What would be the appsn( (p/ ivouz*z.l(lxearance of the Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fleet in the harbox6c4*xel vq;:mmy *ojr of Syracuse by focusing the rays of the Sun with a huge spherical mirror. Is this vq*ml em64oy:;j xcx*reasonable?

Although a plane mirror appears to reverse left and right bb vx1qs1ott08uv.y6 , it doesn’t reverse up and douos6 8.xtvbbt01vq 1ywn. Explain.

If a concave mirror produces a real imagel4* )usgi yk7h w45qwu, is the image necessarily inverted? Expusu74 * li)gqwwyhk45lain.

An object is placed along the principal axis of a2zb), l76bz jnlljna 6uh7mg: spherical mirror. The magnification of the object is -3.zn7l zm lbju7:6 jbn)h ,g2al60 Is the image real or virtual, inverted or upright? Is the mirror concave or convex? On which side of the mirror is the image located?

Using the rules for the three rays discussed with reference to (+e q*r ;r.palj8)m e-yvokrm1Fig. Below a), draw ray 2 for+ae-o)q1kvlmrj* ;rm8ep. yr (Fig. Below b).
(a)
(b)

What is the focal length of a plank.avmi:d4+ordy/1 rwy88w ju e mirror? What is the magnification of a plane mirro 8wdrw +/8:dv ymj 1kr4uoy.iar?

When you look at theje* f*8qdj 9nb Moon’s reflection from a ripply sea, it appears elongated .bn89f jq **dje Explain.

What is the angle of refraction a ,.dzsq:wx mb- nw:j. 9,fqldwhen a light ray meets the boundary between two ma 9.adlwmn.fzs b dwq::xq,j,-terials perpendicularly?

How might you determine the speedzx0 o s+2ag*jz of light in a solid, rectangular, transparent osz*xg 2zoj+ a0bject?

When you look down into a swimming pool or a lake, are you likely86mh2ajm p7wwpzy3ca (m9d x. to underestimate or overestimate its depth? Explain. How does the zm a9da(.j3w76 yhwcp 8pmxm2 apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looklf) 5bxe qtw0zpma wcad8w.:9u05 a:ys bent when part of it is under water (Fig. Blt wpaax: qw). w:a 9zub00f5c 8ym5edelow).

Your eye looks into an aquarium and views a fish inside. One raybf7rpjiww 2eic: 2tn p.u6)z4 of light that emerges from the tank is shown in (Fig. Bel:c.2pwu6twi rejf2 7)pz4inb ow), as well as the apparent position of the fish. In the drawing, indicate the approximate position of the actual fish. Briefly justify your answer.

How can you “see” a round drop of water on a table even ,cp3tx8m5dem though the water is transparent and colorless5p38, mtedxcm ?

When you look up at an object in air from beneath the surface in a swimmina3fy:g 6;lyfo-9o z cq)okd3dg pool, does the object appear to be the same size as when you ; cgf: y9q6kady)3o3ofo-ldz see it directly in air? Explain.

How can a spherical mirror have a negative object u*mt)k(s c kx31f2bwv distance?

Light rays from stars (including our Sun) always b4m( +tki stt mj j,re*)ig5e6zend toward the vertical direction as they passrgtj4 j mee+i i )s,6(*ttzkm5 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 ,sclp nva:k;ary9g. sidu5cj05h,vdm5.3 u w camera lens is to make a sharp image of an objn; whv5vi.smgak3ly0: .9usu, cj d rpcad5,5ect very far away?

What type of mirror is shown in (Fig. Bp+ kox ./8w3+tlmxmsym(bbzch+ r;n+ elow)? Explain.

A photographer moves closer to his subject and then refocuses. Does the cam996 cefh9mjhiq y pd6:era lens move farther from orf96: j i9 dh9cehpq6my closer to the film? Explain.

Can a diverging lens fol(ch/-+88dzcp ig 0wl g/pepsrm a real image under any circumstances? Explain.

Use ray diagrams to show that a real imag f1l k5l8yse+ca+xcxt-r *(pfe formed by a thin lens is always inverted, whereas a virtual image is always upright if the objectcl1(+ lycxa tx e-k*+f rfp8s5 is real.

Light rays are said to be “reversiblee ( i8hs evp6 ws,4ra9jon1y;y.” Is this consistent with the thin lens equation? Explain.avnyy(oep ,1s4ejw 9 i ;sh6r8

Can real images be projected on a screen? Can virtual images? Can either be pd h xll7k0i47m 1gfkfmkx+r0.hotographed? Discuss mllk0x0rkg+7f k4 .dif h 71mxcarefully.

A thin converging lens is moved closer to a nearby object. Does t7ps8 davecym o-r--o; he real image formed change -ro- d;v87-ecmyo sap
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of refra6jxtdhk aq2)* am,:e oction n = 1.30 In air, it is a converging lens. Will it still b:hajk dea 6)*q2o,txme 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 facing a converging lhh l+l(+e te.ipnf+xz 7ig6l:ens. If the nose and the tail are each focused on a screen in turn, which will f6ih et g+x.7nlli(ze:lph + +have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facing a conve,n-0 jn(mnor 4uao8uj. h1ww hrging lens. Under what circumstancesh 8h1mouw.w,o-nurj40aj n (n (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 convemv4hhm- 3 tq1xrging lens have a shorter focal length than the diverging lens if the lm v3qt4mh1x-h atter’s focal length is to be determined by combining them?

Explain how you could have w3ljsv5iu )1l3nlf ufk)6;df a virtual object.

  An unsymmetrical lens (say, planoconvex7):is 3mn ombo) forms an image of a nearby object. Does the image point7o)isb mo3 mn: change if the lens is turned around? ----待选择----yesno 

The thicker a double conf(dwl+/ v ae4pvex lens is in the center as compared to its edges, the shortedepal(4w+v f /r its focal length for a given lens diameter. Explain.

Consider two converging lenses separated by some dista,j)-;xqzcp4ewlbwu j: (r ft0 nce. An object is placed so that the image from the first lens lex:frjju qc,-b)l 0( pztww4;ies exactly at the focal point of the second lens. Will this combination produce an image? If so, where? If not, why not?

  Suppose that you want to take a photogra,(pi*kb3h 4zef*u cycph of yourself as you look at your image in a flat mirror 2.5 m away.ef(z**yc4 chkip ub3, For what distance should the camera lens be focused?    m

When you look at yourself in a 60-o0o kyrrk0n /-cm-tall plane mirror, you see the same amount of your body whether you are close to the mir00-oknorr k/yror or far away. (Try it and see.) Use ray diagrams to show why this should be true.

  Two mirrors meet at a 135i *m+bvp(rdv7(wx hr, $^{\circ}\,$ 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 d 9w+* w5gv amte2drx)c dd61sfront of a vertical plane mirror whose bottom edge is 43 cm abe) 65dg +w2vrda1tdmw9* c xdsove 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 micwm5v qc836gi 6o2wjb rror is used to reflect the rays entering one eye from a point on the tip of your nose if your puwq8m26gbi6 ow3v c jc5pil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plank xx0s7.iy +che 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 concav;(jna;fz3q f )8zxz 2tosecm tid(16ig (5rawe mirror pointed at the Sun, focuses the Sun’s rays 18.0 cm in front of the mirror. What is the radius of the spherica8(megxaa 1r fisw c(q;5d 6tij;zzz)(2 nt 3fol surface from which the mirror was made?    cm

  How far from a concave mirror (radius 23.0 cm) mfl w- 2fgr1 b-m8 ie/echfgk91ust an object be placed if its image is to bbhgec 2kw8mf-g/ef-l9 1ri1fe at infinity?    cm

  If you look at yourse8nh:hkq8ms x 4lf in a shiny Christmas tree ball with a diameter of 9.0 cm when your face is 3nh8smhq x48k: 0.0 cm away from it, where is 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 shows an upright imagt a ;qd5p*mt,je of any person who stands 1.4 m in front of it. If the image is three times the person’s height, wjt*d p q;5a,mthat is the radius of curvature?    cm

  A dentist wants a small mirror that, when 2.20 cm frc/ mi(m3y ,onyom 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 mirrorszo vay /3* efb9y-szm7 produce images of cars behind you that are smaller than they would be if the mirror were flat. Are the mirrors concave or convex? 7myesb3oy*9avz z f/- 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 hdw/ csdmeuyb-k7)k: 8igh is placed 20.0 cm from a convex mirror of radius of curvatb7de sy8u)/m :kc-w kdure 20.0 cm.
(a) Show by ray tracing that the image is virtual, and estimate the image distance.    cm
(b) Show that the (negative) image distance can be computed from Eq. 23–2 using a focal length of -10.0cm
(c) Compute the image size, using Eq. 23–3.    mm

  You are standing 3.0 m from a convex security mirror in a7)3z*car owrom qa+r . store. You estimate the height of your image to be half of your actual height. Estimate the radius ofa mrw.z )q7*+rro3a co curvature of the mirror.    m

  (a) Where should an object be placed in frontov8qva+ ;ve;u7fvn,; jmx(j y of a concave mirror so that it produces an image at the samv,;foxauy7v +vmq ;(j8jne;ve 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 igon3 s/oall 4w i bixr.:tw;iz5q 4/d7s virtual and very small when viewed in a curved mirror. The image appears to b ll:4.i / n473o giidt5xq ww;ab/szore 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 techniques, 6(td 4 mvj8kuv
(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 magnihmx7mn 0m2;hzvaf4d l mz (s*-fication 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 equwm mw/q0i7i n59x 8hqoation, Eq. 23–2, is valid for a convex mirm0oqmw wqi58inx /97 hror as long as f is considered negative.

  The magnification of a co.zeg+ z :;s8a-l vob3udta8v45xhcor nvex 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 spheric6 bl qy15yuqq2al mirror. It is desired to produce a virtual image that is upright and 3.5 cm tyq2 y 5uqbl61qall.
(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 *uvp t1,zpjzu+j f;,wkz eb*5magnify your face by a factor of 1.33 when your face is placed 20.0jb*,,+z; u ppzj1w *5v zketfu cm in front of it.
(a) What type of mirror is it?  ----待选择----convex mirrorconcave mirror 
(b) Describe the type of image that it makes of your face.
(c) Calculate the required radius of curvature for the mirror. r =    cm

  What is the speed of light u9w*bahw b;q :3q-r uyin
(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 is vlc*5) ji8iy lc,rx7 o$2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain substance is 89cx :im-(cp:0f2f juyr% of its value in water. What is the index of refraction of this substance? n =jp( xi:2umr0:c y-fcf   

  A flashlight beam strike yu fzookd: 3( (.r4sdnz:nalm sa+w,;s the 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 flaa 3tb4y dpx3kpx.meyg qvv y871(*5(x ifr2 pcshlight 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 exitsfz;gm26+l(c+ri m wtt j1x8 ys the water at an angle of 6m iw1+cz(s2xgrm+8t ytf l;j66.0$^{\circ}\,$ 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 31.ao 2v;mhs/ z k)s;ccn00$^{\circ}\,$ 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 who;8s /z,p du ktgd-o)mbse index of refraction is 1.52. A beam of light from outside the aquarium strikes the glass at zpb8ug)- m k,/d;td osa 43.5° angle to the perpendicular (Fig. Below). What is the angle of this light ray when it enters
(a) the glass, $\theta_2$ =    $^{\circ}\,$
(b) the water? $\theta_3$ =    $^{\circ}\,$
(c) What would be the refracted angle if the ray entered the water directly? $\theta_3'$ =    $^{\circ}\,$

  In searching the bottom of a pool at night, a watchma9qlxu zq8mx7, n 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 hqmu,789 xq zxlis foot, if the pool is 2.1 m deep?    m

  Light is incident on an equil plr2m .4 5bs;bbr3nsqateral glass prism at a 45.0$^{\circ}\,$ angle to one face, (Fig. Below). Calculate the angle at which light emerges from the opposite face. Assume that n = 1.58.    $^{\circ}\,$ from the normal

  A beam of light in air 95ckg ndzt 5 -f0djat*strikes a slab of glass (n = 1.52) and is partially reflected and partially refracted. Find the angle of incidence if 590an5 z-jtdd* ktgfcthe angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam incident on a uniform cyelbqn.3n7l5 y 0h j1layer of transparent material, as in (Fig. Below), the direction ofyq3l1.ly75b e cnhj0n 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 fla(m60mhj i/nzyvibhlz 8v+ csf4//( gft piece of glass with index of refraction n as in (Fig. Below). ( 8 0 gvhj cm/4nz/lf(biiy z6+vh/sfmShow that if the incident angle $\theta$ is small, the emerging ray is displaced a distance $d=t\theta(n-1)/n$ from the incident ray, where t is the thickness of the glass and $\theta$ is in radians. [Hint: for small $\theta,\sin\theta\approx\tan\theta\approx\theta$ in radians.]

  What is the critical anglvicnwo 5l x;-:e for the interface between water and Lucite? To be totally internally reflected, the light must stal:;-xwnicv5o rt in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle fr7qpd;mg6dhg3 q,- + fvsjj0bor a certain liquid–air surface is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in a pool of water from a depth of ev-5f jba3 xd+62.0 cm. Where must it strike the air–water interface, relativvb5+a-fjx3 ede 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 andt;i ru0mv5k 1e strikes the surface 7.0 cm from the point directly above the source. If total;vk5m ruie01t internal reflection occurs, what can you say about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face of the prism in (Fig. Bep.f)-iejh8q2s8mot( zj ya(gbp oi o5 0q4i)ylow) 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 an optic fiber as shown in (Fig. Bxj17a08y caw delow). 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 the angle the light beam c aw7y801xj adreflects back into the material at point a.

  (a) What is the minimc:3mv2j7abklwcv fo*1 rwawx i z.5**um index of refraction for a glass or plastic prism to be used in binoculars (Fig. Below) so that total internal reflection occurc2or*i5acb*x f. lw3w*ajz w:vvkm 71s 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 65.0.6s w;iiezj l*u3a wg:-mm-focal-length converging lens. Find the objeeu *wa :zij3 6s.wlig;ct distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.oi jiwdi /:mhivq e:b1r83n815 cm behind a lens.
(a) What kind of lens is it?  ----待选择----converging lensdiverging lens 
(b) What is its power in diopters? P =    D

  A certain lens focuses light from an object 2.75 m away as z+i 6euwi792aa;u: eztvvb e*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 vireu 9:awib ;t6ez7vi2zeav*+ utual?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the power of ac;q-uzh jy m6,lcg5x; 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 length 24 cm to view a 9ptt:ggxd m ;59r q7gnstamp 18 cm in fronn 9gg97rgp5t dmt qx:;t 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 posi;avv c pcsz4t *tz;k)4tion, type, and height of the images*k; tpcv)zvc;4tz a4?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to fodcn b(6jvu n /crc;13dcus an image on the film of a camera. The u 6dj; v/cnn(1cbrc 3dmaximum distance 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 magntw/w 198wj t+ di3nw(klr 8mr b:4mphoify reading material by a factor of 2.5× when a book is placnw: + 4w8wiol/wjbk pm8r 1dt9hr3tm (ed 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 15kh14a ozg,2js 3krmr .5 m from an 8.0-D lens. By how much does the image move if the ob3r mj21ar s5 h4zkk,ogject is moved
(a) 1.0 m closer to the lens,    cm away from the lens
(b) 1.0 m farther from the lens?    cm cm toward the lens

  How far from a converging lens with a focal lju)xeca x g-;2ength of 25 cm should an object be placed to prjgx;ac- uxe2) oduce 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 object be placed if is cuczi iz; :z*d68av7ts image is cdiz*cs i86;zvu7: zato be magnified 2.00× and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm

  (a) How far from a 50.k3jbo ha4j(pqq81dt/.,-epu-a aa2f ggfr 0 y0-mm-focal-length lens must an object be placed if its image is to be magnified 2.0h8kf1j 2ap4e,bp aqag0-ujtgoyf(a3-dr./ q0× 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-for5)pk sj6rq n)cal-length lens. Where is the image, how high is it, r6j)q5s )rnkpand 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-foak+ v ;+bmjt*yy4t.cp cal-length converging lens if the image is 2.5× larger than the object andv.btym*t++ pj; 4caky is real?    m

  A bright object and a viewing scrbk i28ngji.n+rb5 c n91xintj/ (nm5oeen 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 the screen? [Hint: f+( 8j5cjio x/nb9 nt r kb.2gnmnii1n5irst draw a diagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length converging lenses are placed 16.5 cw-0 jy zxs svnpr,+l84m apart. An object is placed 36.0 cm in front of one lens. Where will the finxsv+jly 0n4-z,prsw 8al 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 wit44am;w bqk1x 1jdfk,.ge7k s oh $f=-31.5\mathrm{~cm}$ 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 divergiv -a3ua0mbkgz, .6l )m zx xf5 s6lxwt3isx+3ing lens. Parallel light strikes the diverging lens. After passing through the converging lens, the light is again p-v3xa mi m, xl6zx)w lab3ufki5 xs+ t360sz.garallel. What is the focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Example 23–12 are now placed 3o ssnom/,4ot only 20.0 cm apart. The object is still 60.0 ,o4noso t/m3s cm in front of the first lens as in (Fig. Below). In this case, determine
(a) the position of the final image,    cm
(b) the overall magnification.    cm
(c) Sketch the ray diagram for this system.

  Two converging lenses are placed 30.0 cm apart. The focal length:8qiwi-vnc o ) 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 left of the 15.0-:ivio8qc)- wn cm-focal-length lens is the original object?    cm

  A diverging lens with a focal length of is placed 12 cm to the rig-/ czog)014t bxhhb5 whsncw9 *y gheb.cbb 22ht of a converging lens with a focal length of 18 cm. An object is placed 33 cm to o c4-*0gczww2bh9 sgn5)1b/hyh tx2b. hb becthe 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 len.w.zpr1m 4 i qyh5xdd(.8e eazz auafb-*5fn)gth 20.0 cm and one diverging with focal length are placed 25.0 cm apart. An object is placed 60.0 cm in frondy zr- amq..(ef)ah4p1 n*fbi .8 5xzz wadue5t 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 rsiadq 4zfun4 /:p,,9yp y )obof 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 23.856 7p8lbh9wsafhr;m 1 0kaalg cm. What is the focal length if rs h baplw1flh0ga5;mk7968a n = 1.52?    cm

  Both surfaces of a double convex lens have radii of 31.0 cm. If the focal lengtevvtv pm:b+i9, 35b ajh is 28.9 cm, v,+9 bpvvetbm5j3 ai: what is the index of refraction of the lens material?    cm

  A planoconcave lens (n=1.5cdm+t 6 0j13mlfehwzaj+ (g(s0) has a focal length of -23.4cm. What is the radius of the concave surf3fm+e 1+mst(hl6 gjdj zca0 (wace?    cm

  A Lucite planoconcave lens (see k * ux)3jyoa1gFig. Below) has one flat surface and the other has R = -18.4 cm. What is theajkx*y1 3)gou focal length?    cm

  A symmetric double convex lens with a focal le2- xwj36w/y zj-/mvfuv ez(da 4bp9k jngth of 25.0 cm is to be made from glass with an index of refraction of 1.52. What se-m( 3 uj yd 9wvjfb xzz2k6/p4w-avj/hould be the radius of curvature for each surface?    cm

  A prescription for a corrective lens calls for +1kfsbak5 cwo l: (6axg+.(w-t e.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 kx5t l kw(oa+c:fe -.6(abgws the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m ap*dg 6bit;1gqw:sos v(art as in (Fig. Below). You stand 1.5 m away from one of these mirrors :;wo* 1 (qtsvgis6bdgand 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 w7qspw sctbx1o a7y7 jk9+oqx,cud6-(ith water. We measure the width (x=5.50m) and then note that the bottom edge of t1cak7qubt-od+xc97 p6wo,(qss 7 jy xhe 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 plastic inooke2r q9s;;k 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 carab/p al b*6fnqyb688ukd56mse of a spherical mirror. Specify wh k/6 bul6ab86qa*5rb8y ndfpm at 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 forub xw po+gf8o v7jq-l2ff pz3t72;7 itm a 90$^{\circ}\,$ angle as in (Fig. Below). When you look into this double mirror, you see yourself as others see you, instead of reversed as in a single mirror. Make a careful ray diagram to show how this occurs.

Show analytically that a diverging lens can never form a rf ;)h js:j;badeal image of a real object. Can yosf b; :a;jd)hju describe a situation in which a diverging lens can form a real image?

  Each student in a physics lab is assigned to find the locat (6f dh5kkv7sj j,2ahlion 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 tk7j lsa2v f6dj,(hh5 khe 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 pri wk/)cza4a hq;sm 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 cylin huz e2y4u7s)i-;eykudrical 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 o9k5fa t*hgin:. *dww0 zikw s;f 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 6kdbnuo vdvy pv/nv;3 9r0*z7of focal length f, and a white screen for vind 3o/kn6vr;bv7 * u0 ypzd9vvewing the image is on the opposite side. The distance $d_T=d_i+d_o$ between the object and the screen is kept fixed, but the lens can be moved.
(a) Show that if $d_{\mathrm{T}}>4f,$ there will be two positions where the lens can be placed and a sharp image will be produced on the screen.$d_T$>4$f$
(b) If $d_{\mathrm{T}}>4f,$ show that there will be no lens position where a sharp image is formed.
(c) Determine a formula for the distance between the two lens positions in part (a), and the ratio of the image sizes.

  In a slide or movie projof f0lhh4ib bgu .5:a3ag3m*nector, the film acts as the object whose image is projected on a screen (Fig. Below):ughhob in3 ab30m afg5 4.f*l. 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 by 36 mm) is to be rz t/ 5jms+s+zprojected 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 the sczmjt/+z 5+rs sreen?    cm

Show analytically that the image formed by a dr-5rqv*3ragi6 - cjkxrp 4 p/converging lens is real and inverted if the objeprrkxd c5-*rj3g4ri av6p /q -ct 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 claimeg: )mefddn+*+yh 1r zs 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 tee+n)gf1dmd +y: *z hrhe camera lens was 210 mm. How far away from the subject was the reporter standing?    m

  How large is the image of the Sun 6ch,;) 8pj*z pogoazkon 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.

  (a) An object 34.5 cm in front of -dz;ia z)y9u q/q*z :nmiygq0a certain lens is imaged 8.20 cm in front of that lens (on the same side as thqqing-zi*yzya0 q:)md9/z u;e object). What type of lens is this, and what is its focal length? Is the image real or virtual?    cm (diverging)  ----待选择----virtualreal 
(b) If the image were located, instead, 41.5 cm in front of the lens, what type of lens would it be and what focal length would it have?    cm (converging)