:wz nlq 7hbf diu.(26azy(6daonverging lens, it forms a real 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 lewu.y (iadh(q:d zf7z662lb an ngth of this lens.    cm