What would be the appearance zf fvx5i8. q-cof 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 thevgcjf2ypy43.2 mr f f4v0of 1h harbor of Syracuse by focusing the rays of the Sun with a huge spherical mirrof4ff2g jfy cv2y10vm 4phr 3o.r. Is this reasonable?

Although a plane mirror appears to revesqpv2 o+8u;4tal s0j vrse left and right, it doesn’t reverse up and down. Explaia0 2tlp4ou s;+ 8jsqvvn.

If a concave mirror produces a real image, is the image necessarily inverkjqht4l 1 4 jk*y/h4cfted? Explh4ky*cjf /14q4 hltjkain.

An object is placed along the principal axis of a sphekvfg5ov3t 9 nsxn ,t8d/r09t erical mirror. The magnification 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 if9g359rt ot,v0 evkn/ txsn8 dmage located?

Using the rules for the three rays discussed with reference to (Fig. Below 5mc0sg1 bqk8 da), draw ray 2 for (Fig. Be1 c q0dsgb85kmlow b).
(a)
(b)

What is the focal length of a plane mirror? W2jx8q 0fheth;i i,:nk hat is the magnification of a planenf ; txki:0j e2hiq8h, mirror?

When you look at the Moon’s reflection from a rs 2f:lv-if.jk)xdoc .-9:ysxin)cxy ipply sea, it appears elongated . Explain..o :2sivx)x.)yj csff 9cn--d:yxlik

What is the angle of refraction when a light ray me7)e;b6 vzxsz5v ,kbrzets the boundary between two materials perpes,5kb76 vzb rzx)zv;e ndicularly?

How might you determine the speed of light in a solid, rectangulw(nss3oqm-k ;z1r 1xyk ),na war, transparent object yo-,1s (wmznnr qkw)1;xsak3 ?

When you look down into a swimming pool or a lake, are you likely to undere 6z:8g n2v6qiwvg l;ukstimate or overestimate its depth? Explain. How does the aq:v;giz2n6 wglv6 8u kpparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks bent when part of it is under wat(p6u 8irnvttm 6(1gsa.e;muker (Fig. Belon((umks8v6. e giu;mr1t6t a pw).

Your eye looks into an app.0g5 (yogfcc-hz:; kc+ sn lquarium and views a fish inside. One ray of light that emerges fro0; c.gskzg(oh-cp:p+ c fn 5lym the tank is shown in (Fig. Below), as well as the apparent position of the fish. In the drawing, indicate the approximate position of the actual fish. Briefly justify your answer.

How can you “see” a round drop of waterv8kb bht6 7yg3*i db( owsd-0g on a table even though the water is transparent ao7 hw 0- tsb gbdv3ik6(bdyg8*nd colorless?

When you look up at an object in air from beneath the surface in a swimming po;l 4+ttl c9ratol, does the object appear to be the same si9 t;cl4tta+rl ze as when you see it directly in air? Explain.

How can a spherical mirror have a negative object dis )6o a3)i n+5qexeabzqtance?

Light rays from stars (ivxy+; 7k 5fqqencluding our Sun) always bend toward the vertical direction as they pass through the E+7fkq y;xve5qarth’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 makrjm j)7.rpwj+-5 ihlqe a sharp image of an objecwhmrq7-5)p j+ir. l jjt very far away?

What type of mirror is shown in (Fig. Bewcstqflq272 0 low)? Explain.

A photographer moves closer to his subo4e n:3g il9pjgfkb: 5ject and then refocuses. Does the camera lens move farther from ofj o:bg kgnl93e4 i5:pr closer to the film? Explain.

Can a diverging lens form a real image under any circumstances? Expla,p(tp t.i.c1;ut/bmpnl 3ad z in.

Use ray diagrams to showt4t5ffy+v rszc *.* fy that a real image formed by a thin lens is always inverted, whereas a virtual image is always upright if the object is reyt54ys tr*z*f+c.ffv al.

Light rays are said to be “reversible.” Is73hmh*zua:bo d ns4- v this consistent with the thin lens equata*734vs ohhzu mb-:nd ion? Explain.

Can real images be projected on a screen? Can virtual images? Can eith , 4 i;r2 j.,wkkuv.icrn-v +q5gjxhmper be photographed x,- w2,r+i . j5i.4mkhvknvrcqu;pj g? Discuss carefully.

A thin converging lens 2g:yg1r*2i (ceel gk6a w yli-is moved closer to a nearby object. Does the real image formed chang2egy1-gw6 e2i*( craligy :k le
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an in+q1n ye2ieun bn/9 *nj m/wki8dex of refraction n = 1.30 In air, it is a converging lens. Willn*ibmn e njq8w+/ n/u1ey29k i it still be a converging lens if placed in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands fao6 cf+au.wf-m0wf.ln qx4+ dgcing a converging lens. If the nose and the tail are each focused on a screen in turn, which will have the gr 0f++xum .-d.f64cww anofgqleater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facing a converging lensje 893.u)zais9:fueok r3inp. Under what circumstances up.i 9e8s3ea : nokzri)39j uf(if any) would the image of the nose be virtual and the image of the tail be real? Where would the image of the rest of the cat be?

Why, in Example 13, must the converging le; 6wynkpi(feb37 l4 nhns have a shorter focal length than the diverging lens if the latter’s focal length is to be determined ; fn7k6lb4h (enyi pw3by combining them?

Explain how you couldkr:p9od r +gt l/s4 eenba+r/5 have a virtual object.

  An unsymmetrical lens (say, planoconvex) forms an image of a nqvkde :y3m* 2 -bnc2nzac7ho6y ;)vot earby object. Does the image 3hnondv2 z*cv;y ocyk)q:bm 7t a2-e6point change if the lens is turned around? ----待选择----yesno 

The thicker a double convex lens is in th tzjm v(*(6l ,y:i).uaziqxxl e center as compared to its edges, the shorter its focal length for a giv v)jlx.i:x( mz*tyu, lai(z6qen lens diameter. Explain.

Consider two converging lenses separated by some distance. An object is placed vn o0t w+p8ht+ad3 5oyso that the image from the first lens lies exactly at the focal point of the second lens. Will 85+ anodt3yp h0ot+vwthis combination produce an image? If so, where? If not, why not?

  Suppose that you want to take a photograph of yourself as you look at yowpeq 8w89: m tsvf*on6ur image in a flat mirror 2.5 m away. For what distancm8wn: fq*v9e8spw 6o te should the camera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mirror, you sw )t(ffxpmk,-w2kst3uk0( qlee the same amount of your body whether you are close to the mirror or far away. (Try it and see.) Use ray diagrams to show why qxw)-f3k 0kkttl,(w mp2fu( s this should be true.

  Two mirrors meet at a 14et oysr y1nj*taa 4 br8+:y.z35$^{\circ}\,$ 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 front of /:vdjt :fg0og a vertical plane mirror whose bottom edge is 43 cm above the floor, (Fig. Below). What is the horizontal distance x to the base of the wall supporting the mirror of the nearest point on th/g:fg v: o0dtje floor that can be seen reflected in the mirror?    cm

  Suppose you are 90 cm from a plane mirroeebrr.o ,1kg5 r. What area of the mirror is used to reflect the rays entering one eye from a point on the e.rrkgeb 1,5otip of your nose if your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors meet at an anhgos5s*cp2-yc s e6q *gle $\phi$. 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, foculx3 z*7q9n: tx3pfcodses the Sun’s rays 18.0 cm in front of the mirror. What is the radius of the spherical surface from which the mirror was*x lpcz973n:qd 3fotx made?    cm

  How far from a concave mirror (radius 23.0 cm) must an obje.tlp ant,l30ui- gq +xct be placed if its image is to be ll+xt03ptg., nqia -u at infinity?    cm

  If you look at yourself in a shipok /jb9j0nzd +x*+lany Christmas tree ball with a diameter of 9.0 cm when your face is 30.0 cm away from it, where is09l*a/opj xd z++jbk n your image? Is it real or virtual? Is it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park 5h 9y cujz eqkj+l1pc /;.m6uoshows an upright image of any person who stands 1.4 m in front of it. If the image is three times the person’chj;o 5 cq+9/u61ekzmyp.j lus height, what is the radius of curvature?    cm

  A dentist wants a small mirror that, when 2.20 y,3pmvy :z* e1 iwdgijc8:,umcm 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 im7- :yq ny-0nhrlqx 7ukages of cars behind you that are smaller than they would be if the m qnl:r7-0-uyq yn7 xhkirror 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 normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is placed 20.0 cm from a conve l10/atxru; fnj(eap -x mirror of radius of curvature 20.0 cm(ae a lx-uf pn1t/;0rj.
(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 storem jzl.t wxuxt;4lo :)5. You estimate the height of your image to be half of your actual height. Estimate the radius of curzxl 5x :lo;)mt4w.tujvature of the mirror.    m

  (a) Where should an object be placed in front of a concave mirror so that it9chi +sda* oajl xb/:7 produces anlj7daxb/h s a9:*io+c image at the same location as the object?
(b) Is the image real or virtual?  ----待选择----realvirtual 
(c) Is the image inverted or upright?  ----待选择----invertedupright 
(d) What is the magnification of the image?   

  The image of a distant tree is vir223eom ek7+qy: c zlf-ztk5hutual and very small when 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 radius ofk72zceyl 3o -h5ez:m+utkfq2 curvature?
 ----待选择----convexconcave 
r =    cm

Use two different tecrhm;; xj38-to ;m bgbihniques,
(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 napuek6/cgg0 b; 1(k:h4kydi magnification m of a convex mirror is $m=-d_\mathrm{i}/d_\mathrm{o},$ just as for a concave mirror. [Hint: consider a ray from the top of the object that reflects at the center of the mirror.]

Use ray diagrams to show that the mirror equation, Eq. 23mxp,m;, iu/x m–2, is valid for a convex mirror as long as f imx;x immp, u/,s considered negative.

  The magnification ofpsmycl5v8fd,k52eo+u2wx :r a convex mirror is $+0.65\times$ for objects 2.2 m from the mirror. What is the focal length of this mirror? $\theta_2$ =    $^{\circ}\,$

  A 4.5-cm-tall object is placed 28 cm in w 3 tvesme285ofront of a spherical mirror. It is desired to produce a virtual image that is upright atm23e wsoe 85vnd 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 f0bsekfx( +f;r0f/u5nt owpdcwxv; r 1;7,ozyour face by a factor of 1.33 when your face iszn1;fxws /o (5+v0ubf krx0;7petorc; ,fd wf 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 lig+w,ab)jns0pi ad st( 3ht 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 ao.rl* pzsh 611agv9t is $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain substance is 89% of its value in way)7t,- m7k1gc3gti7 4o0 vfxcffjf qqter. What is the index xoj7cff0f vgq,g74 t ycqikft) 7-3m 1of refraction of this substance? n =   

  A flashlight beam strikes the surface of arjfx*nvm b.n40ul d .g( q3gr- pane of 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 flashlipfga95,zo5of( p (wazght 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 unde tf-n zurp.2y:rwater spotlight exits the water at an angle of 66. yfpt-:2nrz u.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 m8id,4 :f2 x.koho: 5dmh epbfkake 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 hijoxf 4x vyksz7g -h ;ed(;s):as flat glass sides whose index of refraction is 1.52. A beam o:e- xyh;k sx)7 szgd( oijv4f;f light from outside the 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 +sqr3az f r 04 uu*szy1zr r(dmf92s3tnight, a watchman shines 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 the wall beneath his foot, if the pool (darz2 s tuyq334r9f z rr+0m ssfz*1uis 2.1 m deep?    m

  Light is incident on an equilateral glass 9e,l b:bcnr6*hld (zfprism 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 q-b. kcshi2l*vb5pj: (n = 1.52) and is partially reflected and partially refracted. Find the p2 :lcbhbvsjik q5 .*-angle of incidence if the angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beamun 5mg9n(z0ts incident on a uniform layer of transparent material, as in (Fig. Below), the direcs9zg(unt n0m 5tion 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 refraction qga,kdu-q5- ak 5b3jon as in (Fig. Below). Show th5k dqa-5qga- 3bku, joat if the incident angle $\theta$ is small, the emerging ray is displaced a distance $d=t\theta(n-1)/n$ from the incident ray, where t is the thickness of the glass and $\theta$ is in radians. [Hint: for small $\theta,\sin\theta\approx\tan\theta\approx\theta$ in radians.]

  What is the critical angle for the interface between water and Lucite? zm)ds 57l qp x7kbzfx ,7ry+x1To be totally internally xl7zx, m7x5sb qd7py)+zf1rk reflected, the light must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–air surface is 47.0sctj )wiy,u;hr-/(k mg bkj;7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in a pool of water frou st)zk3j*2 zaot1o k/m 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 does not exitot3s2 oj/1 u*zz)t kak the water?    cm

  A beam of light is emitted 8.0 cm beneath the sunlcgfov 4+71 hrface of a liquid and strikes the surface 7.0 cm from the point directly above the source. If total internal reflection occhv 7c+g1 4nlfours, 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) atvq)n *74(kmff8v6qd5s b;gjasmw /cw 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 fz3 m, zbmxot81iber as shown in (Fig. Below). Show that we can guarantee total internal reflection at the side surface of the material (at point a), if the index of refraction is greater than about 1.42. In other words, regardless of thezm38xozbm t 1, 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 prism to be x 8nz3 fqc iwf/5a(t7eused in binoculars (Fig. Below) so that tottc fna/58 wf7qx( 3zieal 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 behi -ndwu6j*kkn9 nd a 65.0-mm-focal-length converging lens. Find the69-kud* nw jnk object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.5 cm(t m*q tty)ra3by/hy: 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 obje scveg0khv.9.y4 w a)yct 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? Is the image real or virtual cy. h.vkvge4ya)9 0sw?  ----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-fot48wyp: rd.u-wg -vurcal-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 nb 0vnqz qabp p5uim3qk;xr)l 1 5+,v:converging lens with focal length 24 cm to view a stamp 18 ;p)qa,q+xbniz q 5:vbn v0p m51r uk3lcm in front of the lens.
(a) Where is the image located?    cm behind the lens (virtual)
(b) What is the magnification? m =   

  A -5.5-D lens is held 14.wzh,fe:: jfn os)ua ()gpgr.30 cm from an object 4.0 mm high. What are the position, type, and height of the )fe, jnfrw:h3u pg.(g as :oz)image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to focus an image on the film of a camera. T,fkm/ mfk x4 i)j9i63 wnvlb)nhe maximum dm ) k4f ixln/i3v,9kfj6bw)mnistance allowed 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 magnikh k;g,s-5eb tp5 pi+vfy reading material by a factor of 2.5× when a book is placed 8.0 ckb-pt p+;ik segh,v55m 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 nh 4hn45w fw, t-p2fehimage move if the object w,henn42-h t4p 5wfhfis 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 converg:iw.0vm jmfxqmee8vq8t1q)+ing lens with a focal length of 25 cm should an object be placed to.jqmi:1ev8 +et)qmqvx0 fmw 8 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 l21*w 9kmiipp an object be placed if its image is to be magnified 2k iml*9iwp p12.00× 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 place 0 qgm/s7c kxbpk7u1*zd if its ima0pgs77kb /zqx1*mkuc ge is 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 i(-l p)n.,hn z whht(bensect is 1.20 m from a 135-mm-focal-length lens. Where is the image, how hn(l h.tpz)nh,wb-e ( high is it, and what type is it?
$d_i$ =    mm (real,behind the lens) $h_1$ =    cm (inverted)
(b) What if $f=-135\mathrm{~mm}$?
$d_i$ =    mm (virtual,in front of the lens)
$h_1$ =    cm (upright)

  How far apart are an object and an image formed by a (ncx/cw15u2w0f v9 z,vnve*k97 u n8 uxky hxv75-cm-focal-length converging len09/ hevyk* 8c wvcnuw7n5nfk , zvvx9xu(u21xs if the image is 2.5× larger than the object and is real?    m

  A bright object and a vyo ;iyg; zbjltt0o76,y3q0 bdf:sdi.iewing 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 placed in order to produce a crisp image on dd b o :. i;7gs0lib,zt0jf3yo 6qyty;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 pla ) qej.5tvfhlhle.a l72 cp.*qced 16.5 cm apart. An object is placed 36.0 cm in front of one lens. Where will the final image formed by the seh t ja)q7evl el5qc2fp.*.l h.cond lens be located? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens wit2nh(e4pffw a +b;6unpb6/ftp 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 converging lens is 21.0 cm behind 8e2hsjxje zc * .t4zd5a diverging lens. Parallel light strikes the diverging lens. After passing through the converging lent 2cx d.j8e4zs5*hj ezs, the light is again parallel. What is the focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lensiymi rxkh-. htonsfrqwp)kk7r7)m34 0/7. f mes of Example 23–12 are now placed only 20.0 cm apart. The object is still 60.0 cm in fronnwkfhkfti .qk .-/0im7y 3r 7mp hr7r)osmx)4 t 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 thka;up / ,.mjplaced 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 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 lens tjap/h ku,;m.es. 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 ofc y+oqx:k+n ;u e.ev bf:hd6+j 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 cond+.: fy; hn+vq+ecbxeuo6jk : verging 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 lef 4j:m0a aa* xvwhgnn761j4 zq mum8l4ngth 20.0 cm and one diverging with focal length are placed 25.0 cm apart. An object is placed 60.0 c8 h4x0g 4j:7l1j4a *m vnn6zmfuaqmawm 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 focalf:.cqk7mizzo 5b. br* 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. What is the /lp,fe4go/5n fkhy c0focal length if n lypgc,/k5n/fofhe 40 = 1.52?    cm

  Both surfaces of a double convex lexc7.y8 f kvtbhg0v , d3sojk2+ns have radii of 31.0 cm. If the focal length h.vxd2o ,y80gjt b+f3 skck7vis 28.9 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: m:j0tur( pelo;w(f d. What is the radius of the concave surd:pf lrwj;tmu(: o(0eface?    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat surface and the othqugiq*m2n nxa,).z*(rr p5mo er has R = -18.4 cm. What is the focal lqopng (rz,nqxmm. * 2)iu*ar5ength?    cm

  A symmetric double convex lens with a focje nfgm njk 9r1.zh+,*u7 fdb7al length of 25.0 cm is to be made from glass with an inde jf ngefbumdnjz1,h*. r+k977x of refraction of 1.52. What should be the radius of curvature for each surface?    cm

  A prescription for a corrective lens calls for +1.clz b( gm87d325wrirf50D. The lensmaker grinds the lens from a “blank” with n=1.56 and a preformed convex front surface of radius of curvature of 40.2 r(5cb3igm7zwf8rld 0 cm. What should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fig. Beud8s +m 0w+bxc,mgfq 0low). You stand 1.5 m away from one of these mirrors and look into it. You will see multiple images owxcb u0qf+0+smm , gd8f 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 uheo h1, 7lm ukiq-*ju;afo 52measure the width (x=5.50m) and then note tha5k7m1;o ,uhulj uheifo*q 2-a t 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 plasvvjx a5y3ppf9nik1eosy6m s rkni 8w* (.142qtic 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 mnk/a dbn6d (t52pz+n case of a spherical mirror. Specify 6tn b2(d z p5nk/mand+what this limit is.
(b) Determine an equation that relates the image and object distances in this limit of a plane mirror.
(c) Determine the magnification of a plane mirror in this same limit.
(d) Are your results in parts (b) and (c) consistent with the discussion of Section 23–2 on plane mirrors?

Stand up two plane mirrors so they form a;ic in: cc:u,invn e/, 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 reaxopx1/ 24okbtb3t,g 1mmx d: ml object. Can you describe a situation in which a diverging lens can form a real image?mbk do m/xog3 x2,xttm4p 11:b

  Each student in a physics lab is assigned to find the location where a br; 8cy2q b aj;qnoep8kv7w 1mb7ight object may be placed in order that a concave mirror with radius of curvature r = 40 cm will produce an o 8kqa77 b wm;qp1;bvey28j cnimage 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 a pr ;5 1kk tx5s vibt7kdja6-ty,bism 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 cj3+ sq0;uxeo wz7uep-ylindrical glass rod $(n=1.54)$ are perpendicular to the sides. Show that a light ray entering an end face at any angle will be totally internally reflected inside the rod when the ray strikes the sides. Assume the rod is in air. What if it were in water?

A lighted candle is placed 33 cm in front of a converging lens of/2,t -foita(6nh .egyg *tzag 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 sid7/ko hsh bc82r an,bo2j x:vmj;+b *sne of a converging lens of focal length f, and a white screen for viewing the imagr7+/2 bjh 2sa8,;ncomko sx *bjnvb:he 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 r j2x10us th7hfilm 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 should the slide be? If the slide is 36 mm wide, how wide will the pictur1 xh7 0jurhts2e be on the screen? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (picture size is actually 24b* x 19ct u3*xuv.ihcm 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 fmuh9 b1ti* *xcx3uc.v ocal-length lens should be used if the image is to cover the screen?    cm

Show analytically that the image formed by a converging jk0)gv.gip s2 lens is real and inverted if the object is beyond the focalgs k)jgp2v0.i 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.iijtxexn:uv44mhs 6)40e;f g She claims the reporter was trespassing. To prove her point, she gives as evidence the film she seized. Her 1.75-m height is 8.25 mm high on the film, and the focal length of the camera lens was 210 mm. How far away from the subject 4 s 0vnm:tu4gjh; xf4i)ei 6exwas the reporter standing?    m

  How large is the imagr7 g oyew)*ey6e of the Sun on film used in a camera with
(a) a 28-mm-focal-length lens,    mm
(b) a 50-mm-focal-length lens,    mm
(c) a 135-mm-focal-length lens?    mm
(d) If the 50-mm lens is considered normal for this camera, what relative magnification does each of the other two lenses provide? The Sun has diameter $1.4\times10^6\mathrm{~km},$ and it is $1.5\times10^8\mathrm{~km}$ away.    for the 28 mm lens    for the 135 mm lens.