What would be the appearance of the Moon if it ham +kg1dju(b2mrh 8qs9d
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fleetf*d imen (nk)s v7jt4, in the harbor of Syracuse by focusing the rays of the Sun with a huge s,di)v e74(*tnms f jnkpherical mirror. Is this reasonable?

Although a plane mirror appears to reverse left and right, it doesn’t rw)ki ),wa5n2q ;e ezq k(;tq((exzzhweverse up and dow,qn k;) qxw ((2zzaeit5zqee (hk;w w)n. Explain.

If a concave mirror produces a retuyne8p50 c. ual image, is the image necessarily inverted? Exppc ye0u.n8u5t lain.

An object is placed along the principal axis of z 4gn ,d8u5:9he emj v6fjew(ja spherical mirror. The magnification of the object is -3.0 Is the image real or virtual, inverted or upright? Is the mirv fh8,4u6neg:e5(9j mwjj dez ror concave or convex? On which side of the mirror is the image located?

Using the rules for the three rays discussed with reference toc -m.dbj.a;c y (Fig. Below a), draw ray 2 for (Fig. Below jc.cdbma y-. ;b).
(a)
(b)

What is the focal length of a plane mirror? What is the magnifp7b : qvk7utd- vwe 5imipn3x69ppcv0 ,a6n, sication of a plane mirror?pq ,kne65vdu, sp9im vv b77pxwa:-p3c0i n6 t

When you look at the Moon’s reflxiu )w 1w28.xetuxq5h eqw 00hection from a ripply sea, it appears elongated . Eqix2xuw x h.0)h80wu1qe5t w explain.

What is the angle of re2.x: *iwlwqcns1 .swrfraction when a light ray meets the boundary between two materials perpendicularl*x 1nw2iws.s lq wrc:.y?

How might you determine the speed o1,9 i,:ul jhu xbcaes(f light in a solid, rectangular, transparent obsxu,l(1he j,a:b u9ciject?

When you look down into a swimming pool oro dgq9 nha31co/eomj1z -+9oe a lake, are you likely to underestimate or overestimate its depth? Explain. How does the apparent depth vary with the viewing angle? (Use r3qm-a1o coo1e 9/d gze9jo hn+ay diagrams.)

Draw a ray diagram to show why a stick looks bent when part of it is under watwt2:kou/cbe m+u.id0 er (Fig.e0m +/bkdt :c.wi2o uu Below).

Your eye looks into an aquarium and views a fish inside. One ray of light that y2iqaw; ( x7gmemerges from the tank is show7ga2i ( yx;qmwn in (Fig. Below), as well as the apparent position of the fish. In the drawing, indicate the approximate position of the actual fish. Briefly justify your answer.

How can you “see” a round drop of wa5xu7 p j pizbk0zo4bm 5c4r9e1ter on a table even though the water is transpa 59x k4z50obpzib cempr174ujrent and colorless?

When you look up at an object in air from beneath the surface in a swimme +dnei;r)3 iting pool, does the objirni te3d);+e ect appear to be the same size as when you see it directly in air? Explain.

How can a spherical mirr1 .zmbuzi*:a. g*ounx or have a negative object distance?

Light rays from stars (including o)( r.mm9ybrk2m) tqh;tm pw7pdkr6j0ur Sun) always bend toward the vertical direction as they pass 6.wr)pk(hy mtkr 7tpq)0b ; m9jd2rmmthrough 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 csff7so x0i (w,amera lens is to make a sharp image of an object very far awaf0sos 7f(,ix wy?

What type of mirror is shown in (Fig. Below)? Expwxi ghtkc)flc/:(v6a39kcot yw uh1i, 74nn*lain.

A photographer moves closer to his subject and then refocuses. Does the camera 74:p0 9idsgn iunmkv l +)tza/lens move farther from or closer to the :0iv9 4mdnza p +s/)ignl7kt ufilm? Explain.

Can a diverging lens form a real image under any* ez1 qpkf(i/e circumstances? Explain.

Use ray diagrams to show that a real image formed by a thin lens is alwac)7i3ep9qwtzr.a7dp rmlh * 7 ijp 16jys inverted, whereas a vj16 alzci. jpdw)e3q 9p ir7hr7 *tm7pirtual image is always upright if the object is real.

Light rays are said to be “reversible.” Is this consistentnx68bb9r av9v with the thin lens equation? Explain.xb6r 8anv v9b9

Can real images be projected on a screen? Can virtual imakj0oy+o y;kds+kl7 d5ges? Can either be photogra5dk+ y;k07ldksy o o+jphed? Discuss carefully.

A thin converging lens is moved closer to a nearby object. wm)x mdf(8v8 cx+g /;jd/pkg bDoes the real image formed chfg+ ;xm) bw8kmx(/8d/gdvpc j ange
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of refractitp 7y/7b6q3 da hugp+eon n = 1.30 In air, it is a converging lens. Will it s/a u t7gyd7+6ep3pbhqtill 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 lens. If the no8q7c ju7/+aqva 6exo4 0 uvctg,9n7pevl9 uusse and the tail are each focused on a sc uleqoa4j89,7uvnuvc9pc0q6 se t 7va7/+ugxreen in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facing a c4(vwkbhf 8bym6 y5t 11i qajy;onverging lens. Under what circumstances (if any) would the image of the nose be virtual and the image of kviy1 m 8j1ahwfq6(yy5 4t;bbthe tail be real? Where would the image of the rest of the cat be?

Why, in Example 13, must ttijp v3tpr1 8;he converging lens have a shorter focal length than the diverging lens if the lattt;vjtp r p183ier’s focal length is to be determined by combining them?

Explain how you could have a vir8so;pplj pb2w00e5ir(n y4xx- (of whtual object.

  An unsymmetrical lens (say, planoconvex) forms an image of a nearb(r*8k qnz nj3ey object. Does the image point changejnr3* (enkz8 q if the lens is turned around? ----待选择----yesno 

The thicker a double convex lens is in the center as compared to its edges, thnb;0 y bffxfe7xt+6 +fe shorter its focal length for a given lens diameter. + tn0f;exf6b+yb f 7xfExplain.

Consider two converging lenses separated by so :nxk,egrnh;/w+ro5 ome 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 imageg :o;wrkr,o/ n5xh n+e? If so, where? If not, why not?

  Suppose that you want to take a photograph of yourself as you look at youz4 tm5duyjh.4 r image in a flat mirror 2.5 m away. For what distance shoudtum4j.5yh 4z ld the camera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mirror, you see the same amo is ekavh8 j2q7w383tgunt of your body whether you arwat8e 8i7v2h3sg k jq3e close to the mirror or far away. (Try it and see.) Use ray diagrams to show why this should be true.

  Two mirrors meet at m+4o-nsbr9l g 53ymbq qb0u vl-lrlj : a:t:4oa 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 m above the floor stands 2.20 ,kqq;j l;4px:wrb ;d lwux,7im in front of a vertical plane mirror whose bottom edge is 43 cu7x jr; ;, wpqb,di:;q4klw lxm above the floor, (Fig. Below). What is the horizontal distance x to the base of the wall supporting the mirror of the nearest point on the floor that can be seen reflected in the mirror?    cm

  Suppose you are 90 cm from a plane mirror. What area of the mirror is zlwt -ouj ycr*us.0 ,(osj+s ; jum:s,used to reflect the rays entering one eye fromjoousl* +;,,j 0 c(syj s-m:us.z wurt 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 mir 140mk.f;3 wjn3s0jzytw l ehrrors 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 concan**fg p,qz 5p8p2xnidve mirror pointed at the Sun, focuses the Sun’s rays 18.0 cm in front of the mirror. What is the radius of the spherical surface from which the mirror* zp *ndx5nfi p8gpq,2 was made?    cm

  How far from a concave mirror (radius 23.0 cm) must an z (jjtb5z7l4q object be placed if its imagetz4qjj(lzb75 is to be at infinity?    cm

  If you look at yourself in a shiny Christm.kskf: qd- y;bas tree ball with a diameter of 9.0 cm when your face is 30.0 cm away from it, where is your-dy kbqfk;: .s 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 image of any person who ste/2hi klr9ea-ca m(j4ands 1.4 m ii/9 mrlhajee2k c a-(4n front of it. If the image is three times the person’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror w)m)xate0u m ,that, when 2.20 cm from a tooth, will produce a $\text{4.5×upright}$ image. What kind of mirror must be used and what must its radius of curvature be?
 ----待选择----convexconcave 
r =    m

  Some rearview mirrors produce images of cars behind you that are smaller nbo) mb qz705pz81mhgthan they would be if the mirror were flat. Are the mirror0 g5m8bz zpnoqm)71hbs concave or convex? What is a mirror’s radius of curvature if cars 20.0 m away appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is placed 20.0 cm from a conz 7 ujfjf,y*isqs1)9yosuhgu ;-7oc1vex mirror of radius of curvature 20.0 sfos*)7o1ujhq-;y7,1s 9g yuu jfizc cm.
(a) Show by ray tracing that the image is virtual, and estimate the image distance.    cm
(b) Show that the (negative) image distance can be computed from Eq. 23–2 using a focal length of -10.0cm
(c) Compute the image size, using Eq. 23–3.    mm

  You are standing 3.0 m from a convex security mirror in a stb,nm;3 lv di:rore. You estimate the height of your image to be half of your actual height. Estimate the radius of curvature of the mirrol v;d3nm:i br,r.    m

  (a) Where should an object be placed in front of a concave mirror so thatxo,(* qm:ouvgb6 vh5fwx;je-0 p. q yk it produces an image at tm (qv y ;0j:5ouq.x*v bh-6pokwfg,xehe same location as the object?
(b) Is the image real or virtual?  ----待选择----realvirtual 
(c) Is the image inverted or upright?  ----待选择----invertedupright 
(d) What is the magnification of the image?   

  The image of a distant tree is virtual and very small when viewed in a cgq10dev/ yz c5urved mirror. The image appears to be 18.0 cm behind the mirror. What kind of mirror is it, and whd ecg50z1 /qvyat is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniques, wp,0e9 6is0r lj.xwq m
(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, :h+ nta/opk.j;m :h / kemiabuw+vd1,that the magnification m of a convex mirror is $m=-d_\mathrm{i}/d_\mathrm{o},$ just as for a concave mirror. [Hint: consider a ray from the top of the object that reflects at the center of the mirror.]

Use ray diagrams to show that the mirror equfh1r 6 v).axowation, Eq. 23–2, is valid for a convex mirror as long as aorx6.w h1f)vf is considered negative.

  The magnification of a convyjd1o3 -23/7bbn2ozvdoft mpwym5 l*ex 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 kq*1ug69o *ieoj2uk8tase ) nspherical mirror. It is desired to pr 9 ak*)8sko n6 ouiee2gujtq1*oduce a virtual image that 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 your16i81jxh myok face by a factor of 1.33 when your face is plamxh 1k6y8j1 ioced 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 iik 1j3jz3)q1j 1w cv.c- wmtpun
(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 a1.jnb 9izma-hhj5o0 is $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain 5epsw mj o(2dst857km m )s; k2fcfyj:substance is 89% of its value in water. What is the index of refraction ofskm(wdyjs8f ecm:2f 527 j to )kpms;5 this substance? n =   

  A flashlight beam strikes the surface of a pane of glkl4h1j sx;m7h9xk.,alogt /zf -e5icass (n = 1.58) at a 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashlight upward from ben ).y/cipew ao, xa :pawx+8/vwo-c (ct( qc9hbeath 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 exits the wateriu ib1js 7oib 08xt .k8o/al7l at an angle of 6a8tiub8o .0lx io / 1b7lsi7kj6.0$^{\circ}\,$ 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 31.03;k5vpwn s*popty 9fpg : d5;a$^{\circ}\,$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?    $^{\circ}\,$

  An aquarium filled with m2zz ikl,n, .- 0whqnewater has flat glass sides whose index of refraction is 1.52. A beam of li ih,we0zm n.kznq,l -2ght from outside the aquarium strikes the glass at a 43.5° angle to the perpendicular (Fig. Below). What is the angle of this light ray when it enters
(a) the glass, $\theta_2$ =    $^{\circ}\,$
(b) the water? $\theta_3$ =    $^{\circ}\,$
(c) What would be the refracted angle if the ray entered the water directly? $\theta_3'$ =    $^{\circ}\,$

  In searching the bottom of a pool at night, a watchmankv dq6di,hosfe* 4 1 q-txgn-* shines a narrow beam of light from his flashlight, 1.3 m above the water level, onto the surface of the water at a point 2.7 m from the edge of the pool (Fig. Below). Where does the spot of light hit the bottom of the pool, measured from the wall beneath his f*1q d,nvdeqto 4f 6*- gi-skxhoot, if the pool is 2.1 m deep?    m

  Light is incident on an equilateral glass -gf) a5rqtr:bprism at a 45.0$^{\circ}\,$ angle to one face, (Fig. Below). Calculate the angle at which light emerges from the opposite face. Assume that n = 1.58.    $^{\circ}\,$ from the normal

  A beam of light in air strikes a slab of glass as9/txhjjs8 1 ppep)m25 g )yo(n = 1.52) and is partially reflected and partially refracted. Find the anglh gs ))8jtsa/ey51j2xpom 9ppe of incidence if the angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light 6sfbp* xyzx9w)-s6l14uy 1s vst2jo obeam incident on a uniform layer of transparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the incident beam, independent of the incident angle l xyyo)1os x*v2 j9ws1fsp4z ut6b6s-$\theta$. Assume air on both sides of the glass.

A light ray is incident on a flat piece of glass with index of refraction n ludqi+*w0e,kyz)w 4hqp:7pbe l**thas in (Fig. Below). Show that if thi4whteh p+:p,ql eu**w7d)yk0bl z *qe 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 wat; tv+ f tmw7)a9p1oiraer and Lucite? To be totally internally reflectpivto9a+; a)1r tmwf 7ed, the light must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liqua)z 6iheag n01id–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 62.0 cm. Where mvg 2(du buviv89ib 5p;/a y)ffust it strike the air–water interface, relative to the spot directly above it, in orda fv8p(bu2 9v)bidf5 vg iuy/;er that the light does not exit the water?    cm

  A beam of light is emitted 8.0 cm beneath the surface of a liqui3o4*uytx o 33wbwmt mu br1w*:d 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 i3ouow : 3mby *ux1t 4ww*tm3rbndex of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the lef7a4p kz88k fkdt 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 an optic ,z2mu7ezudm 1 ;0t *nle5whys fiber as shown in (Fig. Below). Show that we can guarantee total internal reflection at the side surface of the material (at point a), if the index of refraction is greater than about 1.42. In other words, regardless of the angle the light beam reflects back into the mater*,uzz wm2 ; e1uenhsyml70dt 5ial at point a.

  (a) What is the minimum index of refraction for a glass or p,lu w))i ohr2wlastic prism to be used in binocuoh)2i,wr)u l wlars (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 78im +i;xcuo zkjx enyx,r5+* +..0 mm behind a 65.0-mm-focal-length converging lens. Find the object dis x;.uxm+rok j+i eixzy*,n 5+ctance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed 5.vpy4 d;k o lmv-vm0oto focus 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 m away as an image 48.4j c z;7joxsi(xhz7(3inht:z3 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 virtuai7(ztihh (s:jjzc x;z7x3no4l?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the power 8/f7)t7e -7zobazeogt a/ hgf 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 useslxw;a3-qlhhx:1 a /ihk noo3y(5xa)q a converging lens with focal length 24 cm to view a stamp 18 cm in front ofan)1h y:( 3w35l /xx xolqqio;hhak a- 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. W4 9fn7wzmab:z((t t2gv iz(p zhat are the position, type,g( t92f zvz (b7pa m4in:zzwt( 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 on the filmzwf i-5hl; sz9 of a camera. The maximum di-s5f 9iwz zlh;stance 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 mag1ru3 /fs 7t ;s4(gqblp;7dddrjn5frs nify reading material by a factor of 2.5× when a book is placed 8.0 cm behind a lebjpr rsg1sdrl ;3td( fq4d7u;n7 f5/sns.
(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. B/mz(7okwtg 9lzfb8 6z0 fy a5ky how much does the image move if z/b tfzm7y0w96ko agflk5z( 8the 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 with a focal l5-iew9jz 7lh )o;lfxjkkim9ic q y-ns0rq 2/ )ength of 25 cm should an object be placed to produce a real image which kix j/c ;se nl7-m2irk)w5lqo)f-q9 0z y jh9iis the same size as the object?    cm

  (a) How far from a 50.0-mm-focalrmemy 3c,-*kp09mm wi r z1b7o-length lens must an object be placed if its image is to be magnified 2.00×ciky epzm-m790 ,mrb13rom * w 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 len wp,cawi u.1ru jwy578s must an object be placed if its image is to be magnified 2.00ap y.wi81u ,5w 7jucwr× 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-lengthofog9/9no 9fck :0fmkift( fhkr g420 lens. Where is the image, how high is it, and whatfc 9gf:rfgfk00k4 9oimn/hk 9(t2ofo 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-focalzl 0u 1iks7k9q-length converging lens if the image is 2.5× large9ilq7kk1s z0 ur than the object and is real?    m

  A bright object and as tqz *5sv)ms+74gx5ld* ee gl viewing screen are separated by a distance of 66.0 cm. At what location(s) between the object and the screen should a lens of focal length 12.5 cm be placed in order to produce a crisp imlv ge*xgm5q )sl47s5zs d +*etage on the screen? [Hint: first draw a diagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length converging lenses are ploco n,v(k.x40 wjq:vhjzm6c zq c70 b;aced 16.5 cm apart. An object is placed 36.0 cm in front of one lens. Where will the final image formed by the second lens be located? What is the total magnifk;,0(mc.zco n:jvjobc zw0 6 vq 4q7hxication?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens witls*,nqcr:d*: 4wu8fbs:og/ g l:sbboh $f=-31.5\mathrm{~cm}$ 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 dp3zjj fu01/xf1e) zs.pi*ejp iverging 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 a ray diagramp.z fjujp pi0s e*zj/x1)3e1f.]    cm

  The two converging lensegpn6pmj+k 4r :hbdq1: s of Example 23–12 are now placed only 20.0 cm apart. The object is still 60.0 cm in front of the first lens as in (Fig. Below)b:pgmd:+rn46p j1hkq . 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 of th2 l sri;5dkjm7zbad4 :e 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 betw:b4sdzamki ; r 275ldjeen the two lenses. How far to the left of the 15.0-cm-focal-length lens is the original object?    cm

  A diverging lens with a focal length of is placed 12 cm to tt-pm8x 3hu i8whe right of a converging lens with a focal length of 18 cm. An object is placed 33 cm to thep -8xw83 mutih left of the converging lens.
(a) Where will the final image be located?    cm to the left of the converging lens
(b) Where will the image be if the diverging lens is 38 cm from the converging lens?    cm to the right of the diverging lens

  Two lenses, one converging with focal length 20.0 cm and one divergingvs 7br b,jr7 jhnct81,-sp 4dshqh) 0cq,xrz. with focal length are placed 25.0 cm apart. An object is placed 60.0 cm in front of the converging1hbs,,xcdq- s4zrp. n svr7,bj ch8hj07t)q r 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 ofak d8ttrmeb-r* 7)i-(e s8mqz*zt w* x focal length $f_C$ as in (Fig. Below). If $f_T$ represents the focal length of the combination, show that the focal length of the diverging lens, $f_D$, is given by
$\frac{1}{f_\mathrm{D}}=\frac{1}{f_\mathrm{T}}-\frac{1}{f_\mathrm{C}}.$

  A double concave lens has surface radii of 34.2 cm and 23.8 cm. Whuzj /7 wcmq+4sat is the focal length if n = 1.52mqj+/w4c7uzs ?    cm

  Both surfaces of a double con. tqv x60fye8;5i*whvf.lhwr vex lens have radii of 31.0 cm. If the focal length is 28.9 cm, wh v.wf*f8q 5 ie0wlr6;vx .htyhat is the index of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal length vc,n7 vf4/tu,7ovopa; 9wub j of -23.4cm. What is the radius of the concave su7cu 9w/4bpvv o ;uf,tn,avo7jrface?    cm

  A Lucite planoconcave lens (seei7k . ly/qdvo. Fig. Below) has one flat surface and the other hdiqvk.7l yo /.as R = -18.4 cm. What is the focal length?    cm

  A symmetric double convex0;f9 rw1ubhf9qn; wo0bcpf5yrlj* yboh-- m2 lens with 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 e9wm-p1f-bh*hyfn9 ;b0f2 jw orr;5c qlbu 0y oach surface?    cm

  A prescription for a corrective lens calls for +1.50D. The bsp+e:16mm lh: m8m nvlensmaker grinds the lens from a “blank” with n=1.56 nl+mmv 6mhm18::pb seand a preformed 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 mz5gzdad(f sq/uq..)5;l6w z5 tay1 :scoogjr apart as in (Fig. Below). You stand 1.5 m away from one of thestc.6s5.1gj(5d:wz) l;q dou5oazq a /rzg fys e 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 swiz mic e(t )55c uv)4zh6ef/vpjmming pool filled with water. We measure the width (x=5.50m) and then note that the bottom edge of hi 6pu4 )55/v)mjftze vccez( the pool is just visible at an angle of 14.0$^{\circ}\,$ above the horizontal as shown in (Fig. Below). Calculate the depth of the pool.    m

  The critical angle of a certain piece of plastic in air is v/.o szgq0)olp*sk 6e$\theta_{\mathrm{C}}=37.3^\circ.$ 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 on3bdps,;w m: hf a spherical mirror. Specify what this limit isb 3:;pnh mw,ds.
(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 th7qp:ehv+z/ap/ ha ,v+6o xit fey 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 form a l 8 pikkpn05+8jvipt8li kqno4: 2o-0+idy qhreal image of a real object. Can you describe a situation in which a divergiippkp- y8qjiv0d h+80 ook+ ql:in 852tlin 4kng lens can form a real image?

  Each student in a physics lab is hvef446p6+yqro4a+tlo .xrcassigned 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 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 labo 4qalxohcr6 fpvy 6++r44t.e, and justify your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of a prismsyz)))cd7wc4ue1h rb 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 cylindrical glass rod t84s,dz ed83 ot3 th;jj;km bj$(n=1.54)$ 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 lensqlrk jqf1hc.,j *n3 mi(4ag8w 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 sideot,:f4s(w.pfy z gk uf,f5*qo of a converging lens of focal length f, and (,f. f u:ogo5qwf zpykst4*,f a white screen for viewing 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 projector, the film iz,8m(oouu mmc+w3d fueh+ 50acts as the object whose image is projected on a ,d+3+u8m e05iwumzcmuo(ofh screen (Fig. Below). If a 105-mm-focal-length lens is to project an image on a screen 8.00 m away, how far from the lens should the slide be? If the slide is 36 mm wide, how wide will the 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 projecbcew-o q/j 5wn5;-;htg*a de pted 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 im- g q- odp;ew/*55jwa ;chetbnage is to cover the screen?    cm

Show analytically that the image formed by a converging lensu f(z,ft*ga6(r:p1jczomqy+. 4d ahm is real and inverted if the object is beyond the:zf,6p1z atmaqchf4o(+jmy*ur d g.( 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 syv;/u3s g ,iwfhooting 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 the reporter standing? f /yu,3vsigw;    m

  How large is the image of the Sun on film used in a camer1v0lz n/h l2fu nrg9ipwg)6c4a 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.