What would be the appearac.gw-qpr n +-knce of the Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman f3l )d)ovz b.hclru5c32n.c sw leet in the harbor of Syracuse by focusing the rays of the Sun with a huz5cbs3 h2cow) .3dluv n )r.clge spherical mirror. Is this reasonable?

Although a plane mirror appears to reverssh6 yms2j u6q2e left and right, it doesn’t reverse up and down.u66hm y ssq22j Explain.

If a concave mirror pr ,5x7e/dv (n 9inq9w.lbm jki m,dfs);w6mleioduces a real image, is the image necessarily inverted? Expla d5k;i 96,wdxmmmii)n7nqje . lsw(v, el9 bf/in.

An object is placed along the principal axislsnyj,s j, g(gf7i46d of a spherical mirror. The magnification of the object is,4 j,76jglsd g(nyfis -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 dis-xp)d ps1 3mx qn-n66a d8b8fbxqri 3scussed with reference to (Fig. Below a), drawsbnpx d38i-m183qxqa nd prb-f x)66s ray 2 for (Fig. Below b).
(a)
(b)

What is the focal length of a plane mirrorazd(3k3*yxvihui x) * ? What is the magnification of a plane mirzx a(33d*iu)y kivx h*ror?

When you look at the Moon’s reflection f8xtdtf),9lmbeo+ x,k (m6xberom a ripply sea, it appears elongated . Expla)(t9bmxx8,m be+k,l6x e otfdin.

What is the angle of refraction when a light fc6stq b; y sfsf(gcb/1mt**3ray meets the boundary between two materials perpeysf/s *fqtm ;6*csbc1b( gt3f ndicularly?

How might you determine t(bld1x u lggqo ,v0z(0b /n-onhe speed of light in a solid, rectangular, transparent ob bun ovg0, l1x(/0oblzgn (d-qject?

When you look down into a swimming pool or kv*x5f/)fo b ja lake, are you likely to underestimate or overestimate its depth? Explain. How does the apparent depth vary with the viewing angle? (Ufo* f/)vxk 5bjse ray diagrams.)

Draw a ray diagram to show why a stick looks bent when part of it 2yz ; z/uf+:u.auq oeyis under water (Fig. Below)euuqzy2.o z:fu+/; a y.

Your eye looks into an aquarium and views a fish insi6eqhm-u s( m7ic 1b-vladqu:* de. One ray of light that emerges from the tanu i s-evmqclb:(d *7a61muqh-k 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 table even though the1yannncc8 6e*zrm2i -l4iwa 3 water is transparent and colorleca4n cl1n 6 2na*zy3- iwirm8ess?

When you look up at an objecf g:w 6ebp+5nxd(1q yct in air from beneath the surface in a swimming pool, does the object appear to be the same siz:(cdbfg5w y pex6n+1 qe as when you see it directly in air? Explain.

How can a spherical mirror ha0wuc0kld+/ 7mctt2ba ve a negative object distance?

Light rays from stars (including our Sun) always bend toward the verticssh7./(aoc5 hf hl*y 62v3ur lm z4apfal direction as they pass through the Earth’s atmosphere.la h7y.shp 6/usha 3rl(f5of*c4v2zm
(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 7ygj-poa9h 04- zzsvfhk,p7g to make a sharp image of an object v, 94 g0pz7jfsyh7ha-pkzv - ogery far away?

What type of mirror is shown in (Fig. Bel sv1i8yb9cdatn/ qh:+,i hhv-ow)? Explain.

A photographer moves closer to his sqvx uw y sp;ewysl027v3543m iubject and then refocuses. Does the camera lens l02swvywq 3v;7yeps3 i4mxu 5move farther from or closer to the film? Explain.

Can a diverging lens form a real image under any circumstances? Explaicz+w q5i o9, y7dnsnvo n2-rb5rm4v 9un.

Use ray diagrams to show thbc0 4ru 5pi7xyat a real image formed by a thin lens is always inverted, whereas a virtual image is always upright ip0 bux 547yrcif the object is real.

Light rays are said to be “reversible.” Is this consistent with the thin 0tyc q59d aa3vlens equati0a c3dv 9tqya5on? Explain.

Can real images be projected on a screen? Can virtualnvq(tn1h xrs 4cd 33z; images? Can either be photographed? Discuss carefullyq(rxc14snztv 33nh d ;.

A thin converging lens is moved closer to a nye:9 l xxt/xogv/t /) l4wpsz)earby object. Does the real image fo)x: zvlgwe x)lt/oy/4txp / 9srmed change
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a lzjp)b, .)oyzmaterial with an index of refraction n = 1.30 In air, it is a converging lens. Will it still be a converging lens izp ),l) oj.zybf placed in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands facingn;7boe/ f os8n a converging lens. If the nose and thnb;eo n87o fs/e tail are each focused on a screen in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail inszu 15emaw16py4.) tqiqyo ,c the air stands facing a converging lens. Under what circumstances (if any) would the image of the nose be virtual and the image oe1q i yp1.mqw5tzo6s)u,c y a4f the tail be real? Where would the image of the rest of the cat be?

Why, in Example 13, must the converging lens have a shortcxnz:egr, bt.b i ;w 8jra6q 6:c:3ylger focal length than the diverging lens if the latter’s focal length is to be determagrigz:rjnw6b l8cte .,x;q6:: y bc3ined by combining them?

Explain how you could have33kt;he- b czkd:h9hx a virtual object.

  An unsymmetrical lens (say, planoconvex) forms an image of a+e 0; . (iujno;jufmft nearby object. Doesi ; f+;u.o0njtuejf (m the image point change if the lens is turned around? ----待选择----yesno 

The thicker a double convex lens is inn 8 )lblfcr7m0 the center as compared to its edges, the shorter its focal length for a given lens diamet r flc78mnbl)0er. Explain.

Consider two converging lenses separated by some distance. An object is place:by1)qdp zq.vkc t cpht0 1(/xd so that the imagepy)q dt pc(:b1/hv. xzk1 tq0c 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 photograp dc1lyn ;1v8pchl0+ hih of yourself as you look at your image in a flat mirror 2.5 m lc h1l+vd0iy8n; ph1caway. For what distance should the camera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mirror, you see the same amou uzlckxnl4+/ ur;1 f0(;jdxku nt of your body whether you are close to the mirror or far away. (Try it and ser4lx /fj;kuzxc(1ld;+kuu 0 n e.) Use ray diagrams to show why this should be true.

  Two mirrors meet at a 1jb4*6i ;aqjvbivyx 2/6e w,d h35$^{\circ}\,$ 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 1.6polgzre 2) 24x8 m above the 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 mirror24eolrx2p g)z 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 pw,egi0x4xz1 of the mirror is used to reflect the rays entering one eyewg1,x4e0 z ipx 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 o7f vrlyxj-c s-5 kf 0v/)gu30-raciemeet at an angle $\phi$. a single ray reflected successively from both mirrors is deflected through an angle of $2\phi$ independent of the incident angle. Assume $\phi<90^{\circ}$ and that only two reflections, one from each mirror, take place.

  A solar cooker, really a concave .hmnkz/2/qkq r8r vs) mirror pointed at the Sun, focuses the Sun’s rays mvkn 2h).kqs r/8 r/qz18.0 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 mirror (radhqx6lap7 tsa( 0(jzs5et36 hri2x st p x:8d4nius 23.0 cm) must an object be placed if its image i(ax638hrhxpx l0s(jtps2id st n 6:zqt 4ae5 7s to be at infinity?    cm

  If you look at yourself in a shiny Christmas treg*f9in g+kyc zu;s qw7)db (3pe ball with a diameter of 9.0 cm when your face is 30.0 cm away from it, where is y f7n ip* zugcqbk)9y3dw+;sg( our 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 any person who stands 16ilz of4 r7;,govlbkj qab)9 8ns4z1h.4 m in front of it. If ka,j 4 zv7 frb l1b)9o4;hgqol86iz snthe image is three times the person’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror thaq r.tprb *o46ot, 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 prod * e0fyda0t4tha(/tavuce images of cars behind you that are smaller than they would be if the mirror were flat. Are the mirrors concave or convex? What is a mirror’s radius of curvature if cars 20.0 m away appear 0.33× their norma/ahyt aav4 t0f0* de(tl size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is placed 20.0 cm fro1)iidzdpy.q- 0zj)n ev: fg.q m a convex mirror of radius of curvature 20p .ydz1jid)).vqg i0znefq: - .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 secur2 (iky3 76cd,uq8 o55t wdfdfgaru-usnj2* j bity mirror in a store. You estimate the height of your image to be half of your actual height. Estimate the rad*tq cg,5 u a d722b5dnfri-od3 u wuskf8j(jy6ius of curvature of the mirror.    m

  (a) Where should an object be place shu8b lu36ei)d in front of a concave mirror so that it produces an image at the same location ass8e h6b3ul u)i the object?
(b) Is the image real or virtual?  ----待选择----realvirtual 
(c) Is the image inverted or upright?  ----待选择----invertedupright 
(d) What is the magnification of the image?   

  The image of a distant tree is virtual and very small g /+w,ohqko m(xar(-fwhen viewed in a curved mirror. The image appears to be 18.0 cm behind the mirror. What kind of mirror is it, and what is its radiawro ,-((g+q/xokmhf us of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different tenjb;*/d*no- aiau al 5e mi5/jchniques,
(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 magnificatio 6vm6s,;vjezt h1g wpk9e67+je;yr yvn 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 q wl6 3hiume(q37b+cp o;ny.wmirror equation, Eq. 23–2, is valid for a convex mirror asl( nq3+3oyubm7e6cwwiq. ;hp long as f is considered negative.

  The magnification of a convex mirror kghh (pq,b;9b dn.+ gfis $+0.65\times$ for objects 2.2 m from the mirror. What is the focal length of this mirror? $\theta_2$ =    $^{\circ}\,$

  A 4.5-cm-tall object is placed 28 cm in front of a spb- jz :ju.0fl(vb pj0fherical mirror. It is desired to produce a virtual image that is upright andf blfu p0.j(z- j0vb:j 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 of 1.; p5regf( tk5oo8 wr1l33 when your face is placed 20.0 cm in front of it. ( rp1 5fotrwg5;o l8ke
(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 lig4/ kjteg 6):egsypb ,iht 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 in ice k+ )yx wh/nd+his $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a c 4bai p xrmb942i0gv)certain substance is 89% of its value in water. What is the index obv9m 2pgac4x biir40) f refraction of this substance? n =   

  A flashlight beam strikes the surface of a pane of gz6 qb,juoi,n+yr+;ws lass (n = 1.58) at a 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashlight upward fr9k( ob:bz ;bgcom 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 underwater0el1rch*l6sb-pq l c 0 spotlight exits the water at an angle of 6q06r l lbsl*e0c h-c1p6.0$^{\circ}\,$ 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 se 3e(slsjj 1v,len to 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 indy5 a :jirs chd31gjd70oe9 2avex of refraction is 1.52. A beam of light from outside the aquar r0dy 2ehdjja975oa cg3sv:1i ium 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 shine-9gd1/ zwln jgs a narrow beam of light from his flashlight, 1.3 m above the water level, onto the surface of the water at a point 2.7 m from the edge of the pool (Fig. Below). Where does the spot of light hit the bottom of the pool, measured from tzwlj 91/n d-gghe wall beneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equilateral glass prism att 2e (yzjlb89v 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) +z 4z4oll,uok o5a-kq and is partially reflected and partio,qu-oa4z 4z k+ol kl5ally refracted. Find the angle of incidence if the angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a sqqlb+ d:k - rw)adxi;*x;w n3light beam incident on a uniform layer of transparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the incident beam, ik+*; l w-snrxqwi b) xqd3;:dandependent 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 qi 3gd s2dbi3edz3 kq23:hot2 refraction n as in (Fig. Below). Show that if the incidq gz:tbed 2hsq2i i3ddo23k33 ent 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 watef u 1s5v 3gzvo j7n4s/tv 5iyk.d5l,w6yp; oexr and Lucite? To be totally internally reflected, the ligt/k d vu vlv4z j37sy, swx15fp.ge6oiy 5no5;ht must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–axf+ hfe.c)m z6ir 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 mu7 /bivlln.tti0 c65sl9* dos est it strike the air–water interface, relative to the spot directly above it, in order that the lc7le5s/.lt6i9n*o 0stdli bv ight does not exit the water?    cm

  A beam of light is emitted 8.0 cm beneath the surface of a ln)9 3 csykc ;xmhrl3p0iquid and strikes the surface 7.0 cm from the point directly ah); x3 3msc9nclk0 yrpbove the source. If total internal reflection occurs, what can you say about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face of the prism in (Fig. Below) acay6b5ywv/c 8t,+ujv t 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 as shown in (Fig. Below). Sv2fh7l5nfd/ kqam0uot ;4c4p how 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, regardpt mv 0ucn27f/ lah do4f5k;4qless of the angle the light beam reflects back into the material at point a.

  (a) What is the minimum index of refraction for a glass or plastic dt1mh71wb fag5 (ye.kc 9j k3m13sc peprism to be used in binoculars (Fig. Below) so thathfj 11td (9 gac5s1w.emkckeb 7y33pm 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 locnfv j7+es a82yated 78.0 mm behind a 65.0-mm-focal-length converging lens. Find the object disnj2v8 syef7a+ tance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at, b*nv*i sxwn bl8,w47v j8eae a point 18.5 cm behind a lens.
(a) What kind of lens is it?  ----待选择----converging lensdiverging lens 
(b) What is its power in diopters? P =    D

  A certain lens focuses light from an object 2.75 m away as an imx92rd jyt8wj -r //ctgage 48.3 cm on the other side of the lens. What type of lens is it and what is tdcj-/wxt 8 /gr 9jyr2its focal length? Is the image real or virtual?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the power of a 20.5-cm-focal-+u c9vhrt(yf790 abrw 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 fo,j *x*t10vuefjumwnifei4j7d9 ( ,rr cal length 24 cm to view a stamp 18 cm in front of the j91*if7tu,0w,nm 4x djf rvr (euij*elens.
(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 3 *(fp8mn1bx jq s v/u;86j wvog-jasnobject 4.0 mm high. What are the position, type, and height of thenum-qv1o /jbj8n6fxw*gjp(3 ;vs8 sa image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to focuds y74c:dv3jmor+j fa/ 2gyaq:4oq9vs an image on the film of a camera. The maximum distance allowed between the lens and the film plane is 3 fg vjod7 j:+vcqsr4/a:yq42ydoa9m 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 ic9nsnm)q8 * d 4hhnqel *hb48a factor of 2.5× when a book is placed 8.08nh q)4me9bdn 8 lis4c*hnq*h cm behind a lens.
(a) Draw a ray diagram and describe the type of image this would be.  ----待选择----realvirtual 
(b) What type of lens is needed?  ----待选择----converging lensdiverging lens 
(c) What is the power of the lens in diopters? P =    D

  An object is located 1.5 m from an 8.0-D lens. By how much does the im7s 6hf/0i qd1:z0/ dr nflowcmage move if thcr:s0 7m oz/d fi lw6d/nqf01he 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 with a focal length of 25 cm should a+s4mcw*ke,j y n object be placed to producm+wj4ce y ks*,e a real image which is the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an obj8gsn mwt/hv .(4qkmm1ect be placed if its image is to .kwm1vsn4mhqg8 tm(/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 placed if its imajgw lsh--73wm ge is to be magnified 2.00 wwmgsj-37lh -× 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-l.:8.sq ,qfqgnq t0c-drjl g0dength lens. Where is the image, how high is it, and whafc.j-qqdn0g8: qdt,l g.r0s qt type is it?
$d_i$ =    mm (real,behind the lens) $h_1$ =    cm (inverted)
(b) What if $f=-135\mathrm{~mm}$?
$d_i$ =    mm (virtual,in front of the lens)
$h_1$ =    cm (upright)

  How far apart are an object and an image formed bywgv 8r/ p//n:ekenw+p a 75-cm-focal-length converging lens i8p w/r /pk:eegnvnw/ +f the image is 2.5× larger than the object and is real?    m

  A bright object and a viewin*x7z1njksj( : d, dyosg screen are separated 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 placed71 *joj kzdy,s xnsd:( 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 con6w any9y9u8 gba dr(tql r/l8a:f(mj6verging lenses are placed 16.5 cm apart. An object is placed 36.0 cm in front of one lens. Where will the final image formed by t 6/aaujl (68(qfn:y drtl9g 8brw9amyhe second lens be located? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens wit lq6:/c a.8/m2 vk2rauk g .phgeamc:hh $f=-31.5\mathrm{~cm}$ 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-lengthhv zstn8r,26e converging lens is 21.0 cm behind a diverging lens. Parallel vze8t2nh,r 6s light strikes the diverging 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 Exom9j,lhx5;ycgrgp g30.pis/ ample 23–12 are now placed only 20.0 cm apart. The object is still 60.0 cm in front of the fymj ,r9p.3hgsg cxp0/g oi5l; irst lens as in (Fig. Below). In this case, determine
(a) the position of the final image,    cm
(b) the overall magnification.    cm
(c) Sketch the ray diagram for this system.

  Two converging lenses are placed 30.0 cm apart. The focal length o g -+hc0ommv3ef the lens on the right is 20.0 cm, and the focal length of the lens on the left is 15.0 cm. An object is placed to the left of the 15.0-cm-focal-length lens. A final image from both lenses is inverted and located halfway between the two lenses. How far to the left of the 15.0-co vc3e0-g +mhmm-focal-length lens is the original object?    cm

  A diverging lens with a focal length ofwx evjr;13s )f is placed 12 cm to the right of a converging lens with a focal length of 18 cm. An object is placed 33 cm to the left of the converging lens.1 f3;vxewrs)j
(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 convergingk ys 9)vye-*gy with focal length 20.0 cm and one diverging with focal length are placed 25.0 cm apart. An ob*-g )yky9vse yject 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 leng1f:*-aryg2t md8w x i+5y chyfth $f_C$ 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 a. oxc,c* xhf npd90au,urf-u4nd 23.8 cm. What is the focal length if-p,xf o *d49 nxcauc 0.ru,hfu n = 1.52?    cm

  Both surfaces of a double convex lens have radii of 31.0 cm 2x mmioccy6 :zd*)n(m. If the focal length is 28.9 cm, what is the index of refraction of the lens matzon)c* i 6 ym2dc:(mxmerial?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm.ag; jx 4h*q 2sg(zz 544g1zne9rr tuif What is the radius of the concave surfacxtg 9e ag12 ;5jz4ihf u4 zrs4rzq(gn*e?    cm

  A Lucite planoconcave lens (see Fig. Belowq.2mu ck :kuwg6ed +c/) has one flat surface and the other has R = -18.4 kd+qmc/6ue2 ck u.:gwcm. What is the focal length?    cm

  A symmetric double convex (:v9v kp -uaxrlens with a focal length of 25.0 cm is to be made from glass with an index of refr- (ur k:xvv9apaction of 1.52. What should be the radius of curvature for each surface?    cm

  A prescription for a corrective lens calls forxgyij 0:xm ikp zcq6 1r,q:0l; +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 be the radius of curp m6i:: 1qzlicr0;0xqx,yj kgvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in1)qe qqbj 3rkbd 5n4d* (Fig. Below). You stand 1.5 m away feqnqb j5qdb 4d3k)1r* rom one 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 the depth of a swimming pool filled with dgs -4txp-s6l 3r -qe: w kmvne(/c1gwwater. We measure the width (x=5.50m) and then note that the bottom edge of the pool is just visible atg6/ww:t3 eg l-( qcv srxd4 npe-sm1k- 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 o7g-ld vbn* )iwf 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 ofx-t 8ti6bijyvp o isf+k3-;;s a spherical mirror. Specify what this-- x;i f8vjittspb6io3 +;ksy 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 mirvr3dfpgw+):vn9be 2 ounrs 8,rors so they form a 90$^{\circ}\,$ angle as in (Fig. Below). When you look into this double mirror, you see yourself as others see you, instead of reversed as in a single mirror. Make a careful ray diagram to show how this occurs.

Show analytically that a diverging lens can never form a real image of a z2w0rfq1c3 r2q y-kj xm hwa22real object. Can you describe a situation in which a diverging lens can form 2x r-hy 2 q3a2k10rf2wqw zcjma real image?

  Each student in a physics lab is assigned to find the loct/dr*- ,m cwartdoak::xzl 7,ation where a bright object may be placed in order that a concave mirror with radius of curvature r = 40 cm will produce *tc, zarwt,m x7dkod r:a:/-l 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 ofl oddv8q.js et6c cy+ai.)+ j1 a 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 rod1pd w eto :yeapmb*qv r6cg9i059en4 9 $(n=1.54)$ 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 conv lwg9t i0wiwk1. p m/h50v od9-7ilysberging 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 o 5 mqmq3*alu,5 bxst)ef a converging lens of focal length f, and a white screen for viewing the image is on the opu),btal 5 3x5meqqs m*posite 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 tjlkt z2+g9 p+az4z )wrhe object whose image is projected on a screen (Fig. Below). If a 105-mm-focal-length lens is to project an image on a screen 8.00 m away, how far fr zp)rj2 g+tlzzw+ak49om 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 actmx3ta0qg9 x0vovr1; o ually 24 by 36 mm) is to be projected on a screen 1.80 m by 2.70 m placed 7.50 m from the projector. What focal-length lens should m 1 0;xtrvox0agvo93qbe used if the image is to cover the screen?    cm

Show analytically that the image formed by a converging tnx in jzd(l.l /6c(5qlens is real and inverted if the j/lx .5t l6dzcqn( in(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 repov/vr-uo39j3t3cqv p ta4s 9 iyrter shooting pictures of her at home. She claims the reporter was trespassing. To prove her point, 3yv-9votr4ca p/tuj933vsqi 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 uhsru q; m) r)73fwmp9lsed 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 8.20 cm in qqj2e4*gk(r1qx8pdg3c , ( yfzhd1p efront of that lens (on the same side as the object). What type of lens is thisdek pred3xfq(j q,gc8hpg 4 1yq(2*1z , 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)