What would be the appea7 d+p1a-mgh0 j6q kxgjrance of the Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned thbrwc no4pc t6f8 e:q876t;t qce whole Roman fleet in the harbor of Syracuse by focusing twr6t qn8t cf;t76 qo4 ce:cb8phe rays of the Sun with a huge spherical mirror. Is this reasonable?

Although a plane mirror appears to reverse left and right, it ds ai rz)t;pge;szq* 59oesn’t reverse up and down. Ex); i;a*pqt e5zz 9grssplain.

If a concave mirror prob*i ,v( i:h;ega;ge trduces a real image, is the image necessarily inverted? Explai,;; ive agg(*ieth:rbn.

An object is placed along the principxh 5ifb 4slnaqcb)09za6+tf aqs 7q.5al axis of a spherical mirror. The magnification of the object is -3.0 Is the image sx5+cfs)q b0.lh5 4baaf6 az i7qqnt9real 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 xp6*djgw6*s74 fvmv lthree rays discussed with reference to (Fig. Below a), draw ray 2 gv4vw pl67*xm6j *d fsfor (Fig. Below b).
(a)
(b)

What is the focal length of a plapkf2 (z ;mek )2wvfjagy.z.f) ne mirror? What is the magnification of a plane mirr .(z ef2y)a2pvw )fk.jfm;gzkor?

When you look at the Moon*y1evutjuy ) fe9*ks+r wa (/j’s reflection from a ripply sea, it appears elongated . E uf evjte*k*9)u+ y ja/ryw(s1xplain.

What is the angle of re f..y*m/r4)cmyw dlni fraction when a light ray meets the boundary between two materials perpendn./m .*l 4ydmicyw)fricularly?

How might you determine the speed of light in a solid, rectang qj7 wyf6a3;h08 hgm-9szhkfsular, transparent objekfh3f0w7hjay h6q mss 9z-;g 8ct?

When you look down into a swim5ox3uzv997le cf9ri qming pool or a lake, are you likely to underestimate or overestimate its depth? Explain. Howifz 95uc3l9oeqx9r7v does the apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram t+o.5 n3 ./*-w) emlfdf qqqsm(lq a,wdh9oikyo show why a stick looks bent when part of it is under water mie 9l.q(sf q.dm-*ao5qq+kw)o nwf yhl/,d 3 (Fig. Below).

Your eye looks into an aqua*jxslow)fhgwh,0 )j)cp00a* ye g q4r b-re8g rium and views 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 hq8 gy sr)h0c fo l-je0jgpbe a4, x*g)*0)rwwthe approximate position of the actual fish. Briefly justify your answer.

How can you “see” a round drop of water on a table even tnr2 9pr:gpm8v3 gf9sp fm6d /hhough the water is transparent a3p6prdp9m ng8s: 2mv 9g/ hfrfnd colorless?

When you look up at an, vaddq+fok:cvz0 5k3xd;v : c object in air from beneath the surface in a swimming pool, does the object appear to be thed;c va0cxdkoq,f:: d+kv 3vz 5 same size as when you see it directly in air? Explain.

How can a spherical mirror have a negative object distance?h.9go, gjc(h d

Light rays from stars (including our Su- iv g zj*r83g9fkr4psn) always bend toward the vertical direction as - vgi *z fkgps4jr9r38they pass through the Earth’s atmosphere.
(a) Why does this make sense?
(b) What can you conclude about the apparent positions of stars as viewed from Earth?

Where must the film be placed if a camera lens is to make a sharp image of an o6q4m1ojiet 8 xbject very far awajqem64 it18x oy?

What type of mirror is y(pt d sgv5e,peb60-b shown in (Fig. Below)? Explain.

A photographer moves closer to his subject and then refocuses. Does the cy ng3+1xc +mpfamera lens move farther from or closer tcn+my1xpg +3f o the film? Explain.

Can a diverging lens 9u xr abj1 nold4n,yj k(.h:+sform a real image under any circumstances? Explain.

Use ray diagrams to show that a real image formed by a thin len(* 05u 7e0jvjyya nhjos is always inverted, whereas a virtual image isyay( e00juoj 5n *jvh7 always upright if the object is real.

Light rays are said to be “reversible.” Is this consisvuwf g5/2, 6h3wqfv aatent with the thin lens equation? Ex3f/gvww, a6vhqa2 f5u plain.

Can real images be projected on a screen? Canj1 )t0)y k 1llx,,xdm njkk0py virtual images? Can either be photogr1)nl ydp1kt ,0lx y)mxjk k,j0aphed? Discuss carefully.

A thin converging lens is moved closer to a nearby object. Does thaz6rykslb6+ g, -ppc-e real image formed chan-p brl6ycg,a- 6sz+ pkge
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of refraction n = 1.30 In air, 1 dm-4xkocdk+ 9mkv+iit is a converging lens. Will it still be a converging lenkmck -9 +ikx+4mdd 1ovs 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 no(8c-syo ps2 jwse and the tail are each focused on a screen in turn, which will hav28( -pjwscs oye the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facing a converging l :t 47 (,w3xbsn /yo8azesopdwens. Under what circumstances (if any) would the image of the nose be virtual and the image of the tail be real? Where woul( to: ew8xsw bnyd4a/ s7pz3o,d the image of the rest of the cat be?

Why, in Example 13, must the converging lens have a shorter focal lex4xha3 xj9;( do 1xxelngth than the diverging lens if the latteaex94j x (h o;lx31xdxr’s focal length is to be determined by combining them?

Explain how you could havx fg2dj/ji,. .0qnqyce a virtual object.

  An unsymmetrical lens (say, planocl f/r7da/hc+0re i(8g xmtn(;z2kj f ponvex) forms an image of a nearby object. Does the imae/k7 mz;r(lx02tc pj8 (irhf +/adnfgge point change if the lens is turned around? ----待选择----yesno 

The thicker a double convex lens is in the center as comvcl8ysh1e(zpf8; w+qf(:b(hl 1 6fqkab mlm 8pared to its edges, the shorter its focal leyksl:q1fcf z bm+6lh(m (aewqlhv b88(;8 1pfngth for a given lens diameter. Explain.

Consider two converging lenses separated by some distance. An object is plac oegaqj*x; bxsc6. 26;dncaxyv88*ered so that the image from the first lens lies exactly at the focal point of the second lens. Will this combination produce aevcc gs 8a8an jxx 2ex .rd*;6y*;qb6on image? If so, where? If not, why not?

  Suppose that you want to take a phot8ey.u xjo1/g mw(m(pyograph of yourself as you look at your image in a flat mirror 2.5 m away. For what distance should the camera lens be m8yj g up/(x .o1ymew(focused?    m

When you look at yourself in a 60-cm-tall plane mirror, you sg6m8:cx hgff/n)lbi; m9j r;nee the same amount of your body whether you are close to the mirror or far awa9cn8g mrmh;6 ibfj )n/:fglx; y. (Try it and see.) Use ray diagrams to show why this should be true.

  Two mirrors meet at a 1/9 26y.e/behkx iby/2 thysg*p xgvu635$^{\circ}\,$ angle, (Fig. Below). If light rays strike one mirror at 40$^{\circ}\,$ as shown, at what angle $\phi$ do they leave the second mirror?    $^{\circ}\,$

  A person whose eyes are 1.68 m above the floor stands 2.20 m in frlx aup-(75iw(d ad q ut:6//.ki bfyuoont of a vertical plane mirror wh6t-daabufql ( i(p7u// dwyxo.uik:5ose 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 that can be seen reflected in the mirror?    cm

  Suppose you are 90 cm from a plane mirror. What area of the n kgzc8w4u2 przw** p/mirror is used to reflect the rays entering one z8*r*pku2wpn/ 4gwcz 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 ang ej-4o8z/ fsy *uuxmr3le $\phi$. 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 mirror pointed at the Sun, focuses the j 5*v ocpj3ept1) hm7lSun’s rays 18.0 cm in front of the mirror. What is the radius of the spherical surface from which the mirror wasc ljpe57j)h* o3 vpmt1 made?    cm

  How far from a concave mirror (radius 23.0 cm) icez9i+yfvo .84ns5wvil-o 4 must an object be placed if its image isyv5eonv8cii 4+ z-.ls94 wofi to be at infinity?    cm

  If you look at yourself in a shiny Chri0p/ob tgi 5)bkic. :6;nsxibt stmas tree ball with a diameter of 9.0 cm when your face is 30.0 cm away from it, where is your image? Is it real or virtual? Is n6b bt) s0 k;:bi/p.icgt5xioit upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shows an upright image of kw2wabt*6 f0 nany person who stands 1.4 m in front of it. If thew6n*waf20 ktb image is three times the person’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror that, when 2.20 cm from a 9zsc7 1w-*)4qkzqn*udf q xprtooth, 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 yo.ibb z eep )*i)vjr9)gu 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 awayjir9.iv)e*e )bp)bz g appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is placed 20.0 cm from a convex mirb jk qx0-.vdkgvoy640lse 1t6*ib) mdror of radius of curvature bx qmijs1g66 b-oyl.d4*e0d 0) kk vvt20.0 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 st1uux.7el2jc * lt pi5 mz(,jzpore. You estimate the height of your image to be half of your actual height. Estimate the radiz zjmj t(p1u.l,2le75uc xi*p us of curvature of the mirror.    m

  (a) Where should an object be placed in front of a concave mirror so thaom3+ a2apiae 6t it produces an image at the siapm3e+6a o a2ame 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 small*(2lian 8q ir4b)plfli gs9;:ak0je n*yvhr9 when viewed in a curved mirrhlv; 8gebpi)ai(nlrslrkf2n*:0 i9j49* ayqor. 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 te/cot mgagc9yoa 7 o8*b p4 00pu3xqws(chniques,
(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 mirrorp ywnlhl .8g) 2q0gga/ 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. 23–2,be 6 7/eq ,x 1ko16 puabst/xm6qxnht3 is valid for a convex mirror as long as f is consideree3hak6xs7 /exu,tq6 o1qbbp/tnx16 md negative.

  The magnification of a conve0h9l fshqaxzpg ,5a 88:8sqayx 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 placed 28 cm in front of a 2ehohgg( u,ey7;4tttspherical mirror. It is desired to produce a virtual image that is upghhet t4e; g(t 27uy,oright 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 md7pwyv ;2) /hh;v:m.yu .ll w4vulmwyagnify your face by a factor of 1.33 when youu;ylwh.lpdy2h/7vw .4;ul wmm yv) v:r face is placed 20.0 cm in front of it.
(a) What type of mirror is it?  ----待选择----convex mirrorconcave mirror 
(b) Describe the type of image that it makes of your face.
(c) Calculate the required radius of curvature for the mirror. r =    cm

  What is the speed ofay qep) sp)k9 xbf-/jilv 2sr*.yd f4c87qkb ) light 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 h -rf(qgjj0+q is $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a :j gyb5+vw8wkh/dsm9 certain substance is 89% of its value in water. What is th gbhv5wkd:8+m9w js/ye index of refraction of this substance? n =   

  A flashlight beam strikes the surface of a pane of6 )uwef wu2kf1 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 flashlsl03 uulv : rb0v/ g:;emtzjs9ight 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 e ()x*tbrbqaw)4xvam6xits the water at an angle of 664)a vwq)x*6atr(mxb b .0$^{\circ}\,$ to the vertical. At what angle of incidence does it hit the air–water interface from below the surface? $\theta_1$ =    $^{\circ}\,$

  Rays of the Sun are seen to make a v :si/ckc9 y6qrtq *o9mei;b.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 flatc q2nd:k3 8 gxpso97zwdmr2 1o glass sides whose index of refraction is 1.52. A beam of light from outside the aquarium strikes the glass at a 43.5° angle to the perpendicular (Fig. Below). What is wz9:2278rn qxkopdcodg13 ms 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 shi 3w j-,fs/lay1rx a0gones 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.fls ,3-jy/1w a0agorx 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 equilateral ,y5u ktj)6k4j 7vitrpglass 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 ais08 b6wqtxi,;jq l*xv r strikes a slab of glass (n = 1.52) and is partially reflected and partialv;6q0qw8 xxljtsb i,* ly refracted. Find the angle of incidence if the angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for dlfdl8u)7 w9s:2jyf9c.h zuy a light beam incident on a uniform layer of transparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the incidentwy djd9f.9y2c ul)l usf8hz :7 beam, independent of the incident angle $\theta$. Assume air on both sides of the glass.

A light ray is incidentw,. p k7kic6pj on a flat piece of glass with index of refraction n as in (Fig. Below). Show t 6cwi k.,j7ppkhat 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 an2+qh wa**y t 4nggl3jzgle for the interface between water and Lucite? To be totally internally reflln h aj4z+3 g*tw*2qygected, the light must start in which material?
$\theta$ =    $^{\circ}\,$
 ----待选择----waterLucite 

  The critical angle for a certain liquid–air surfacg/l2 qi,ywpe p1+uu* e m1t(hlbic3 +we is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in jn0nvd0awz l(,be;8 plw 9 gx.a pool of water from a depth of 62.0 cm. Where must it strike the air–water interface, relative to the spo.8p,xd0b(0n wgzla ;ne vwjl9t directly above it, in order that the light does not exit the water?    cm

  A beam of light is emitd;ji5 cqfd0yo8+ 0m mw3s6 gwxted 8.0 cm beneath the surface of a liquid and strikes the surface 7.0 cm from the point directly above the source. If total internal reflection occurs, what can you sacdxj; g ymm5w do0 q8+is0w3f6y about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face3iedoioo4 3 8g 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 e 37:l4moe8rcwvac: c jnd of an optic fiber as shown in (Fig. Below). Show thlco8 rw3 vm :a7:e4cjcat we can guarantee total internal reflection at the side surface of the material (at point a), if the index of refraction is greater than about 1.42. In other words, regardless of 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 pruttx*1 /v jui k2*n.ooism to be used in binoculars (Fig/ 1*kuvj.u2nito o* tx. 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 78.0 mm behind a 65.0-mm-focal-length cqnjutpi21fc4 s m 97-e.:ebytonverging lens. Find the obcny qm7p:u ee.bs - 92ftt4ji1ject distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at 9) tu:gxcw,pr 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 a4hk0vamzn/9mc v:)r ypm-60 ju.bkivn object 2.75 m away as an image 48.3 cm on the other side of the lens.k m4kvzhuym):pc0vm90 brvj/i -a n6. What type of lens is it and what is its focal length? Is the image real or virtual?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the power of a 20.5-cm-focal-kqku8lzzb :* /.4qejelength 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 68og)udh u 1iolength 24 cm to view a stamp 18 cm in front of t)6duh8o1 goi uhe 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 objeb5ppa +4/ rjtwct 4.0 mm high. What are the position, type, anpjpt 4+r5a/bw d height of the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to focus an image on the film of a cafv3y b fz-2au(mera. The maximum distance 3 v(fzfb-2a yuallowed between 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 magnify reading material by a factor of i6r m:j(o,;lnfp zj e62.5× when a book is placed 8.0 cm behinol;j mn(pf rz,:ei66j d 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 lek)k6rv+g9ygsw qa/d dd7f t8ac2j 1 xa/wo-)ens. By how much does the image move if the object is movedwx ay/o dw eq/a))s-d+gdvjack8f 7grkt9612
(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 converghohy5yl d862) b4ai 1 o2xgusning lens with a focal length of 25 cm should an object be poy6 bi8u1n2 )xh aosghy24l5 dlaced to produce 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 obe-ixr *e2a hhntg;qs;tk)*)aject be placed if its image is to be magnified 2.00× and be real? kqhhxr ) tag i;s *-e;e2*at)n   mm
(b) What if the image is to be virtual and magnified 2.00×?    mm

  (a) How far from a 50.0-mm-focal-lengthd3 h,bkouy 4.o lens must an object be placed if its image is to be magnified 2.0kuy 3boo.dh 4,0× 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-m 0pa:g*kfkj5 rzk gr.*bk8t 9t2uc4 ucm-focal-length lens. Where is the image, how high is it, and what type is it? ur4 cgkjc.5*gtp*ar8fkz: kk90 u2bt
$d_i$ =    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 t5 9pwozh/-n mmqne7v3 *t+ej a 75-cm-focal-length converging lens if the image is 2.5× lh5z e jepm +nv-*o973mqt/nwt arger than the object and is real?    m

  A bright object and a viewing screen are separatb:ua(uq:,xy i y00q lped by a distance of 66.0 cm. At what location(s) between the object and the screen should a lens of foca0( ua:up,yl0 qqxi b:yl 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 q858bkogi .ok16.5 cm apart. An object 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 totgo5 kibk8qo. 8al magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens with+pac 8)2(ie5 ry.hwfb wifj. y $f=-31.5\mathrm{~cm}$ is placed 14.0 cm behind a converging lens with $f=20.0\mathrm{~cm.}$ Where will an object at infinity be focused?  ----待选择----realvirtual ,    cm beyond second lens.

  A 31.0-cm-focal-length converging lens is 21.0 cm behind a divergim lagf.1ucw0y*sicm c2d1/6dxu0-pkng lens. Parallel light strikes the diverging lens. After passing through the converging lens, the lightakipwl02u d us fx m/-6c0dmc1.y1gc* is again parallel. What is the focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenswkvijn gv.3p*y7r ,or o u1q;,x0c zx;es of Example 23–12 are now placed only 20.0 cm apart. The object is still 60.0 cm in front of the first lens as in (Fig. Beloo3jkg1v onq.ri;p;xy* vc xu,z0, w7rw). 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. t:vib-wt ujyzo )p3/e placed 30.0 cm 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 obowvp tu -.) :jtzi/3ybject 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 placedy kl1+d1ys/xi 12 cm to the right of a converging lens with a focal length of 18 cm. An objk+ysy 1d/ 1lixect is placed 33 cm to the left of the converging lens.
(a) Where will the final image be located?    cm to the left of the converging lens
(b) Where will the image be if the diverging lens is 38 cm from the converging lens?    cm to the right of the diverging lens

  Two lenses, one converging with focal length 20.0 cp1njh748b ,hcbwj w *9)z( bwbagjav.m and one diverging with focal length are plhv)* 8gazb,j .7 hcwbajbw(wbj9np41aced 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 nex5wwyul(w r 00jt to a converging lens of focal 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. W2k: u mz7pdnw yguc.gbgg8f ums/,,)2hat is the focal len,fpugg/uu )gy wg7 z2.mkb8 ms n,:2dcgth if n = 1.52?    cm

  Both surfaces of a double convex lens have radii of 31.0 olufcc,cjg3 4wu /8y19iw2 fji vxi ,5cm. If the focal length is vu5clg ,iw2x9o483yfufj 1/ jcw ci,i28.9 cm, what is the index of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm. Whai2v1tka3jwo2q e /wt(t is the radius of the conq32wito2 je1k/ va wt(cave surface?    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat surface and the/szk ki5 ukl(2 other has R = -k/zks( k52 uli18.4 cm. What is the focal length?    cm

  A symmetric double convex lenrpp5 )ct.w ed-s with a focal length of 25.0 cm is to be made from glass with an inde.dct5- e)pprw x of refraction of 1.52. What should be the radius of curvature for each surface?    cm

  A prescription for a corro/qvh5 56k 623nm uysvt2djnv+rk8 pcective 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 be the ra qtu2vk yn5rk5/np2+ sdo8hm3vv6 jc6dius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fig. Below).rpo 3:uq0/,cpa gnp8 8nq/v aj)a:odl You stand 1.5 m away from one of these mirrors and look into it. Y0o 3uqj,rp 8lcdn:a:)pa8a /v p ogq/nou 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. We mem*0*rswxp3: *rsap( 5zm wbu tasure the width (x=5.50m) and then note that the bottom edge of the pool is just visible at an angle of 14. r*xzuw p3w(m*s50m:b* ptsra0$^{\circ}\,$ above the horizontal as shown in (Fig. Below). Calculate the depth of the pool.    m

  The critical angle of ax oft p35wc0)ep(f9gnd*a mgs 6s6: dl certain piece 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 canl5 2,piheyu.bm;xnh ck8tz,bwb:( :g be considered a limiting case of a spherical mirror. Specify what this limitx8 tzp w,c(k 52hm:.e:ugl;b b,hniyb 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 fw1 kztcfe;z; p ),pv8korm 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 tha jov1d0 /0sc5waebqs 8t a diverging lens can never form a real image of a real ob50 dos a8/e0wb1 csqvjject. Can you describe a situation in which a diverging lens can form a real image?

  Each student in a physics lab is assigned to find the locat7(1 ,iivfan x3snn9yqk-k e:bion 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 differq,73(ns-ix b1 i:nkn e9vfyk aent times using identical equipment, but when they compare notes later, they discover that their answers for the object distance are not the same. Explain why they do not necessarily need to repeat the lab, and justify your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of a prism ihhw9f(1r.hn67/uhrv ic q vb4s $\phi=72^\circ$ 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 r;nk((0jx g:o sd 9guws/pprr2od $(n=1.54)$ 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 1a;pch(spdr+ 7,fcevm )ul0 l placed 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 sm9hvwdiydiqahe8+r vx( 7)4:ide of a converging lens of focal length f, and a white screen for viewing the image is on the opposite side. yv9mq(a 87 ddxi+:ehh) rw4ivThe 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 projecti44vobh cd-7k ts .:keor, the film acts as the 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 from the lens sho .b:4ckihot-7vs ed 4kuld the slide be? If the slide is 36 mm wide, how wide will the picture be on the screen? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (picture size is actually 24 by 36 mm) is to be project4-ul g fe38tp**y lk0aadxat.r+f4z hed on a screen 1.80 m by 2.70 m placed 7.50 m from the projector. What focal-length lens should be used if the image is to cover*+4a3rthdaz 4-uk0x .yg8 tflfp a el* the screen?    cm

Show analytically that the image formed by a convergik+qsrqx, r 7byd w8.y9ng lens is real and inverted if the srb 97qy ,w.+qdk8ryx object is beyond the focal point $(d_0>f),$ and is virtual and upright if the object is within the focal point $(d_0>f),$ Describe the image if the object is itself an image, formed by another lens, so its position is beyond the lens, for which $-d_0>f$, and for which $0$<$-d_0$<$f$.

  A movie star catches a reporter shooting pictures of her at home. She claims th p42fhpw.)d;p8f*2gdl z irt ne pzhtn4r ;w)d8ppfl fd2.2*g i 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 reporter standing?    m

  How large is the image of the Sun on film usjay6f27f/r xhra;sy vvs9j;9u, 4x hqed 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 n7p8)a zo8wpqimaged 8.20 cm in front of that lens (on the same side as the object). What type of lens is this, and whponqwa)87 p8zat 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.)o 2jwqa)il z+ehtc+o:uqz8//s.(nfz jskk 2 0 cm 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 lens. Fito.:/ znous ) hak/(z8kcf2)sjj+le+ i2qwz qnd the focal length of this lens.    cm