What would be the appearance of t.6th24c0okj trk 8ah jhe Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fleet i kn3r.yl8**qofpd +u7t w -uxp0xsm7wn the harbor of Syracusdx p7s-x*n8uw*m0lf tkwrupy7o+3q . e by focusing the rays of the Sun with a huge spherical mirror. Is this reasonable?

Although a plane mirror appears pab.dp6 07f mkto reverse left and right, it doesn’t reverse up and down. Exd7fpka6p. bm0plain.

If a concave mirror produces a real ima*vs( 4zsdy+o1n frre sbrs /-)ge, is the image necessarily inverted? Explf-r )e r4*+s s zdysno1r(sv/bain.

An object is placed along the principal axis of a spherical mirr2bje4 c(a0*;njlc)m * ajhqmcor. 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 image )b2jjaa; (m ce4q*lnh*0cmc j located?

Using the rules for the three rays discussed with reference to (Fig. Below a), dqsb1v 2zo 7kodg ztg rat)i77 q./3y2draw ray 2 for (Fig. Below 2gz/kbz.1odgi2 3rv77o tatqsy) qd7b).
(a)
(b)

What is the focal length of a plane mirror? What is t cugn;,7-o 2/ -rra /jjyg/dqwz*ykaghe magnification of a plane majryg/jr u*y/kg wd; nq2-,z7a -cg/ oirror?

When you look at the Moon’s reflec f9xwbwv,c/1etion from a ripply sea, it appears elongated . Expfc be/xw 9w,v1lain.

What is the angle of refraction when a light ray meets the boundary between two ka6j.3 h 4:fnyl cvh2qmaterials perplvfj3k2h4qnh:ca6y. endicularly?

How might you determine the speed of light in a solid, rectangular, transyfct69-viu4y parent obvyy if4ctu9- 6ject?

When you look down into a swimming pool or a lake, are you likely to und1 t gv/ma8it:aerestimate or overestimate it8 a/t1i:m gavts depth? Explain. How does the apparent 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 vsadt g-f ukg4gl7u5*3auzkc 3lr61 ,under water (Fig. Below).t*v-36k lg1u4 ds c3fg,5 lgu7r zakua

Your eye looks into an aquarium ag 5) c-q1h++ d psgm1wtag;tssnd views a fish inside. One ray of light that emerges from the tank is shown in (Fig. Below), as well as the apparent position of the fish. In the d+ g1s m 1sdt5p g+c)wstgaq-;hrawing, indicate the approximate position of the actual fish. Briefly justify your answer.

How can you “see” a round drop of water on a table even though the water 9 pl geusx+sl:.rk f ;a5s(.vqk )na1ais transparent and1.fna v9sx a;5 :ks.+a ru)ekqplgs(l colorless?

When you look up at an object in air from be top ci,k 5yyx-6i0s-sneath the surface in a swimming pool, does the object appear to be the same size as when c iytyk,p0i 5o- xs-6syou see it directly in air? Explain.

How can a spherical mirror have a negative object di (mvlji) 1u+q2, sjgnrstance?

Light rays from stars (including ou6t5w9 +y5ffvl te: duwr Sun) always bend toward the vertical direction as they pass through the Earth’s atmosph tdvwt9 :fl65 y5wu+feere.
(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 cam x515/cnav);y okdd leera lens is to make a sharp image of an object very far awavy5d/)ao 5d1ce nx;kly?

What type of mirror is shown in (Fig. Belowy:i0jfunk e1+e,c-wt)? Explain.

A photographer moves closer to his subject and then refocuses. Does th1iru7*boe3xock u* 68oxuny km:j17v e camera lens move farther from or closer to the fil*oyik68un1 c1:e3b 7 mourk*ovu7 xjx m? Explain.

Can a diverging lens form a real image undhnco+ tfk7 ,0ser any circumstances? Explain.

Use ray diagrams to show tha*gu jc)aca.hr7ju03 r cgq3)xt a real image formed by a thin lens is always inverted, whereas a 7 ar))ucaj.g uc33hxgr0cj *qvirtual image is always upright if the object is real.

Light rays are said to be “reversible.” Is this consistent c0fb51z/z5 n7uy qkqgwith the thin lens equation? Ex7qzn5c u0/f5y1gzb kqplain.

Can real images be projected on a screen? C/ 0ecjwsn) a*han virtual images? Can either be photographe 0c wn/seh*j)ad? Discuss carefully.

A thin converging lens is mz *r- 9hcy3il sir)qd5olfws e5q0//soved closer to a nearby object. Does the real image formed change zrr/5 si59l*olqfsecysi-q w0 d3)h/
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of reo cf2rhv(9+dx fraction n = 1.30 In air, it is cf9 + 2hdv(xora converging lens. Will 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 facing a converging lenql-2iatpmh7 aktb .r2bu80 2f s. If the nose and the tail are each focused on a scree8l2 ab 7bh0k2.tra2ipumtq- f n in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the aiw8g *, yqiyasg:vs) ar1b* nm jvl;-f1r stands facing a converging lens. Under what circumstances (if1fnayqgab;m ly*,v-v *gw :1ri js 8s) 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 th215wytli q1hl e converging lens have a shorter focal length than the diverging lens if the latter’s focal length is to be d 1lhyi5qwl2 1tetermined by combining them?

Explain how you could have a viqixeq3g : *r-srtual object.

  An unsymmetrical lens (say, planoconvex) forms an gn +/r.zcca+5 vmnjc 1image of a nearby object. Does the image point change if the lens is tu c1/+.cr+jcngnv 5z marned around? ----待选择----yesno 

The thicker a double con4uj) .wzfz8wuvex lens is in the center as compared to its edges, the shorter its fo 4 .zfw8)jzuwucal length for a given lens diameter. Explain.

Consider two converging lenses separated by some distance. An object is p8hud a0r5 4orbq-:,gon+n/io m 5xwxolaced so that the image from the first lens lies exactly at the focal point of the second lens. Will this combinationb5i5d8uqg 0 m- rho4 x,oonwo axnr:/+ produce an image? If so, where? If not, why not?

  Suppose that you want to take a photograph of yourself a65il uz/k rf2rdv94w0jp2aj as you look at your image in a flat mirror 2.5 m away. For what distance should t jafzk2pji 5wdu0rl 2a /94r6vhe camera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mirror, r,f;i/9dbf5q896+rxt ddq ,am(0rtregp fk k you see the same amount of your body whether you are close to the mirror or far away. (Try it and see.) Us,ktrgm 9 pb;r+d(rf t0/6de8qa qkidrffx,59e ray diagrams to show why this should be true.

  Two mirrors meet at 0r sfj3nj(ny-zu3 mi8 a 135$^{\circ}\,$ 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 n54b3r2(d;mubgrn,y g y r ;qjm above the floor stands 2.20 m in front of a vertical plane mirror whose bottom edge is 43 cm above the floor, (Fig. Below). What is the horizontal distance x to the base of the wall supporting ggm;ry(ryj 2d ,bub45;n3r nq 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 aressbde 8 )*d,og+,fb mla of the mirror is used to reflect thed le*,8o,gd fss)m bb+ rays entering one eye from a point on the tip of your nose if your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors meet at an angle k 6rzm77rfss 18 kyz5q$\phi$. a single ray reflected successively from both mirrors is deflected through an angle of $2\phi$ independent of the incident angle. Assume $\phi<90^{\circ}$ and that only two reflections, one from each mirror, take place.

  A solar cooker, really a concave mirror pointed at the Sun, focuses the Sun’;-gb yuye6j8o8ph c)c)p 0rb +au/ttss rays 18.0 cm in front of the mirror. What is the radius of the spherical surface from which y8uch /6)g-b u ac0 p;t8obe)yrps+ tjthe mirror was made?    cm

  How far from a concave mirror (radius 23.0 cm) must an objectl 3indg* k amapq17-m3 be placed if its image is to be at idk3-7lg*maapn miq 13 nfinity?    cm

  If you look at yourself in a shiny Christmas tree ball with a diameter of 9.0 c 0lhte ehk-+g4tdw0a3 m when your face is 30.0 cm away from it, where is your image? adhetl0hk3- g +4te0wIs it real or virtual? Is it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shows an upright image of a+gybn paz* 4-fspl0o2ny person who stands 1.4 m in front ofas p40n*flp-z2g b yo+ it. If the image is three times the person’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror that, when 2.20 cm from*lfyn6k, 0h sd 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 images of cars biquasvm +u ,fo(-+2 gzehind you that are smaller than they would be if the mirror were flat. Are the mirrors concave or convex? What is a mirror’s radius of curvature if cars 20sv+zfuo( 2+g ,am-iu q.0 m away appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high d6ckq0at:v,iah;r c( 31l cakny7 uq sh.om21 is placed 20.0 cm from a convex mirror of radius of curvature c 160tiayloh r,qmc.k q12k(nau :avd3c;7sh20.0 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 m0qg)msb v yf*u7euy/ , ,ga( s*5xwnqzirror in a store. You estimate the height of your image to be half of your actual height. Estimate the radius of curvature of the mg/qm( w 7qe,yvz*aus) ,gns0xbu*fy5 irror.    m

  (a) Where should an object be placed in front of a concave mirror so that d* :mskv;p1ve it produces an image at the same location as t:kvd1vs *;emphe object?
(b) Is the image real or virtual?  ----待选择----realvirtual 
(c) Is the image inverted or upright?  ----待选择----invertedupright 
(d) What is the magnification of the image?   

  The image of a distant tree is virtual and very small d u;8st4n n:wq j59,rzthzb*owhen viewed in a curved mirror. The image appears to be 1n4 z9oqn td:zrhbw,j t;us8*58.0 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, q-67nyk+hivwc, 7 dnmq 5fm:j
(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 ojfa7 d0pzc )an52x chpam8w4 4f 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. 23–2, is valid for a),6bhz-ue fyltpb1 ;g convex mirror as long as flp)ub-bt1 6fye ,z;hg is considered negative.

  The magnification of a convex mirror *-axjsf 5t58n.q3eeep4o4xafx3 myg 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 sphericalq l/rzto)/xvhx 9 1:yb mirror. It is desired to produce a virtual image that iyh// 9xz: x) orbqlv1ts 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 your facet h(uysb1w/1 o by a factor of 1.33 when your faceb1osu ( /twhy1 is placed 20.0 cm in front of it.
(a) What type of mirror is it?  ----待选择----convex mirrorconcave mirror 
(b) Describe the type of image that it makes of your face.
(c) Calculate the required radius of curvature for the mirror. r =    cm

  What is the speed of light (, tta3 //1rk zui pg3fhlu:nrin
(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 ic-9. e+*mye*t ntb eefle 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 jr v; 1st(/pien 0sth489% of its value in water. What is the index of refraction of this substance;et0ss /rih 4tv(njp 1? n =   

  A flashlight beam strikes the surface of a pane of glass (n = 1.58) at a u goq0kr fclo+(+hv/. 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashlight upward from beneath 2fy,ucg/ i2vwib 08iel)k6euthe 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 exits the2cmd7de6n va, water at an angle of 66m7d2ne 6,dacv.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.wbr2/ kn+gjo :f 4 rn3sh.fet;0$^{\circ}\,$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?    $^{\circ}\,$

  An aquarium filled with wath iiq esz79saj1u 8ctz 9w*y-i9/8cgner has flat glass sides whose index of refraction is 1.52. A beam of light from outside the aquarium strikes the glass at a 43.5° angle to the perpendicular (Fiay-hg8si9 8 7wui9tzis91nc */ zjqecg. 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 nigh61b9*y dqvfc mi:ud (qt, a watchman shines a narrow beam of light from his flashlight, 1.3 m above theu6cb9q: fyq1d dmv* i( 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 is 2.1 m deep?    m

  Light is incident on an equilateral glass prism at a 45.vf )baob5- *opvog ksl421;oh0$^{\circ}\,$ 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 = 1.56j+ej a31hdd p2) and is partially reflected and partially refracted. Find the angle of ined6jjh pa3d1+ cidence if the angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam i-f ajvhrozt2od t;,;4 oxo2-uo2ka0hncident on a uniform layer of transparent material, as in (Fig4 ,2-t2kz;av of2taoru 0o-xo ; hdhoj. Below), the direction 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 reg k3/m8nkgt hsi1,e2xfraction n as in (Fig. Below). mg, s1ixne38 2/kkgth Show 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 angle for the interface betwee-; 21trc :wiwq pve: irn/h6vin water and Lucite? To be totally internally reflected, the light mi6crh :w1-iw/ipn:v; 2q trveust start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–air e)bo(qvo/c 7 jsurface is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in ab7eh1d6queuco()6r jirt(1 i r:s.ah pool of water from a depth of 62.0 cm. Where must it strike the air–water interface, relative to the spot directly above it, in orr6oui6ct)e a7 1jhsr bd1e (ih(urq:.der that the light does not exit the water?    cm

  A beam of light is emitted 8.0 cm beneath the surfarwcbl; *a- ub;ce of a liquid and strikes the surface 7.0 cm from the point directly above the source. If total internal reflection occurs, what can you say about the index w; rbubl-c* ;aof refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face of 7 ausdzx-24.w;pc .cbntd o/jthe 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 an optic fiber as shown in (Fig.som)m3jyk++rr ck( +-kee-ii 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 the angle the light beam reflects ba)om ee (3mi+rrkk+--j cyi+skck into the material at point a.

  (a) What is the minimum index of refractfy x *m.zm6ha3ion for a glass or plastic prism to be usedz3mmha*.x6 y f in binoculars (Fig. Below) so that total internal reflection occurs at 45$^{\circ}\,$? $n_1$ $\geq$   
(b) Will binoculars work if its prisms (assume n=1.50) are immersed in water?  ----待选择----totally reflectingtotally transmitting 
(c) What minimum n is needed if the prisms are immersed in water? $n_1$ $\geq$   

  A sharp image is located 78.0 mm behind a 65.0-mm-focal-length conve*kp7jtj94 rztp0a3xw rging lens. Fikw07 zxrat j p4t3*p9jnd the object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focusyk;uy b;r aj8 tw1.m2 (xa0des at a point 18.5 cm behind a lens.
(a) What kind of lens is it?  ----待选择----converging lensdiverging lens 
(b) What is its power in diopters? P =    D

  A certain lens focuses light from an object 2.75 adbf0,,k jpby-)rt*o m away as an image 48.3 cm on the other side of the lens. What type of lens is it anpa,-r otyd,f0b j b*k)d what is its focal length? Is the image real or virtual?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the power of a 20.5-cm-focal-length lens? Pm9r v,2) r zud.jkun-i:vk bb(:9uv y bkd6ki9 =    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 7mxvixs d 7id3l1:f/cfocal length 24 cm to view a stamp 18 cm in front o/ixd71dimfs3 cxvl7 :f 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. Whalhsw* n rj 0dmr,y43ia5 1+rext are the position, j+yinr0xas ,dw e* 43rlmr5h1type, and 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 onn7-v)n d(:ug ze-fzez the film of a camera. The maximum dz(f7vd-:ueez- nz n)gistance 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 magnify readin6*eao/l vj -mwg material by a factor of 2.5× when a book is placed 8.0 cm behiaemj6*-w vl o/nd 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 gjd(x* rq/)vsfrom an 8.0-D lens. By how much does the image move ifg*)/sqdv (x rj the object is moved
(a) 1.0 m closer to the lens,    cm away from the lens
(b) 1.0 m farther from the lens?    cm cm toward the lens

  How far from a converging lens wu6p;) i2j4pm/,u ib pw(uqaxf7ilq i1ith a focal length of 25 cm should an object be placed to produce a real image which is the same size asiuqpp,4p l qj amiu6 bfx7)i21u (/iw; the object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an object be placed if itiu t2p-cp3yw 5r)o; 9v4x tnqks image is to be magnifix2n ow93;54 kp- tc)vutripq yed 2.00× and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm

  (a) How far from a 50.0-mm-focal-length l2h 0bhdvoa(- gens must an object be placed if its image is to be magnifiaho 02g b-vdh(ed 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-foik9 e4 brn j18hjj83qgcal-length lens. Where is thjjk8rn1bh 34eg 8ij9qe image, how 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-c :a,s:3r3bk(rrqu qgzm-focal-length converging lens if the image is 2.5× larger than the object aq3brg:arzus: 3 ,(k rqnd is real?    m

  A bright object and a +56qs bt 0l;8(b,ee sqsl ons-iwrg*dviewing screen are separated by a distance of 66.0 cm. At what location(s) between the object and the screen should a lens of rlqs6os+*ws;bd5 (besq-gen8 ,lt0ifocal length 12.5 cm be placed in order to produce a crisp image on the screen? [Hint: first draw a diagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length conp g dho/fubhb +p8uk n;4im9* qw0/(wgverging lenses are placed 16.5 cm apart. An object is placed 36.0 cm in front of one lens. Wk*pf4pnh;h 8 b//+bqug0ww9 mdig ou(here 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 9t)kiz+n9 qfv $f=-31.5\mathrm{~cm}$ 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 21v//(qu her20 j,h+ fnaqajmn8a3ys t+ .0 cm behind a diverging lens. Parallel 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 +/8nvh+02e(/mshqaa,r jy n ja ufq3t a ray diagram.]    cm

  The two converging lenses of Example 23–12 are now placed only 20.0 c3-/yzwr d9qtb zyz8f 15diyh0m apart. The object is still 60.0 cm in front of the first lens as in (Fig. Below). In this case, detbzzyt/ 9ddiyh -fr zq58310ywermine
(a) the position of the final image,    cm
(b) the overall magnification.    cm
(c) Sketch the ray diagram for this system.

  Two converging lenses2u9nb6jzzk.s6hc5b803lvp q iedq9x are placed 30.0 cm apart. The focal length of the lens on the right is 20.0 cm, and the focal length of the lens on the left is 15.0 cm. An object is placed to the left of the 15.0-cm-focal-length lens. A final image from both lenses is inverted 8.dk2px6bi h9 j6uz0qce5bs nz 9vql3 and located halfway between the two lenses. How far to the left of the 15.0-cm-focal-length lens is the original object?    cm

  A diverging lens with a focal length of s+ogs ic)a gcq:8b.gx): /lbi 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 t+gig:xsc a):8bgqbc o li)/s.he converging lens.
(a) Where will the final image be located?    cm to the left of the converging lens
(b) Where will the image be if the diverging lens is 38 cm from the converging lens?    cm to the right of the diverging lens

  Two lenses, one converging with focal length 20.0 cm and one diverging 1dle4k cx4pujx:2i -f with focal length are placed 25.0 cm apart. An object j4p u kc1- iefld:xx24is 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 foca(cc:c-*rby neixgeexf x zjx/n8-)88 l 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 3zm1+0)y+njzw2cix.dc:mo4i ifu( z( bdifqcm. What is the focal length if n = m fx+cyj q0 ((ic4 )23.bdf:iodzizwzm niu+11.52?    cm

  Both surfaces of a double convex lens have radii of 31.0 cm(l 3w.(isjkp( bk e/gr. If the focal length is 2sw ikprjl/k(3be (g.(8.9 cm, what is the index of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) hav2d9nufaj fy e6py543bg 0j7ys a focal length of -23.4cm. What is the radius of the concave surface6adfefguvjy bpy2j0 734ny95 ?    cm

  A Lucite planoconcave lens (see Fig.pz f72iszd2yj u d0:(v Below) has one flat surface and the other h y(fz2zi2sp:vdju0d 7 as R = -18.4 cm. What is the focal length?    cm

  A symmetric double convex lens mh(1:f w8h ezbq-yhyhar+g;2with a focal length of 25.0 cm is to be made from glass with an index of refraction of 1.52. What should be the radius of curvature for each surfacmrg2 wbfh8aqeyhz:1hhy +;(- e?    cm

  A prescription for a corrective lensh2pv x anlk4 qj4r15i- calls for +1.50D. The lensmaker grinds the lens from a “blank” with n=1.56 and a pre2 4kxap1vrqnhli45j - formed convex front surface of radius of curvature of 40.0 cm. What should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 t3o bcky (869wj9 iba*2wbm wy1q:jbm m apart as in (Fig. Below). You stand 1.5 m away from one of these mirrors and look into it. You will see multiple imag3w*qybo1m8k9ijbja by:wb9 t6w ( c2mes 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 meas )9)sh,i:vku)1ukwkhe q d4 eoure the width (x=5.50m) and then note that the bottom k wv)h4o:ui, )19euesk qhkd)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 qzjfua;5 5z, cof plastic in air is $\theta_{\mathrm{C}}=37.3^\circ.$ What is the critical angle of the same plastic if it is immersed in water?    $^{\circ}\,$

(a) A plane mirror can be c5+:xk r n( bkuq(7nwnoonsidered a limiting case of a spherical mirror. Specify what this limit is.bun(:5( 7 xr no+kwnkq
(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 am7j9c +xkh8dq 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 ca n;qd. -oztwc)n never form a real image of a real object. Can you describe a situation in whwtzqc dno.)-;ich a diverging lens can form a real image?

  Each student in a physics *oyn+m /eh o 9g2uex1slab is assigned to find the location where a bright object may be placed in order that a concave mirror with radius of curvature r = 40 cm will produce an image three times the size of the object. Two students complete the assignment at different times using ide1h/eu+2ogn 9 xo*mysentical equipment, but when they compare notes later, they discover that their answers for the object distance are not the same. Explain why they do not necessarily need to repeat the lab, and justify your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of a prism iuqzp5l/ , q-rcph+mxy*mn l5 0s $\phi=72^\circ$ 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 cylindric/xkm (lhe7n 6cal 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 ou(bb a2ia : gvvu/p0 6nn2gy2gf 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 ij9y d1uiyh 8amj7 -/nfocal length f, and a white screen for viewing the hijayi 1j/yu 9dn 8-7mimage 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 film acts as the object whose image is proj a4(grj: g4vz 5fynu)zw6yb9z ected 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,z 4zy5jw yg6a(g vzubf:9r n)4 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) i6kppho.ox 02cf sv op /;:5kxss to be projected on a screen 1.80 m by 2.70 m placed 7.50 m from the projector. What focal-length lens should be used if 26 c;xppkfvo/pk 0:soosxh5. the image is to cover the screen?    cm

Show analytically that the +o/-z) a en0abhoz2dp elzv f8p1ya.. image formed by a converging lens is real and inverted if the object is be1/ h-ov.)8+a al2z pzfdoea.0 pynbzeyond 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. She0bwe : 9eilus9 claims the reporter was trespassing. To prove her point, she gives as evidence theswb9lie e :u90 film she seized. Her 1.75-m height is 8.25 mm high on the film, and the focal length of the camera lens was 210 mm. How far away from the subject was the reporter standing?    m

  How large is the image of tm kjh; zbmz7ozl44w2 ;)qi 2zkhe 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.

  (a) An object 34.5 cm in front o 1pj49x zla fu)rce);if a certain lens is imaged 8.20 cm in front of that lens (on the same side as the object). What type of lens is this, and what is its focal length? Is the image real or virtual 1)lj4ef;)ca9uirp zx?    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 6rk3a*3 iv)ivw b0(hwu7boge zk*bch /3a46kb0.0 cm from a certain converging lens, it forms a real imagerbco/k* kgv wib3v6 h)b huzb *43ki07aw 3ea(. When the object is moved to 40.0 cm from the lens, the image moves 10.0 cm farther from the lens. Find the focal length of this lens.    cm