What would be the appearance of the Moon if eujke * t+(yd/j w 1/uc4gx/zmit had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fleet in the harbor o cw(dcdtn)*fgj,3i *e/b 7xrvf Syracuse by focusing the rays of the Sun with a huge spherical mirror.end*(bw )/*c ,d7i rgx3jftcv Is this reasonable?

Although a plane mirror appears d2d obeooba6 6l(ct.6 to reverse left and right, it doesn’t reverse up and down. Expdet b6o2 c6bdl6 .(aoolain.

If a concave mirror produces a real image, is the image necessar -;+5*vk wc+oircgyrkily inverted? Expwryi 5;kv+c kr-*c g+olain.

An object is placed along the principal axis of a spherical mirror. Trxw de8.dr1xavfmk0x;) j.z .he magnification of the object is -3.0 Is the image real or virtual, inverted or upright d w.j axr d8.1;xfk0x)m.erzv? Is the mirror concave or convex? On which side of the mirror is the image located?

Using the rules for the three rays discussed .a21b 7mj)n*dmogkg1 j8c ldkwith reference to (Fig. Below a), draw ray 2 for (Fig. Below jd7d.*b g2gj1l1kcmk8a)nmo b).
(a)
(b)

What is the focal length of a plane mirror? W46hn4 fe.7eou, erklehat is the magnification of a plane mirrh, en74.4eku6f erelo or?

When you look at the Moon’s reflection from d215+7cogybakn1jok iw7l . zav su- 5a ripply sea, it appears elongated . Explain.asa zd k7gi2ouo-171n5kb .v jcwl+y 5

What is the angle of ryi gso53rngb.01yyj(,peo ; aefraction when a light ray meets the boundary between two materi s; 5,ynojy3ap .g0y o(ig1rbeals perpendicularly?

How might you determine the speed of light in a solid, rectangular, tr*zb.cmkrk taolt/e5ekv:66s 1j . od9ansparent object1t6km .5:9a.s/bkevz k*dljoo e6tr c ?

When you look down into a swimming pool or a lake, are you likel/u tx)r+ sv/rr:1, lcwn:tymny to underestimate or overestimate its depth? Explain. How does the apparent depth vary with the viewing angle? (Use ra + s1u: )crxr, :tvrl/m/ytwnny diagrams.)

Draw a ray diagram to g +sh +n,e yo.opbz8h3show why a stick looks bent when part of it is under water (Fig. h,yno++s38e.p bzhogBelow).

Your eye looks into an aquarium and views a fish insi rzzc+nf p+1v/de. One ray of light that emerges from the tank is shown in (Fig. Below), as well as the apparent position of the fish. In the drawing, indicate the approximate position of the actua cn/+f1zz+r pvl fish. Briefly justify your answer.

How can you “see” a round drop of water on a table4 cy/1 +ciej f1;b u0gnmlcs3i even though the water is transparent and co1j gsiblye14c;c+3/ unim c0florless?

When you look up at an object in air from beneath the surface in akqm r*ccjl0i/b *ghk4w 4-3 wa swimming pool, does the object appear to be the same size as when you see it dir* aq4j-m4rw/hk cl3bi wk0 cg*ectly in air? Explain.

How can a spherical mirrxpgcc1; 6t m43snv2n cor have a negative object distance?

Light rays from stars (including our ris vv q2+pe8nv5./jhSun) always bend toward the vertical direction as they sq.+v5 2ni/v8ph erj vpass 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 i/ :c,ffbjkqz:bc8+b z mage of an object very far away?, /zb jzq:kfcbf +:b8c

What type of mirror is shown in (Fig. Below)? Ekry uvc -2m ,ch:+n/ g 6u-kis.u1jzan v,fz)rxplain.

A photographer moves closer to his subject and then refocuses. Does tm4e vikm;bp:975 inbu he camera lens move farther from or closer to tenim;94p ubiv 57kmb :he film? Explain.

Can a diverging lens form s u;axlo4 y4b9b 1jmj)a real image under any circumstances? Explain.

Use ray diagrams to show that a real image formed by a thin lens is alwaysqk6zllzxn :(1 u-yjx- inverted, whereas a virtual image is always upright if the jzlqx6n(kylz- u1:-x object is real.

Light rays are said to be “reversible.” Is this consistent with tb4nr j*u cvz+1ixuy43 he thin lens equation? Exp yib3uv4cr *+j1zuxn4lain.

Can real images be projec7ks nb.ty/a rr3y,o3i ted on a screen? Can virtual images? Can either be photograp /3osk73ia,.tyrnry bhed? Discuss carefully.

A thin converging lens is moved closer to a nearby objqp 5r oja6l vv8j .3plic3b4y6ect. Does the real image formed chaj63ll v 5j.v6bp c8y o34aqpirnge
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with c5 6bo ;lzocn)an index of refraction n = 1.30 In air, it is a converging lens. Will it o5)clz;cb n6ostill 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 facivld*g0c w gc:d628w unng a converging lens. If the nose and the tail are each fc l2wu6ng8d* :0d vgwcocused on a screen in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facing a;)px a3l1f:ecri3 et t converging lens. Under what circumstances (if any) would the image of the nose be virtual and the image of the tail be real? Where would the image of the res3l;:c fr)tpea t1ei x3t of the cat be?

Why, in Example 13, must the converging lens hav:0u2odnwi1z2 ( oovt be a shorter focal length than the diverging lens if the latter’s focal length is to be determined by combinin 2dit0o1v2o(:w uzbo ng them?

Explain how you could ha9x5z fom i 65-s9jykq1lbgxss*a x/ u.ve a virtual object.

  An unsymmetrical lens (say, planoconve )fzmrh( (d hxe+a2/pex) forms an image of a nearby object. Does the image point change if the lens is turned around?) e(+zmdephax hf/r2( ----待选择----yesno 

The thicker a double convex lens is in the centicsly):/t 4ucer as compared to its edges, the shortu/cyt:i l 4)scer its focal length for a given lens diameter. Explain.

Consider two converginjs/hmu qt+j.5 g lenses separated by some distance. An object is placed so that the image from the first lens lies exactly at the focal point of the second lens. Will this combination produce an image? If so, where? I jq+.jm5 us/thf not, why not?

  Suppose that you want to take a photograph of yourself as you look at your i oe .iv66.z2k gqiry-mmage in a flat mirror 2.5 m away. For what distance sh..m-6zog yrvqk6e ii2ould the camera lens be focused?    m

When you look at yourself in a 60-cm-tall q d4a6 2kbcxp*+y xp8pplane mirror, you see the same amount of your body whether you are close to the mirror or far away. (Try it and se8 kxp*c4xdpqy2+ba6 p e.) Use ray diagrams to show why this should be true.

  Two mirrors meet at a 164sbancx hjq,yec-5r-5yum q25q h0 g35$^{\circ}\,$ 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 a verqf sy4;a s2ove zl8;+ctical plane mirror whose bottom edge is 43 cm above the floor, (Fig. Below). What is the horizontal distance x to the base of the wall supporting the mirror of the nearest point on the floor that can be seen reflected in the mirror?;v ;lo4c8y+ eazsq 2fs    cm

  Suppose you are 90 cm from a plane mirror. What area ostf:2.akme k qqx76/if the mirror is used to reflect the rays entering one eye fro /76qxk. iqa:tmkfs2e m a point on the tip of your nose if your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plapzrf)q(: 3bf1y kxb(cne mirrors meet 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 mirror pointed jo . f4m dgji7 ,a9*amf/gvmjbd9*7y/gj a8zd at the Sun, focuses the Sun’s rays 18.0 cm igm8g/9 m7*9jjj/d zydb g7mja4id .v aof,*af n 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 (radius 23.0 cm) must an object be placed v/0hn*x hb.bu /ek e.uif its image is to beuuvh b./ee xhk/0*.bn at infinity?    cm

  If you look at yourself in a shiny Christmas tree ball with a diameterr vc;,jqas y4)x 7lx.r88wavo of 9.0 cm when your face is 30.0 cm away from it, where is your image? Is it re8 )xy; swr4xajc.78vlo,qv aral or virtual? Is it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shows an e znvh:ip-) ;) yg5 yg;id-gfzupright image of any person who stands 1.4 m in front of it. If the image is three times the person’s height, what is the radius of cu- ggfi v5eg) iz)pyd-:n;yz; hrvature?    cm

  A dentist wants a small mirror that, when 2.20 cm from w9fi 32v wmib5a tooth, will produce a $\text{4.5×upright}$ image. What kind of mirror must be used and what must its radius of curvature be?
 ----待选择----convexconcave 
r =    m

  Some rearview mirrors produce images of cars behind you that areq2o y;jh.up m i9f)su+ smaller than they would be if the mirror were flat. Are the mirrors concave or convex? What is a mirror)+ pqu;2 iyu.hsj9mof’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 placeddx4i*d0d4 s pf 20.0 cm from a convex mirror of radius of curvature 20.4*dxp0d i 4dsf0 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 security4swqc5m-o t ,o 9fhhj2npaf98 mirror in a store. You estimate the height of your image to be half of your actual height. Estimate t5 sn-fpwq8j2,9oa4oh th c m9fhe radius of curvature of the mirror.    m

  (a) Where should an object u ,yu(6npbqh( be placed in front of a concave mirror so that it produces an image at the same l uhquy6, b((npocation 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 vi- a;c7r+j 9s aocpj*gwrtual and very small when viewed in a curved mirror. The image appearrpsc7w-gj +a9; *oacjs 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 tec *o,z2ara erm;hniques,
(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 mir25 inucd87fp wfd 8+uhror 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 equati,jh m (a+ym5gjon, Eq. 23–2, is valid for a convexj ,+(m hg5yjam mirror as long as f is considered negative.

  The magnification of a convex mirrorc zm 3;pd2-bgn1+arvx 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 mh t/gl v36bb828 cm in front of a spherical mirror. It is desired to produce a virtual image th3 /lbhmt6vb8 gat is upright and 3.5 cm tall.
(a) What type of mirror should be used?  ----待选择----convex mirrorconcave mirror 
(b) Where is the image located?    cm behind the surface
(c) What is the focal length of the mirror? $f$ =    cm
(d) What is the radius of curvature of the mirror? r =    cm

  A shaving/makeup mirror is designed to magnify y*0e+x)8mgc u: *qinihw sbg;u -og f9cour face by a factor of 1.33 when your face is place*usco :hi+mg; gb) c0*i8nqwufe-9g xd 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 9 :djl1fcdg z: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 ijece11wfel) 0s 2 c6gbs $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain muffh3 l i33;n:qvp)dsubstance is 89% of its value in water. What is the index of refraction o)ilnf3vdhu: fq 3m;3p f this substance? n =   

  A flashlight beam strikes the)6o(oa obyb5bi j3w9x surface of a 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 flashlig lker x4sc3b0jaw2c07ht 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 h5uab;n ,p sjs)8aaw3spotlight exits the water at an angle of 66.u aj8) bwph;an5s3a, s0$^{\circ}\,$ 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 ogzu;lbgh/m8 t)6ez 5to 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 index of refractionb+ 2bg1 unz+rm is 1.52. A beam of light from outside the aquarium strikes the glass at a 43.5° angle to the perpendicular (Fig. Below).gub+m+r n2z1b 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 shin7r sud-c,zoz:y e 5 )ql)3imv)amacpbnl*l :8es a narrow beam of light from his flashlight, 1.3 m above the water level, onto the surface of the water czlvd lo5 mb s l:ez c)),nip)*y7q:38mau a-rat 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 is 2.1 m deep?    m

  Light is incident on an equilateral glass prism az9d 7,zyrq0 b+vn 0tfct a 45.0$^{\circ}\,$ angle to one face, (Fig. Below). Calculate the angle at which light emerges from the opposite face. Assume that n = 1.58.    $^{\circ}\,$ from the normal

  A beam of light in air strikes a slab of glass (n = 1.52) and im 9s3v)q/rx. z8c. p qox(c:)ciftwb qzl7u 1ts partially reflected and partially refracted. Find the angle of incidence if th3x)pq..c ic1q z(xscuq/ m)b9:tv lowz8t rf7 e angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam incident on a uniform3gmww gz.yz70 layer of transparent material, as in (Fig. Below), the direction of the emerging beam is parallewzwm3 0g7 y.zgl 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 n asi2b /a wm17hrz in (Fig. Below). Show that iamb/ 7rh2 z1wif 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 iov.v gyc-7rv**x x1l water and Lucite? To be totally internally reflecc*x-i.xvvvol r*7 1gyted, the light must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–air surfacea vpr/.q whujxi6v. .3z2noa8 o*n0js is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in a pool ofdk(dl zutb2 ;c4t+b4k water from a depth of 62.0 cm. Where must it strike the air–water iu+4dl2 bkt;zk(d4bctnterface, relative to the spot directly above it, in order that the light does not exit the water?    cm

  A beam of light is emitted 8.0 cm beneath the surface of a liquid ahj2b 0xf+ 1yh yt/g(7w5lgwnxnd strikes the surface 7.0 cm from the point directly above the source. If total in +hxy5ggt w( 7hw yxn0/1bf2jlternal reflection occurs, what can you say about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the le h zko/2kwm6rahh9y 6,ft face of the prism in (Fig. Below) at 45.0$^{\circ}\,$ as shown, but is totally internally reflected at the opposite side. If the prism apex angle (at the top) is $\phi=75.0^\circ,$ what can you say about the index of refraction of the prism? $n \geq$    (retain three decimal places)

A beam of light enters the end of :fmro.3;o9,h*feiwmbj: + x r.kg ajtan optic fiber as shown in (Fig. Below). Show thagfm.r;xh:3.j jk w, bi ooa:t9*ef +rmt 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 refracti3e,-: c7.1xylmon q bvibzrs/ on for a glass or plastic prism to be used in binoculars (Fig. Below) so that total internal reflection oc qrznx-i1: by3/bc o.vel7ms,curs 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 beh (cr73innac,k ind a 65.0-mm-focal-length converging lens. Fnc ck(,7nai r3ind the object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.5 cm behind a lens.kq v 6;shvnkld7af ,08
(a) What kind of lens is it?  ----待选择----converging lensdiverging lens 
(b) What is its power in diopters? P =    D

  A certain lens focuses light from an object 2.75 m away as an image pi-0l8)ejb3 psz7ikmzji7l7 o:w ;f*pi vgz 948.3 cm on the other side of the lens. What type o* 9v bsg ilij3pi -7zpwfkmi7op; l70ez)zj:8f 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-yg,p zyfc,e8 of a 20.5-cm-focal-length lens? P =    D  ----待选择----converging diverging 
(b) What is the focal length of a lens? $f$ =    cm  ----待选择----converging diverging 
(c) Are these lenses converging or diverging?

  A stamp collector uses a converging lens with focal lengthllu3vj/6 , mrb 24 cm to view a stamp 18 vu /lj6lb3mr ,cm 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 14.0 cm from an object 4.0 mm high. What are the pko i3pni8s2j:1 vq ic1osition, type, andjc8kn:op2 13 visq1ii 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 camera. Thmet.cy4s*hzw8v jx/ 3 ;4*h,ewehqi te maximum distance allowed between the lens h;tts*mx.jvh34,e8 /h eqz wyeiw*c4 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 2.5× when a booam nodrf lj gn/5.pqsp3k+dm( j0.4t. k is placedpls. /q.a 4rpdjgn 3 jn5mf(km+o dt.0 8.0 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 image move7k(12fz.rb mj + dao toz.ilvl)shy97 if the object is mov+szho7fz l.r. jb(dl o7y1 t9) im2akved
(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 convergi vwi+eseg+ )3ang lens with a focal length of 25 cm should an object be placed to produce a real image which is th)ve+w3 iagse+ e same size as the object?    cm

  (a) How far from a 50.0-m26m ;v*aq :sl2sa *zkgch1(eu nq ken1m-focal-length lens must an object be placed if its image is to be magnified 2.00× and bgae1 2s:ez *n(lnc;a2v1u*s6hmq qkke 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 objec t yn3nvn/n(yb(s87idt be placed if its image is to be magnifiens/((b t3nd ivny87ny d 2.00× and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm (formed by some other piece of optics).]

  (a) A 2.00-cm-high insect is 1.20 m from a 135-mm-focal-length8c m vq2eeh1o(a:a wz1lw7:tzs yd-x- lens. Where is the image, ho:elm:aa 1vts-78x (zodcw hz-wey2q1 w 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 75-cm-focal-length converg8s.,nr8fc acz ing lens if the image is 2.5× larger thann sc88frzac ,. the object and is real?    m

  A bright object and a viewing screen are separated by a distancer vk b+d7m zjh u2;6nh:ec/eu. of 66.0 cm. At what location(s) between the object and the screen should a lens of focal length 12.5 cm be placed in order to produce a crisp image on the screen? [Hint: f/ce;:um6 b.ue kn2+jhdvrh7 zirst draw a diagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length converging lenses ark1*ek*hpsnh i7v+*+wm d, *ap a(pg7ro xe2zve placed 16.5 cm apart. An object is placed 36.0 cm in front ox(, wkd7 **p2ega 7 *s+e pnh*vhkzio1p+va mrf one lens. Where will the final image formed by the second lens be located? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens with (7,, d*b:mgtea)jly)n zvu:wye 1sqi$f=-31.5\mathrm{~cm}$ 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 diverging lens. Par6t9eld zzc65d allel 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 6zc5dl9d6z e tdiagram.]    cm

  The two converging lenses of Example 23–12 are now plawvsqde5m 162g8 gdq /skv*xi6ced only 20.0 cm apart. The object is still 60.0 cm in front of the first lens as in (Fig. Below). Id* dvs qgx6sm2q65 k1iewv8/gn 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 plmy )3t .*xg .(wkwykxoaced 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 lenses. How far to the left3*xkkt .owy . g)mwy(x of the 15.0-cm-focal-length lens is the original object?    cm

  A diverging lens with a focal length of is placed 12 cm to the mwiv))u,paq/r6d9l tright of a converging lens with a focal length of 18 cm. An object is placed 33 cm to 6 /l,tiwv 9)amdp uq)rthe 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 20.0zt4;x v) nzes7c dn-d0h4mb.5ex ph *f cm and one diverging with focal length are placed 25.0 cm apart. An objectzx fdn)*d 40hcph5e;4bvnsm z-7e. xt 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 )/v,x:k6 tj.m9 urrn cu,nsu vlength $f_C$ 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 cmj*t b y*qr6s x;kho a,kuq84-i. What is the focal length if us4*k *8h;k, rq yt-oabj iq6xn = 1.52?    cm

  Both surfaces of a double,mgoyx r 7uo)6 convex lens have radii of 31.0 cm. If the focal length is 28.9 cm, what is the index of refraction our6mxo,y7g ) of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm. What e- p,n kg7w9+zeuuy8c q;8 crzz 6de)fis the radius of f8q,k)ercnp e+g6z w-7z zyu98c e;duthe concave surface?    cm

  A Lucite planoconcave lwx+vfs k 225rmh*n 1pqens (see Fig. Below) has one flat surface and the other has R = -18.4 cm. What 52xfpr mqh *+s n2w1vkis the focal length?    cm

  A symmetric double convex lens with a focal length of 25. f*s(veur +htq2.k: xr0 cm is to be made from glass with an index of refraction of 1.52. What should be the radius of curvature foruk:rq (2h t+fsrxv .e* each surface?    cm

  A prescription for a corrective lens 6;g; afsta1wq4 ds9:if g)yxhcalls 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 radius of curvature oh;a6 9s1dswfa)fgx4g q tiy:;f the other surface?    m (convex)

  Two plane mirrors favnf (4 tbei3dd(a:rj )ce each other 2.0 m apart as in (Fig. Below). You stand 1.5 m away from one(e fv)ti ( dnrdaj4:3b 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 water. We mego ez,ec63w2dasure the width (x=5.50m) and then note that the bottom edge of the pooe,g26zw 3ocde l is just visible at an angle of 14.0$^{\circ}\,$ above the horizontal as shown in (Fig. Below). Calculate the depth of the pool.    m

  The critical angle of a certain piece of pla h3-yrhiks+-qp .z( w;6xszqestic 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 of a spherical mir,ny0r6xj)p7txru b 7n ror. Specify yp7, j)rn xr6b7n0uxtwhat 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*quueg5sj(iml(r,p ) 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 fwsn n*wy36xh 1mrlv 3 v(s0jb;orm a real image of a real object. Can you describe a situatiomvw b6sn30n s v;(ywr* xlj3h1n in which a diverging lens can form a real image?

  Each student in a physics lab is assigned to find the location where a brigh p 8d7l03uuubd qam,k3xcss,-t object may be placed in order that a concave mirror with radius of curvature r = 40 cm will produce an image three times the size of the object. Two students complete the assignment at different times using identical equipment, but when they compare notes later, they discover that their answers for the object distance are not the same. Explain why they do not necessarily need to repeat the lab, and justify your responses3lp,-0dskdmbu qu, 7u3a8xc with a calculation.
$d_o$ =    cm    cm

  If the apex angle of aj 8wx1xo 6n nzhxv,n. ))cfa:oc hu/q; 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 cylindricaq pxa ;eg8:;s;kw4ge0fncy (pl 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 o 4sy7y0 d3gdlaf a converging lens of focal length $f_1=15\mathrm{~cm},$ which in turn is 55 cm in front of another converging lens of focal length $f_1=15\mathrm{~cm},$ (see Fig. Below).
(a) Draw a ray diagram and estimate the location and the relative size of the final image.
(b) Calculate the position and relative size of the final image.

A bright object is placed on one side of a converging lens of focal /uct/:3 e9lhc;pdh 5,3 ajk/mvyc jowlength f, and a white screen for viewing the image is o lh ccwke//;o5 ut/vm3 3a:hpc,yjj9d n the opposite side. The distance $d_T=d_i+d_o$ between the object and the screen is kept fixed, but the lens can be moved.
(a) Show that if $d_{\mathrm{T}}>4f,$ there will be two positions where the lens can be placed and a sharp image will be produced on the screen.$d_T$>4$f$
(b) If $d_{\mathrm{T}}>4f,$ show that there will be no lens position where a sharp image is formed.
(c) Determine a formula for the distance between the two lens positions in part (a), and the ratio of the image sizes.

  In a slide or movie projector, the film act 3ulmf9n. *vcdbi+(d os as the object whose image is projected on a scree.do dnv bclmi(+*uf93n (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 picture be on the screen? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (picture size is actually 24 2+rj2 c-8 xm9kwho lokby 36 mm) is to be projected on a screen 1.80 m by 2.70 m placlhxrw jm c-8+o2o9k k2ed 7.50 m from the projector. What focal-length lens should be used if the image is to cover the screen?    cm

Show analytically that the image formed by a converging lens ilf/rv:3 fd1g wqq, 79i y,ybjis real and invertedbd7wi:y,/i9ygrv1 ,fq l 3fjq if the object is beyond the focal point $(d_0>f),$ and is virtual and upright if the object is within the focal point $(d_0>f),$ Describe the image if the object is itself an image, formed by another lens, so its position is beyond the lens, for which $-d_0>f$, and for which $0$<$-d_0$<$f$.

  A movie star catches a reportep k)z q; /gif3tja//2qh/eizdr shooting pictures of her at home. She claims the reporter was trespassing. To prove her point, she gives as evidence the film she seized. Her 1.75-m height is 8.25 mm high on the film, and the focal length of the camera lens was 210 mm. How far away from the subject was ti g h/ /ke;qa3it/)dpj2qfzz/he reporter standing?    m

  How large is the image of the Sun on film used in a camera-gypk9o m i s1xoacmvbg;hh 9+))1q+ s 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 8.20nq.59sp(yd; ;hsqwq c cm in front of that lens (on the same side as the object). Whats;q d(s5y9c n;qwq.ph type of lens is this, and what is its focal length? Is the image real or virtual?    cm (diverging)  ----待选择----virtualreal 
(b) If the image were located, instead, 41.5 cm in front of the lens, what type of lens would it be and what focal length would it have?    cm (converging)

  When an object is placed 60.0 cm from a certain conver mr+ ggn++ k):810rzfsyosh0 bd.ibh uging lens, it forms a real image. When the object is moved to 40.0 cm from the lens, the image moves 10.d b fni:ok++uysg81r hzs. hr0) g0m+b0 cm farther from the lens. Find the focal length of this lens.    cm