What would be the appeap l9 bgzygi5,pk96* hrrance of the Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fleet in the harbor of Syra4 +nu ph(b*f wlq lhv5s)xpd1+cuse by focusing the rays of the Sun with a huge spherical miu* qhp5svhb1++wx dlpfn) (l4rror. Is this reasonable?

Although a plane mirror appears to reverse left and right, iamyouf 5j(i 8ri*,yf; t doesn’t reverse up and down. Explain.r 5amf ;y f,*iju(8iyo

If a concave mirror produces a real image-n csicb . .gl3uvn65na- 9eye, is the image necessarily inverted? Explai-ev9. .bcusl5n3y6 n icage-n n.

An object is placed along the principal axis of a spherical mirror. The magnia0jzbb -g;- w/zql cm5ficati/mbzcwq 0 ljb; a-g-z5on of the object is -3.0 Is the image real or virtual, inverted or upright? Is the mirror concave or convex? On which side of the mirror is the image located?

Using the rules for the three rays di u4t mzh+v:4wgscussed with reference to (Fig. Below a), draw ray 2 for (Fig. Bv+zt4 h: g4mwuelow b).
(a)
(b)

What is the focal length oa2:jjjw2w)+ai 0s m htf a plane mirror? What is the magnification of a plane mirror?jm:tjaw2j wi sa)+ 02h

When you look at the Moon’s reflection from a ripp4e2x 5d+ m-pk)i9a2wzotv0 : sare woily sea, it appears elongated . Exm252)e a oi0awz4kpv dx wir:os -te9+plain.

What is the angle of refraction when a light ray meet0;juc (ohc4mhv o04 yfs the boundary between two materials perpendiculo;cmvyo jh(u4 00 hf4carly?

How might you determine the speed of light in a solid, rectvil2o+2 d7i phangular, transparent object?l2+o 7phivid2

When you look down into as/ ok7q/ xc1fy swimming pool or a lake, are you likely to underestimate or overestimate its depth? Explain. How does the apparent depth vary with the viewing angle? (Use ray diagrams.yc //sxokqf1 7)

Draw a ray diagram to show why aeb(okv:os4. vj d lj3- stick looks bent when part of it is under water (F .jev:vjdl-(3k boos4ig. Below).

Your eye looks into an aquarium and vie rp x uw3,5n)njr/hxf7y9hz2c ws a fish inside. One ray of light that emerges from the tank is shown in (Fig. Below), as well as the apparent position of the fish. In the drawing, indicate the approximate position of the actual fish. Brieflr2,/ fzunh cj95)3pxyhnwx7 ry justify your answer.

How can you “see” a round drop of water on a table even though tl9:jan8w8p 03 ajl zn9whr -qhhe water is transh38q9rll n w-nz:hjj 0w9a8pa parent and colorless?

When you look up at an object in air from beneath the surface iwju7x-1:9uvcb,m b2h ,rt/wts lz 0yvn a swimming pool, does the object appear to be the same size as,t :-cv7 uwu1,wsltvjrm bz2xh0y/ b9 when you see it directly in air? Explain.

How can a spherical mirror have a negativy65mt u.rwov /e object distance?

Light rays from staracxex w7z.gz 9f0+j 7os (including our Sun) always bend toward the vertical direction as they pass through the Earth’s a x e7cgfz.aw0o9 xj+7ztmosphere.
(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 sha(v ogx/p e:q -2yopno,rp image of an object very:p ,-q(n oogopv/ yx2e far away?

What type of mirror is shown in (Fig. Below)? stk 5 )ue7iqg30brhz/Explain.

A photographer moves closer to his subject and then refocuses. Does the camei 1,cjd+hita5 ra lens move farther froa,i i1hjc+5 tdm or closer to the film? Explain.

Can a diverging lens form a real image unv6s ;(tb+fr vnbk/0s tder any circumstances? Explain.

Use ray diagrams to show that a real image formed by a ,-*; f; qz id-irih b4ppg*bvsthin lens is always inverted, whereas a virtual image is always upright if the object is real;zh-qp i-d bps **ib;,vi fr4g.

Light rays are said to be “reversib 1(f hq-vqdqz6*f1 q5p6vha fhgv o0.m.:h lbdle.” Is this consistent with the thin lens equati1 5*qdlv0dq 61h vp:q( q.boh.z mf-ghvfhf6aon? Explain.

Can real images be projected on a screen? Can virtual images? Can either gl-b,wii, t6 s ut3nt-be photographed? Discuss caref6uwtt l,-i-,i3 t gbsnully.

A thin converging lens is moved closer tu; qr5dpm c1 v96wu-bto a nearby object. Does the real image form1-95q w;m 6vutrc bdpued change
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of refraction n = 1.w. vki 98aoblr5ji;m +30 In air, it is a converging lens. Will it still be a converging lenw9.b li 5vm8;jo+rikas if placed in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the atsu5vj q,76 xdir stands facing a converging lens. If the nose and the tail are each focused on a screen in turn, whi xqtju5s,v d67ch will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands fati40agaq dhfcy7hs:)7xo0s - cing a converging lens. Under what circumstances (if any) would the image of the nose be virtual and the image of tcs0s0fhadi a q)-4: xogy7h7the tail be real? Where would the image of the rest of the cat be?

Why, in Example 13, must the converging lens have a shh u,n b/:put2oi wv 8d:np7te7orter focal length than the diverging lens if the latter’s focal length is to be determined by combini:i /woe7udp t8b:vp 2hn n7tu,ng them?

Explain how you could have a virozc4-2ds fsp4h17yq* w igtuc /mu3/7wgg8p ftual object.

  An unsymmetrical lens (say, planoconvex)c.m(db2 ax n 7;k-d3x ttys4svmd3u7g forms an image of a nearby object. Does the image point change if the mc- .ybnx7dtkt g(msx3 vd4a7 32d;su lens is turned around? ----待选择----yesno 

The thicker a double convex lens is in the eoaylq*ou ( xq9s73zo + nz1)ncenter as compared to its edges, the shorter its f oeq n*9n7qyoz3s1a( )xulzo+ocal length for a given lens diameter. Explain.

Consider two converging lenses separated by some dista lvuzgx srxw)-- za-r9 0cl/w/nce. An object is placed so that the image from the first lens lies exactly at )lrag/wcuwv r0 -xx-ls z/-9 zthe 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 b1g b:tjecq 6/of yourself as you look at your image in a flat mirror 2.5 m away. For w be:t/g 1bqc6jhat distance should the camera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mirror, you see the same amount kn2z)zitk5 fc8/w-idof your body whether you are close to the mirror or far away. (Try it and see.) Use ray diagrams to show whyf/ zki zdtn)2 5c8w-ik this should be true.

  Two mirrors meet at a 128xqbg+qjwodv ) u14 w35$^{\circ}\,$ 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 stand t s55j us*hj:rwt74gis 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 nearesjjh:uttgws5 s*74 5i rt point on the floor that can be seen reflected in the mirror?    cm

  Suppose you are 90 cm from a plane mirror. 8heg+wibjt u dk9)3wa8 /t.ixsqf;n*What area of the mirror is used to reflect the ra)d x3we hksaq9/i+tb .ju fi8g*n ;8wtys 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 atu p*a(d ( ,:.yitglebt xry9y; an angle $\phi$. a single ray reflected successively from both mirrors is deflected through an angle of $2\phi$ independent of the incident angle. Assume $\phi<90^{\circ}$ and that only two reflections, one from each mirror, take place.

  A solar cooker, really a concave mirrob-w*/ 3v *s(ilyddtr ir pointed at the Sun, focuses the Sun’s rays 18.0 cm in front of the m w( *t-sbii 3dyvrd/l*irror. What is the radius of the spherical surface from which the mirror was made?    cm

  How far from a concave mirror (radius 23.0 cm) must an object be placed if itsdm0 0v;sginp ko5-i)s image is sgv05p0k -oiinm) d ;sto be at infinity?    cm

  If you look at yourselfj iw4:/l(hiv d 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 virt/h4iij(v d w:lual? 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 any person who tb:x+5 z9uzzkstands 1.4 m in front of it. If the image is t 9bkzuz5: tzx+hree times the person’s height, what is the radius of curvature?    cm

  A dentist wants a smk wgi 8352wgokall mirror 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 9 mfok z3-y-/8ufc nogbehind you that are smaller than they would be if the mirror weren8oo9zffg-uc-mk /y 3 flat. Are the mirrors concave or convex? What is a mirror’s radius of curvature if cars 20.0 m away appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is placed 2--5* wv1gxdew t/mx q rbz1(zu0.0 cm from a convex mirror of radius of/t1 qd g*15 vbw-uw(xx-zmerz curvature 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 mirror in a*tcj ieimc 5gh, .h205ha-cco store. You estimate the height of your image to be half of your actual height. Estimate the radius of curvature of the mirror.e5-h0,jto2c5 .imah h gi*ccc    m

  (a) Where should an object bwqqq74,kg3wtz7m9g)oo o p8 xe placed in front of a concave mirror so that it produces an image g7qwqwm8x3o4k7)o, t gqopz 9at 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 txgu*j-5 gzw2bx k g,b5ree is virtual and very small when viewed in a curved mirwg,bjbx k5xg z-25*ug ror. The image appears to be 18.0 cm behind the mirror. What kind of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techn n+db(pr1-.m2qu n*s ,rmd:ri;rir cy iques,
(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 theiqhva dh:s5mj 8h2 0ms6fa9(n.;fq c a 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 s0jhwc6uqv 11 )ztw1 rphow that the mirror equation, Eq. 23–2, is valid for a convex mirror as long as f is consideredc0)qr uh61 wpv1ztj1w negative.

  The magnification of a convex mirror imccz *p g)6t(ts $+0.65\times$ 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 c o)e 455fehkarm in front of a spherical mirror. It is desired to produce a virtual image that isohef 5k5ar4e) upright and 3.5 cm tall.
(a) What type of mirror should be used?  ----待选择----convex mirrorconcave mirror 
(b) Where is the image located?    cm behind the surface
(c) What is the focal length of the mirror? $f$ =    cm
(d) What is the radius of curvature of the mirror? r =    cm

  A shaving/makeup mirror is designed to magnify your face by a factor lovt+l-r6 j9*e;xqkg3r(y qsof 1.33 when your face i *xkt3vlr 9; ls(-y6+g qjrqoes placed 20.0 cm in front of it.
(a) What type of mirror is it?  ----待选择----convex mirrorconcave mirror 
(b) Describe the type of image that it makes of your face.
(c) Calculate the required radius of curvature for the mirror. r =    cm

  What is the speed of light in )m*o . sfcex;p
(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 0z4ogr:8qrhseh6uh: d )0tiis $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain substance is 89% of its value inhaz k f+ri;y49(jkwvgo y,v+; water. What is th g+(;k,kofv 9z j;+yh y4rwaive index of refraction of this substance? n =   

  A flashlight beam strikes the surface of a pane of glass (n = rpvplws27*b8 , qynj(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 froml/tl-gf9snmr 2vs+ :dd 6jmjsl q)92c 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 u)cney 9yz oh r/n8ald+8 m:tg0nderwater spotlight exits the water at an angle of 66y)ty a/e0z g9rd8c mno n8hl+:.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 m3 ml:phl(p5x make a 31.0$^{\circ}\,$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?    $^{\circ}\,$

  An aquarium filled with water has flat glass sides whose i9ot5*s vfjj7vai 9a (x1gkq(pndex of refraction is 1.52. A beam of light from outside t vqptag va1 x5k9ijo(*7fs(9jhe aquarium 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 watchman shines a narrow beoy jfl4 74*smeam 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 4*lf 4yoej7msthe 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 equilatyeo(ifqsj i3tk 2:3ju11oqn. eral glass prism at a 45.0$^{\circ}\,$ angle to one face, (Fig. Below). Calculate the angle at which light emerges from the opposite face. Assume that n = 1.58.    $^{\circ}\,$ from the normal

  A beam of light in air strikes a slab of glass (n = 1.52) and is partially oc dv)z4+6zmxh9x:j m reflected and partially refracted. Fi6cmo9zxj4)zxv md+ :h nd the angle of incidence if the angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam incident on a uniform layer of transparenm76td qy h8 r(amb6ory,ey 2g0t material, as in (Fig. Bo btq( mr6hmy,8 6ey7dga20yrelow), the direction 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 index of refractibjc357,ggi 8 ; .vok7cwculba04cn qhon n as in (Fig. Belowglg c5w ;c0jvc3i,uabc 4o7qnkb 87h.). 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 c82 kjt56xma4vgnfc- between water and Lucite? To be totally internally reflected, the light mx 4gnjmvac8tk2 c65 f-ust start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain f:jik1 md89 .vmkp1ooliquid–air surface is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in aq9yqq ;j1yt) mi9.t cx pool of water from a depth of 62.0 cm. Where must it strike the air–water interface, relative to the spot directly above it, in order that the light.tc9) qqj ; i9yqtmy1x does not exit the water?    cm

  A beam of light is emitted 8.0 cm beneath thrgneybn43g.29n b tn-- +zpxee 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 index of refraction ofnn- 9pnn + 4xebg. 2yberzgt3- the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left ) m78)h)mrrhytlfyu;(odc aw38 n, jqface 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 4em3 2.8bjc9mr yapabj 1l4l xan optic fiber as shown in (Fig. Below). Show that we can guarantee total internal reflection at the side surface of the materia m3pce8a1maxb4j 4ly 2jr.bl9l (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 minimumt q h lfpt)20pde- p(g;g/b2ao60lmnv index of refraction for a glass or plastic prism to be used in bin geld q6bom0)/p0;t(vln -2fgh 2 pptaoculars (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 located 3upt7 r b.*ymn78.0 mm behind a 65.0-mm-focal-length converging lens. Find then.utp* myrb 37 object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.5 cm behind a lens. erkaf8g35z5 ; c3wljz
(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 li)m- ddnspz)* fght from an object 2.75 m away as an image 48.3 cm on the other side of the lens. What type of lens is it and what is its focal length? pdz)d) m*f-snIs 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-fob.bah +67we:o6jc) oh8 m zpzvcal-length lens? P =    D  ----待选择----converging diverging 
(b) What is the focal length of a lens? $f$ =    cm  ----待选择----converging diverging 
(c) Are these lenses converging or diverging?

  A stamp collector uses a converging lens with focal length 24 cm ou3p;:d thdx*to view a stamp 18 cm in front of hx3o pt:*ud;dthe 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 thvx4p*2djcz5k e position, type, and h5d zjk *42pvcxeight of the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to foc75ko nap(/mey3a2nz c yc 83lous an image on the film of a camera. The maximum distance allowed betck53m/ cln 3y7(oao8aen2zyp ween the lens and the film plane is 120 mm.
(a) How far ahead of the film should the lens be if the object to be photographed is 10.0 m away?    mm
(b) 3.0 m away?    mm
(c) 1.0 m away?    mm
(d) What is the closest object this lens could photograph sharply?    mm

  It is desired to magn6xw/8;*e , jtrvudvehify reading material by a factor of 2.5× when a book is placed 8.0 cm terewud 8,h j6x; v*v/behind a lens.
(a) Draw a ray diagram and describe the type of image this would be.  ----待选择----realvirtual 
(b) What type of lens is needed?  ----待选择----converging lensdiverging lens 
(c) What is the power of the lens in diopters? P =    D

  An object is located 1.5 m from an 8.0-D lens. By how much does the image move/w uvqp e)wq23 if tqw/)3 ewpqv u2he object is moved
(a) 1.0 m closer to the lens,    cm away from the lens
(b) 1.0 m farther from the lens?    cm cm toward the lens

  How far from a converging lens o)30h ebhayt:yv ; lbzv )2a)k +0zuxjwith a focal length of 25 cm should an object be placed to produce a real image wh2bzh)3avo )el0 0:xha yk tyzj u;v+b)ich is the same size as the object?    cm

  (a) How far from a 50.0hsz)u/y l(fr5 -mm-focal-length lens must an object be placed if its image is to be magnified 2.00×fus5y) zh(/lr 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 ckc5nt.f5 jomqcl8x./ xs8 7n placed if its image nx8 .s5cjcno.qm k cx58tf /l7is to be magnified 2.00× and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm (formed by some other piece of optics).]

  (a) A 2.00-cm-high insect is 1.20 m from a 135-mm-focal-lenql7y/:+ wph blw) ppt.gth lens. Where is the image, how high is it, and what tylp t w7/by.)hqp +:wplpe is it?
$d_i$ =    mm (real,behind the lens) $h_1$ =    cm (inverted)
(b) What if $f=-135\mathrm{~mm}$?
$d_i$ =    mm (virtual,in front of the lens)
$h_1$ =    cm (upright)

  How far apart are an object and an image formed by a 75-c ec1rjju d f1sx0baji5df01qctf+ j)828pb :um-focal-length converging lens if the image is 2.5× larger than the object and is real18 cux fq sb:20+fujpd1e0 ifaj 5jrd b8j)1ct?    m

  A bright object and a viewing screen are separatehn0s ljds *4e, 3+-wb.a;dliu4qvw hmd by a distance of 66.0 cm. At 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 wbd .w +;euss* 0i4,-ajlmhdn43qv lhdraw a diagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length converging lenses g)z) mf/z ;-kqsx;uhkare placed 16.5 cm apart. An object is placed 36.0 cm in front of one lens. sh z-kuk)g);m/ fxz;q Where will the final image formed by the second lens be located? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens wity,ta, s9muog* h $f=-31.5\mathrm{~cm}$ 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 converginh:zot46)nq2lnp or. bu/o 3azg lens is 21.0 cm behind a diverging lens. Parallel light strikes the diverg r2o4on.aqb 3to6p z)hlnu: z/ing lens. After passing through the converging lens, the light is again parallel. What is the focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Exam/3 .jmiehk s1j3)ov t0vv1ptople 23–12 are now placed only 20.0 cm apart. The objec1jh) tkivvpeto3. j 30m1so/ vt is still 60.0 cm in front of the first lens as in (Fig. Below). In this case, determine
(a) the position of the final image,    cm
(b) the overall magnification.    cm
(c) Sketch the ray diagram for this system.

  Two converging lenses are placed 30.0 hjvh bl1bz6w 32p (r.rcm apart. The focal length of the lens on the right is 20.0 cm, and the focal length of the lens on the left is 15.0 cm. An object is placed to the left of the 15.0-cm-focal-length lens. A b2h.( z r 6bvrjphlw13final 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 (g z+y22 oac2pma.ggc ofm)e(converging lens with a focal length of 18 cm. An object is placed 33 cm to the left of the converging lena m222gcg(fay(m +)z.oc g poes.
(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 20g3 ) fji epfxf* t(xhe5)t*4fa.0 cm and one diverging with focal length are placed 25.0 cm apart. An object is pgh att3x5)**fjpe)i4eff (f xlaced 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 focaazf 6s2ltep;p qa6kp c7/cg0z; m8jj (l 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 01(kkzn8gf /j8mg hdnradii of 34.2 cm and 23.8 cm. What is the focal mkz 0nh/j1gnd 8k g8f(length if n = 1.52?    cm

  Both surfaces of a doubis6dl vg 85g:ir-lgh9le convex lens have radii of 31.0 cm. If the focal length is 28.9 cm, what-ggii9:dl v s g6l8hr5 is the index of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm- 0sn(upgn rl 7nub870na -jtd. What is the radius of the concln 7unsab-gj(7 ndup 8n r0-0tave surface?    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat surface and tkxq:/afyuqay (/ :;qhb,(-jwjcywl ,he other has y :, y lqb-jwyf(c(/,jaq x/:khuq wa;R = -18.4 cm. What is the focal length?    cm

  A symmetric double convex lens with a focal length of 25.0 cm is to begu9if*vm607 xk o5t lj7xwm-)g fs0ln made from glass with an index of refraction of 1.52. What should be the radius of curvature for each sln0u6 gxxl )ifgt7wj9mko70mvf5s* -urface?    cm

  A prescription for a ;. o 5ocd97x:vchafsccorrective 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. What should ;xho9c:7c .cvf a5sd obe the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m 0/ w5t- /txxh d0vxm/qxk lal)gs96tmapart as in (Fig. Below). You stand 1.5 m away from onel5qm avmxx-l 0kt)/t9sx/gw6 x0thd/ of these 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 thc 3:ttm im/hk+e depth of a swimming pool filled with water. We measure the width (x=5.50hmct+ m t:/3kim) and then note that the bottom edge of the pool is just visible at an angle of 14.0$^{\circ}\,$ above the horizontal as shown in (Fig. Below). Calculate the depth of the pool.    m

  The critical angle of a certain piece of pla*f1pk2s mb,15 nr1m za ykqt-rstic 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 cavqs5c98*dk gk;lw4zn n be considered a limiting case of a spherical mirror. Specify what this limit is ; qcw*s5l4vdk8 gnzk9.
(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 as.6z g gcaa/wg/r tefw19kg-* 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 lensc;38 mucy mn7xemzk, 3dr.g8762 uag0dpfhjr can never form a real image of a real object. Can you describe a situation in which a diverging lens can form a rczrhmx7ym3 mu ddepn6rkc8 8 af;.7g0 j,2u3geal image?

  Each student in a physics lab is assig1zyg+k 5hjnyc7 w /ej2ned to find the location where a bright object may be placed in order that a concave mirror with radius of curvature r = 40 /y1 jjng+k72zyew hc5cm 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 your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of axf,5uyik2g)v 8b ok) i 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 glass rod a-vh5y 8m;vkg$(n=1.54)$ 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 st yx0z lzq;wsakq n;(( j 1tgaa)f:-4converging 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 o9sc; dj*sr6.mqm da r7n one side of a converging lens of focal length f, and a white screen s mr ;r7jdscm 6d*9.aqfor 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 image is projei mjwk5q,ne/m fw: g8/cted 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 thef/wjmk5/ m nig8:, qew 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 2+ iwpws. f,uo3n r(6qo4 by 36 mm) is to be projected on a screen 1.80 m by 2.70 m placed 7.50 m f.+ o nrqw(sp6,wo uf3irom the projector. What focal-length lens should be used if the image is to cover the screen?    cm

Show analytically that the image formed by a converging lens inel ju+jnk4+ 1/domm 2s real and inverted in+2/u+jmm1 dk l4 ejnof 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 picfj8rym+- d/) voi r6qir)/bqktures of her at home. She claims the reporter was trespassing6 rrd-q)ir)jf /qo/+ybmkv8i. 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 reporter standing?    m

  How large is the image of the Sun on film used in a camera withpd(kk(rs /6vdp qd1j,jo*u4p
(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 8.20 cm in front of t ha*4kld b0j7ihat lens (7a*jih 4lkb0 don the same side as the object). What type 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 cm from a certain converging lens, it forms a real8a c1cwe/lh,rz a 2(vu image. When the object is moved to 40.0 cm from the lens, the image moves 10.0 cm farther from the lens. Find the focal length of this lea,2 /hvwec1cu zl(a8rns.    cm