What would be the appearance of t0cz6gi sawewuj3j- :wtc, o1p -0b4nzhe Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fleet*1ka)1vxouu / (ma beq in the harbor of Syracuse by focusing the rays of the Sun with a huge spherical mirror. Is this reaxo1/e u*bk am()uv a1qsonable?

Although a plane mirror ap:( : kr:bv:ubzc2jq sjpears to reverse left and right, it doesn’t reverse up and down. Explai:kbj uqc z:r:2:jbs (vn.

If a concave mirror produc1fva k2kzb+6 res a real image, is the image necessarily inverted? Ex+ kk1z6rbfv2 aplain.

An object is placed along the principal zcla4zoxl5(6bx 2j -u axis of a spherical mirror. The magnification of the 4z6z5jl lxc-xao(2ub 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 located?

Using the rules for the three rays discussed with re hllary (-2ax6x o*+poference to (Fig. Below a), draw ray 2 f2porxhyo+-(la*a6 l xor (Fig. Below b).
(a)
(b)

What is the focal length of a plane mirror? What is the magnificationc2rpb 6 9(y eww)f0igh of a planeiprcw6y9hf2g ) eb0 (w mirror?

When you look at the jszga.t5 7tr6 Moon’s reflection from a ripply sea, it appears elongated . Expla65t7 . zasjgtrin.

What is the angle of resm7,x)stjevn5f t - -x88rolg fraction when a light ray meets the boundary between two materiml-t ) joet8g5,n7xs-rx8 vf sals perpendicularly?

How might you determine the speed of light in a solid, rectangular, trawki /sd8: aww8nsparent s iw:daww 88k/object?

When you look down into a swimming pool or a lake, are you lip: tfw8o/ +zf;vwim+ zkely to underestimate or overestimate itsfw +;mti+ /ozpw8fzv: depth? Explain. How does the apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to ss gvcv;- h-.phhow why a stick looks bent when part of it is under water (Fig. Belv;vcs-.hhg-p ow).

Your eye looks into an aquarium and views a fish insg 69np/ln dkb n*roa(/ide. One ray of light that emenn/bn6(rpd 9*o /lgak rges 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 ty(z 0ik08rp tfd* uu+table even though the water is transparen8ypu0f*0i (kdtz ut+ rt and colorless?

When you look up at an object in air from beneath the surface in a swimmingsogs) *sbf4au8 x,f 0v-i*pk k pool, does the obu sfio,ks-*)a8 0f4pbxvg ks* ject appear to be the same size as when you see it directly in air? Explain.

How can a spherical miry)big/u efqg,k)o yrewdw6.: ,2ms( u ror have a negative object distance?

Light rays from stars (including our Supx6+akcdi axr p 9* h,dmyxx;:. (5xhhn) always bend toward the vertical direction as they pash5a(9*yx;pxxxar :d, pmh+.h kxdc6 is 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 wkjy/6n:8toz a80 j., qextzt make a sharp image of an objec k qx6t.a 8:,jty jwoez8zn/0tt very far away?

What type of mirror is shown in (Fig. Belows+;gp 8g; z0jpvlvxq+ )? Explain.

A photographer moves closer to his85dy8y z qb+wy subject and then refocuses. Does the camera lens move farther from or closer t+5yqd8 8zywby o the film? Explain.

Can a diverging lens form a realf7f 1o-efwdu3t 46sjh image under any circumstances? Explain.

Use ray diagrams to show f2:ny: guuqp wc,l**wthat a real image formed by a thin lens is always inverted, whereas a virtual image is always upright if twu 2yq lc*: *ugwnfp:,he object is real.

Light rays are said to be “reversible.” Is thos ct)4,fn y5cis consistent with the thin lens equation? Etcn)5f 4y,socxplain.

Can real images be projected on a screepi-3n r,fa3rin? Can virtual images? Can either be photographedri -f ripa3n,3? Discuss carefully.

A thin converging lens is moved closer to a nearby object. Does the real image u z0a0vi-xf;mm x)db0 tuiq 3,forme)qitm0f-im x b 0v0,z;3uxu dad change
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of refraction n =t7bnp*j )qnjqx 8v c7) 1.30 In air, it is a converging lens. Will it still bb8ncxq7tv) j7p*n )jqe 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 nose ancu99 vd3qa9dgd the tail are each focused on a svg9q9c9dd3a u creen in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facing a convergic;m4we7dwhik 0ze )+eng lens. Under what circumstances (if any) would the image of the nose be virtual and the image of th 40mwekecwie h;d z+)7e tail be real? Where would the image of the rest of the cat be?

Why, in Example 13, must the convergi0b0miaevvcv5s.49 w 7s ,meleng lens have a shorter focal length than the diverging lens if the latter’sbl7va59m.i, 0se0wv smc e e4v focal length is to be determined by combining them?

Explain how you could have a virtual obje)ygcv3( kcibjb3dx1j( y/j4v ct.

  An unsymmetrical lens (say, planoconvex) fo-zyt44 rnm +erur;uohp-( c i9rms an image of a nearby object. Does t4oh9i ryr+ p-;rcute mu4zn-( he image point change if the lens is turned around? ----待选择----yesno 

The thicker a double convex lens is in the center as compared to its edgesxdd.(s )bkxi3 , the shorte)dk3xbs. i dx(r its focal length for a given lens diameter. Explain.

Consider two converging lenses separated by some distancpsbivg8r+x*z i f7 (j27oo 8koe. An object is placed so that the image from th+7r82oipo zsox7fkgi*(v bj8 e 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 4 flx:+l*vt1tou6xe 1mif9n*msh6j -qsv 8n fyour image in a flat mirror 2.5 m away. For what distance should the camera lens be focuse1m6*-fs9 o1 ut4th j l8mqff*len +sinxx6:vvd?    m

When you look at yourself in a 60-cm-tall m ,w xra43t:vuplane mirror, you see the same amount of your body whether you are close to the mirror or far4,wu3 amtx:vr away. (Try it and see.) Use ray diagrams to show why this should be true.

  Two mirrors meet at 0d lbj g4atqid0j,uix20u yo;- k* q+ea 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 z9)nl- ncesd 7d -mm(ythe floor stands 2.20 m in front of a vertical plane mirror whose bottom edge is 43 cm above the floor, (Fig. Below). What is the horizontal distance x to the base of the wall supporting the mirror of the nearest point on the floor tha-)m9 (edlncn-syd 7mz t can be seen reflected in the mirror?    cm

  Suppose you are 90 cm fromi 4de gsslq g0h1nhrf )2t:+i, a plane mirror. What area of the mirror is used to reflect the rayl,si ethh1f ):4s rqg0di2ng+s entering 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 mirrors meet at an angd..qd a5q(0 euh)uoammp ( /hhle $\phi$. 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 concal):/u64 oz4 hyffhp vcve mirror pointed at the Sun, focuses the Sun’s rays 18.0 cm in fronthvz:4y c o uf)f4/6hpl of the mirror. What is the radius of the spherical surface from which the mirror was made?    cm

  How far from a concave mirror (ral* lbw ,ei tp0txw+85fdius 23.0 cm) must an object be placed if its image is to be at infinit bl8 5ptewl0x, iw*f+ty?    cm

  If you look at yourself in a shiny Ceqj/ fob1 42gea;u9b ahristmas 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 virtua u;o1e9eqf2gba4/ jb al? Is it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement stu1k; 8on d.womm59n park shows an 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 id15o.tm n8k; msou9nw s the radius of curvature?    cm

  A dentist wants a small mirror that, when 2.20 cm from a too n3j)gwcx*0. k )asid9 eydlw9 :r.tluth, 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 awzeg7vu-b 86xre 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 away appear 0.33u 6xz7gwe-b v8× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is pl57c,9 qb 6ryzny lw7naaced 20.0 cm from a convex mirror of radius of curvature 20.0 6c 5nbq9nwl7ra7 yzy, 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 securityz*v gmd9 a n7):fgz6n2.o-t0h9 tbqhmi.of kl mirror in a store. You estimate the height of your image to be had:onzobi6kf9*0q) nl .z v h-9t. mhma7g2fgtlf of your actual height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object be placed in front)- z7gm ilxuhw o59e57tlgo: j of a concave mirror so that it produces an image at the same)z9ejox5 7om uilg5tlhw7g:- 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 smaq0z* qyc)8 mzq: (zfobpslm) 8nyt36 yll when viewed in a curved mirror. The image appears to be 18.0 cm behind the mirror. What kind of mirror is it, aq3qmc(yl*86bqmzy)f zzp yn8ots :0) nd what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniqueshb xqizj-mc 3yai18-1r45i u p,
(a) a ray diagram,
(b) the mirror equation, to show that the magnitude of the magnification of a concave mirror is less than 1 if the object is beyond the center of curvature $C\left(d_0>r\right),$ and is greater than 1 if the object is within $ C (d_0 < r) $.

Show, using a ray diagram, that the magnification m of a convex *y6oeudie64(-hs6bood v u6z 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. 23–2gw:yk w4y6ju (y;ymk3, is valid for a convex mirror as wk ;3uky :4wg(myjyy6long as f is considered negative.

  The magnification of cnz3 x,d1q yq3a 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 placb /r yatgc;0t.3 wnqc+ed 28 cm in front of a spherical mirror. It is desired to produce ayr3/ 0ngc ctt wb+a.;q virtual image that is upright and 3.5 cm tall.
(a) What type of mirror should be used?  ----待选择----convex mirrorconcave mirror 
(b) Where is the image located?    cm behind the surface
(c) What is the focal length of the mirror? $f$ =    cm
(d) What is the radius of curvature of the mirror? r =    cm

  A shaving/makeup mirror is)4tf9oh khog5dx* 8 rs designed to magnify your face by a factor of 1.33 when your face is placed 20.0 cm ing9sxr h h4fot5*o d8k) 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 rl9mt )t3 kok.hs4hr(
(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/ k s,a+pm jppq88a:jq is $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain (/dtny:v33oqs pf jh2substance is 89% of its value in water. What is the indeh/qf 3n:v dpstjy3o (2x of refraction of this substance? n =   

  A flashlight beam strikes the surface of a pane o8y n(sqsjk+f /f 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 flashl qivzs,d. /t3x jhdjiy:n(h*f *8 bsr9ight upward from beneath the water at a 42.5$^{\circ}\,$ angle to the vertical. At what angle does the light leave the water? $\theta_2$ =    $^{\circ}\,$

  A light beam coming from an underwater spotlight exits the water at an angle ob0jnwnos 9i81f 6w9i0 sn1b8 jno6.0$^{\circ}\,$ 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 ma y4s2e4w rop.ske a 31.0$^{\circ}\,$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?    $^{\circ}\,$

  An aquarium filled with water has flat glasw 26knz /yy( (rsn kluy((b0xss sides whose index of refraction is 1.52. A beam of light from outside the aquarium strikes the glass at a 43.5° ang2( nswkyl(rs6kbxnu( z0( yy/ le 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 watchman shines alfl ywet6/b+2rgq 0- c 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 lw0tg/ r2ebyfq6l +-c edge of the pool (Fig. Below). Where does the spot of light hit the bottom of the pool, measured from the wall beneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equib vv/psc h1ue,8j;,em lateral 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 swk 0qr7t 7ur9hv9ha a(t/jxc7trikes a slab of glass (n = 1.52) and is partially reflected and partially refracted. Find the angle of incidence if the a7xhv0hw u7qa(c /99jar7r tkt ngle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam incident on a unaid:pem9cgq v4rgt,y ) wi- :/ghc: 7riform layer of transparent material, as in (Fig. Below), the dii: :,4cw i7d/hac- pg:yrvgr9)t q mgerection 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 a flat piece of glass with inwvxb -e:cft 18dex of refraction n as in (Fig. Bel:tb18-cv e wxfow). Show that if the incident angle $\theta$ is small, the emerging ray is displaced a distance $d=t\theta(n-1)/n$ from the incident ray, where t is the thickness of the glass and $\theta$ is in radians. [Hint: for small $\theta,\sin\theta\approx\tan\theta\approx\theta$ in radians.]

  What is the critical angle for the interface between water and Lucitet/2+2)l futxgm(mbh pk bu/59g, paif ? To be totally internally reflected, the light must upffthg) p/52m( lu29ig/ m bxa+bt,kstart in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a cn d:91jmr25 (qe4dx1udhqlrpertain liquid–air surface is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in a pool of water from a depth of 62.0j sxm-otpjkog ex5o3 (5q66;z cm. Where must it strike the air–water interface, relative to the spot directly above it, in order that the light does not exit k - joz5xj;moxqgtp3 (e56os6 the water?    cm

  A beam of light is emitted 8.0 cm beneath the surface of a lifbqk2v-h0ni caerab *2g n:k..qm3l 0quid and strikes the surface 7.0 cm from the point directly above the source. If qag fl-*.0k02crnkqhm. aevi3bb n:2 total internal reflection occurs, what can you say about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes thew/ldv 0tq+kjf8 jexjd698 s x5 left face 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 optig:u9lq13l. ejg(kvoerd 9cz 6c fiber as shown in (Fig. Below). Show that we can guarantee total internal reflection at the side surfrvd j99elg( gl zckq e.631o:uace of the material (at point a), if the index of refraction is greater than about 1.42. In other words, regardless of the angle the light beam reflects back into the material at point a.

  (a) What is the minimum ind ;m5 8dzbqnppg( e3,g+ fwm: qtwz7)c3qh0enjex of refraction for a glass or plastic prism to be used in binocuw 8 e,z3qmdw (jhq30bt5npc;:g zfqgm7 p)+n elars (Fig. Below) so that total internal reflection occurs at 45$^{\circ}\,$? $n_1$ $\geq$   
(b) Will binoculars work if its prisms (assume n=1.50) are immersed in water?  ----待选择----totally reflectingtotally transmitting 
(c) What minimum n is needed if the prisms are immersed in water? $n_1$ $\geq$   

  A sharp image is locar/wo l87cmg, ited 78.0 mm behind a 65.0-mm-focal-length converging lens. Find the obr ilmc/,78gow ject distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.5 cm bec r4vc9 f mm9.sr77zvghind 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; st/r ah;,vak cm on the other side of the lens. What type of lens is it and what is its focal length? Is the ima;s/v,h rtka; age 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-qhl,sx(l8 p*(gpk41e tqdo* ecm-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 convergim)r bt4vtt3t+ng lens with focal length 24 cm to view a stamp 18 cm in f r)tbt4tm +3tvront of the lens.
(a) Where is the image located?    cm behind the lens (virtual)
(b) What is the magnification? m =   

  A -5.5-D lens is held 14.0 cm from an object 4.0 mm high. What are th4m,f6zue k u0ge position, type, and height of kz egm,u f06u4the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens isq 6t6egj;+g9dfp0g6hu u j+ ebfr2wt5 used to focus an image on the film of a camera. The maximum distance allowed between the lens and the film plane i6qr g9hf0g+j6b+ wep2u ug; t6f5dtejs 120 mm.
(a) How far ahead of the film should the lens be if the object to be photographed is 10.0 m away?    mm
(b) 3.0 m away?    mm
(c) 1.0 m away?    mm
(d) What is the closest object this lens could photograph sharply?    mm

  It is desired to magnify reading material by a factor of 2.5× when a bob-s , 68fqzq).gykkxvc:c3 az ok is placed 8.0 cm b s yv8)x6k-bazg,cc f:z q3qk.ehind 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 ) .q uxovtr5(xgt + izn+7c v4wk6fvw.8.0-D lens. By how much does the image move if the object is movedkxtt o.7qv gv cnzur(fx6vi5++4 w ).w
(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 odl9no,f +o o7q zdhvyu 3n869uf 25 cm should an object be placed to produce a real image which is the same sized9n+ ohlo3dfo vn 6u8y7uq9z , as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an objecw veb1al7)gyb jc,.p/ t be placed if its image is tyge)a7pw/b,1 b l j.vco be magnified 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 plah gfbs5 +tsr*);k5ycz1 p)ank t;y+ occed if its image is to be magnified 2.00× anr51g*)y;c)+h fzcnt;5+y bp oa sst kkd 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.yz8u wv h5:3 /kva)pre20 m from a 135-mm-focal-length lens. Where is the image, how high is it, and what type izy evk)a8w/hpvr 5: u3s 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 obj;+ b+hkbfmm, ject and an image formed by a 75-cm-focal-length converging lens if the image is 2+fm h;mbjb+k, .5× larger than the object and is real?    m

  A bright object and a viewing screen are separated by a di .q3f5l v3kvg s.xf9ulstance of 66.0 cm. At what location(gu vsk93lv3fx5ql . f.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 a diagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length converging lenses are placed 16.5 cm apart. An objectkn j,4 hk6j08v6niyp n 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 tot ki 6j4n6pn ,jn8kvh0yal magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens with fp2k07s*8vg ly 3dkb-h j4hm e$f=-31.5\mathrm{~cm}$ 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 2b0 33;yltt8e u6 nasqgadt+b+1.0 cm behind a diverging lens. Parallel light strikes the diverging lens. After passing through the converging lens, the light is again parallel. What is the focal length of the divergingutab08l 3+se at qgnb +6y;t3d lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Example 23–12 are now placed only 20.0 cm apa c-wvlo9fdj 70rt. The object is still 60.0 cm in front of the first l-odj 7f0 v9lwcens 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 ar,og/ycnv*)6 zxy rvy;e placed 30.0 cm apart. The focal length of the lens on the right is 20.0 cm, and the focal length of thev 6n,co)y ygry*/xv z; 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 length of is placed 12 cm to the right of a conv90o5pm pl4ke serging lens with a focal length of 18 cm. An object is placed 33 cm to the left of the converginge5p9k 4lposm0 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 lenjcu1k czouh8 3wq /ff35b)b: r m4ep-vgth 20.0 cm and one diverging with focal length arhzebom 3 vuu1f43qpfwj:c5k-b r8 )c/e 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 focal(sf,.l/ ibnpa 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. Whaj 89tgybdg/4gl (*;hh*rcbz/kv dr,r t is the focal length if n 4brh/vh(d , *rzg8y/d rlkcbt9*g;jg = 1.52?    cm

  Both surfaces of a double o:y-hexqfe-,j 2ptwd/ kp/r 0 convex lens have radii of 31.0 cm. If the focal length is 28.9 cm, tw r 2ph0jqkyxo-p/ -e,/:dfewhat is the index of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm. What is the.(rby97:m 95i zl6 apsxvfhic radius of the concave surfahi6 az5ycr( i9:7xps .fmlvb9ce?    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat surface and the yfa .u i579grtother has R = -18.4 cm. What is thefi9.7at5r gy u focal length?    cm

  A symmetric double convex lens with a focal lengtvipws:; wn*paid3b. w(i 1d+xh of 25.0 cm is to be made from glass with an index of refraction of nwida; +dp xw.:isvp 1i*(wb31.52. What should be the radius of curvature for each surface?    cm

  A prescription for a hpp2dkj 9y86ondxdxn 8-52 becorrective lens calls for +1.50D. The lensmaker grinds the lens from a “blank” with n=1.52ohx6xkn -b9 2dd8p5 jdep8ny6 and a preformed convex front surface 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 in:eomnn( m,pe/ (Fig. Below). You stand 1.5 m away from one of t/o(ee :, mpmnnhese mirrors and look 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. Wb mjl53nw/(n 9(vt hrpe measure the width (x=5.50m) and then note that the bottom edge of the pool is just visible at an angle of 5(n lrvtw9n(b3/jphm 14.0$^{\circ}\,$ above the horizontal as shown in (Fig. Below). Calculate the depth of the pool.    m

  The critical angle of a certain pieo;k ncm4 3a4ggce 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 5pemsjz 6 t (xj7-z;hpof a spherical mirror. Specify what6-zhe5tz ps7jj ; p(xm 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 mirrors so they form a 90mp9bb m 3:-:v:mmvlra$^{\circ}\,$ angle as in (Fig. Below). When you look into this double mirror, you see yourself as others see you, instead of reversed as in a single mirror. Make a careful ray diagram to show how this occurs.

Show analytically that a diverging lens can never form a real u0 pbolt3mi(24h ylo,5qj i)nrs:z *eimage of a real object. Can you describe a situation in wh4elm: *bhy ( i, 2zsolqp0 no)3iutr5jich a diverging lens can form a real image?

  Each student in a physics lab i ke :r9bac*2f i-ffdoeq:q9*cs 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 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 youb 9r:9kqf-id*2q*eaef: f cocr response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of vcu7w8ge w85la 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 cylindrical.*yx,imp 3 v)zri- qcz;yb-ib 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 plaw k h75akb.z7p9zglu7;nfh2p ced 33 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 co4 bcm8-d9hvbk nverging lens of focal length f, and a white screen for viewing the image is on the opposite si8mdkb4 bhv -c9de. 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 image is p h8.knqh;ggd)q a*y 4projected 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, hodk)g8g ; h.qn4 aqh*pyw wide will the picture be on the screen? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (picture size 7bto g/sm3 tf/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 projector. What focal-lemtogs/7/ fb3t ngth lens should be used if the image is to cover the screen?    cm

Show analytically that th rezz1 t9ikvu 2/9sjcp4fa3 f5e image formed by a converging lens is real and inverted if the object is beyond the focal pointf19ki sa 3zjr2pe549utc v zf/ $(d_0>f),$ 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 picture(oo5do6f *4yh2 habwqb ldh*gl5dc(. s of her at home. She 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 lens was 210 mm. How far away from the subject was the r6(qalhhl(ocoo2y5bg 5*4hd d.fw * db eporter standing?    m

  How large is the image of the Sun o5yai/8e6 ,agp 8pxdjq( luz6b n film 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.k fok/wfdvj1l5 ks,-; 20 cm in front of that lens (on the same side as the object). What typ vlwd skjo, -/15fk;fke of lens is this, and what is its focal length? Is the image real or virtual?    cm (diverging)  ----待选择----virtualreal 
(b) If the image were located, instead, 41.5 cm in front of the lens, what type of lens would it be and what focal length would it have?    cm (converging)

  When an object is placed 60.0 cmr:x+i sp( y77 di -1r ;l jqfkbdy3ml2n.kkm1g from a certain converging 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 len1lqkinp(kb jl;d dxs2fr+ -:yk7 ryi. 1gm7 m3s. Find the focal length of this lens.    cm