What would be the appjqs wr-p; pj+no mb,ozd6+qi44 tt03 fearance of the Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whtp:nmg9 i vt8 3za3(rzole Roman fleet in the harbor of Syracuse v83a9t (3inmzpgzr :tby focusing the rays of the Sun with a huge spherical mirror. Is this reasonable?

Although a plane mirror appears to reverse left and right, it doesn’t revere) 2kr86qcc4 vwl-t:gbhlsr; se up and down. Explain bc-re 6k 4qr)ht:cll2g;8v sw.

If a concave mirror produces a real image, is the image necessarily inverted? Egja/ms *gi64j/9wfbp xpl9 p/fbai46wggsmj/* j ain.

An object is placed along the principal axis of a s*w , 9m8bng9j+gxb0w eu)wh*fra 3 vybpherical mirror. The magnification of the object is -3.0 Is the image real or virtual, inverted or upright? Is the mirror concave or convex? On which side ofwx yfjhgu*r08bab3wwgm )e9n b+ ,*v9 the mirror is the image located?

Using the rules for the three rays discussed with reference to (Fig. Below a)ps4pwev4 8 xzto* x)pdll+d;ehymk44 *- s1 hx, dk)s*8welx;o t+ x*ydh p41d4hxv pl4sme-4pz raw ray 2 for (Fig. Below b).
(a)
(b)

What is the focal length x z ;,bxh 7fewsf+0pbr/u.mn7nja*j 7 of a plane mirror? What is the magnification of a plane +nfn x7efxj70m.z/h7b; p warjs,ub*mirror?

When you look at the Moon’s reflection from a ripply sea, it appears elon+9jf1k p3z znp fn,fb 1:i)xbfgated . Explanif)b,: fx9 f jbzpkz+np131f in.

What is the angle of refc: a.kc4:pub)s7b xl jraction when a light ray meets the boundary between two materials perpendicul js4 :7 .pcauxl:bbk)carly?

How might you determine the speed of lir63j ;3k pf twk7vd9nbght in a solid, rectangular, transparent object?rjkn ;b6vd7 t 3f3kwp9

When you look down into ax 8r.2ib( im;lgm8o yh swimming pool or a lake, are you likely to underestimate or overestimate its depth? Explain. How does the apparent depth v ( ixbr 8i;8g2molyhm.ary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks bent wy0 3q9uftsn1p hen part of it is under water (Fq n0t9up1yf3 sig. Below).

Your eye looks into an aquarium and views a fish inside*+jy l( vx:kbd. One ray of light that emerges from the tank ikjvy( bxd l+*:s shown in (Fig. Below), as well as the apparent position of the fish. In the drawing, indicate the approximate position of the actual fish. Briefly justify your answer.

How can you “see” a round d kexs*6/(jag:jri dz2rop of water on a table even though the water is transparent and colorless?*d:g/ xejisr(6zkaj2

When you look up at an object in air from beneathy 3td/jmjh ka j;*mh.4 the surface in a swimming pool, does the object ammjjy4 3.hh*t;ak/j d ppear to be the same size as when you see it directly in air? Explain.

How can a spherical mirror,: ,9zeeltt uy have a negative object distance?

Light rays from stars (including qxdfcf2y/,y(i uvg3. our Sun) always bend toward the vertical direction as they pass through t c3yuq2,(gdy/xv .ffihe Earth’s atmosphere.
(a) Why does this make sense?
(b) What can you conclude about the apparent positions of stars as viewed from Earth?

Where must the film be placed if a camera lens is to make a shardk oe6h hba-)-p image of an obje)6-bdo-k haeh ct very far away?

What type of mirror is shown in (2y1 ulbv*fkm6 / w 0xivtksd 3sc*a8s1Fig. Below)? Explain.

A photographer moves closer to his subject and then refocusesg,u w:(wg oh 3vez-c,rsji3j9 . Does the camera lens move farther from or closer to:-,ecvg(39 gwj hrio, z j3suw the film? Explain.

Can a diverging lens form a real image unde/pc imxw v :dt-t4wi)5r any circumstances? Explain.

Use ray diagrams to show that a real image formed eo -4lvp(bp.oby a thin lens is always inverted, whereas a virtual image is always upright if th (p-4belp.oove object is real.

Light rays are said to be “reversible.”ryzu5o01 bsslgg, /8r Is this consistent with the thin lens equatioyr/rulb s g50s81 g,zon? Explain.

Can real images be prod s plr1 m6 g69/yf*kdvqby4:rjected on a screen? Can virtual images? Can either be photographedp1dqk:dm9 vfl/yr6 46b y*rgs? Discuss carefully.

A thin converging lens is moved closer to a nearby object. Does the real ima v6x5f*b wh/pr+rx;bf ge formed cha6xr*+;phbxfw 5f r/v bnge
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of refracti*,jz 8dsy2,lh me+zup ckp2 r-on n = 1.30 In air, it is a converging lens. Will it still be a convergingjhu myz zc +le2 d,k*p-2p,rs8 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 gkuzv4 nag;*t 5m2o k(converging lens. If the nose and the tail are each focused on a screen in turn, which will have the greater magnificationn(;gg2m*4uk vako5z t? ----待选择----nosetail 

A cat with its tail in the air stands facing a cvkw (w8 f.guhw, u+dai; kdb2,+ui(0lx vi7kmonverging lens. Under what circumstances (if any) would the image of the nose be virtual and the image of the tail be real? Where would the image of the rest of t7(ivwai,ku+k u8k mh +w d2v0l(.bwux;,gd f ihe cat be?

Why, in Example 13, must the converging ya yo1w- f0gn(nc s-:elz :hgy)n9uo (lens have a shorter focal length than the diverging lens if gy nsuyye01-gl:9fo(n :onzh) awc-( the latter’s focal length is to be determined by combining them?

Explain how you could have (tby 9drrpv*gy, d9 :ra virtual object.

  An unsymmetrical lens (say, planoconvex) forms an image.2 gp3q3 cda.tcqx dk5 of a nearby object. Does the image point change if the l gqkp2at.d35dcx q.c3ens is turned around? ----待选择----yesno 

The thicker a double convex lens is in the center as compared to its edges, the 1wf7 nmrkajdi0t)1*xk nl ,,rshorter its focal lnjk7*airxwlk01)t, m1nd , fr ength for a given lens diameter. Explain.

Consider two converging lenses separated by some distance. An object *1ag,ay 6p wug rr71huis placed so that the image from the first lens lies exactly at the focal point of the second lens. Will th67*p ug1gwu, yarrh1a is combination produce an image? If so, where? If not, why not?

  Suppose that you want to take a photograph of yourself as you look at yo* frnk690ve srur image 9ev6 *sn0rkrf in a flat mirror 2.5 m away. For what distance should the camera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mirror, you u p*/n ,opk,z6 ck:fpfsee the same amount of your body whether you are close to the mirror or far away. (Try it andok f6/pkp,,cpu :n* fz see.) Use ray diagrams to show why this should be true.

  Two mirrors meet at a 135- aqey1izfvqwyx24 s))g)ln )$^{\circ}\,$ 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 arrhb u5bitj7 8ko*(3g we 1.68 m 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 t tb8iju* gh75wb3(rok he 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 hn r)oj(e*f1k+no+y dis used to reflect the rays entering one eye from a point on the tip of your nose if yn+ dehor() j1n ofy+k*our pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two planco lrg p72td ,qak*2tm7iq5e0e 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 conc-g fwh,m, q(t hsw3py)r,hvx 0ave 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 whw,hfvyq)w- 3sth ,r 0px(gm,hich the mirror was made?    cm

  How far from a concave mirror (radius 23.0 cm)i7id7qv9/ s- sul h iz7ofob6v5d zl12 must an object be placed if its image is v2zii ul 1 d7i97v56s-hsob7 f/zqdolto be at infinity?    cm

  If you look at yourself in a shiny Christmas ukqv815j6hpstree ball with a diameter of 9.0 cm when your face is 30.0 cm away from it, where is your image? Is it real or virtual? Is it upright or inverted? u5 p1qkvs86jh
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shows an upright image oct018yjcnna5 f any person who stands 1.4 a nc1j 0ytn5c8m in 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 that, when 2.20 cm from a tooth, will produco,+ljt az64a 8slphr /e 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 cvnci662qytlp++3 +f nmhdtz5 ars behind you that are smaller than they would be if the mirror wfpm+2nn3h+t56q6 z i +dytlcvere flat. Are the mirrors concave or convex? What is a mirror’s radius of curvature if cars 20.0 m away appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is placed 20.0 cm fr(y1cgzq; arov y m)7tnchce2.2qf13 e om a convex mirror of radius of curvature 20.0 af3n1heqyv(g7) ; yzt2moc.q e1 c 2crcm.
(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;pw*g,kqd kemu)ch 21 convex security mirror in a store. You estimate the height of your image to be half dcg*m2kq; k 1e,u )hwpof your actual height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object 8y k 5-:xqt*t tg51atm2pyvbnbe placed in front of a concave mirror so that it produces an image at the same locay8vat1p*:n5 2t-ttmkg y5bqxtion 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 curv s *oaig:ui+6(bd+xky.gz)7y8e nxwaed mirror. The image appears to be 18.0 cm behind the mirror. What kind of mirror is zs)ny+*6aa7 x.x+8ko di(webyuggi: it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniqu1dc/2b, gv*hu .nqjst es,
(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)rojl 0bp lg ,ecp2/m3j)*iro 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 equ+bw.iquit 5 nxua eb1dp:r*+ (ation, Eq. 23–2, is valid for a convex mirror as long as f is considered negatt (5e1.i *nduw+ b:iubrx qap+ive.

  The magnification of achr kss xhb10-it)9 jt;,.:m a 4(x-sxw uxyst convex mirror is $+0.65\times$ for objects 2.2 m from the mirror. What is the focal length of this mirror? $\theta_2$ =    $^{\circ}\,$

  A 4.5-cm-tall object is placed 28 cm in front of a spherical mirror. It is;a4c.ly) u(sjkbgz*ox k 3cn+ desired to produce a virtual image that is uprig4x()l kjo.3cu kb+zcg; ysa n*ht 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 fac 5suktqqg/ggqvg 91eh22/i p1d u4t(3 hbkcw0e by a factor of 1.33 when y(34k2 u whdc b/ g1t0qupsggkq95v/g12qheti our face 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 in ..ogw,j .hj.yelj/x w
(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 :5 +pqpq z+f zkbq0-nxis $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain substance is 89% of its value in water. What isp q*9b 1k4aou(w8mj hm the index of refraction of this substance? n = 4j(89o*1 bmpq hmukaw  

  A flashlight beam strikes the surface of a pane ofmg ygr0zs1g(t g da0:5 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 flashlight upward from beneath the 1ili s)wahhz 1 )1a:fywater 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 water at a4ysnb2a+n y +h :ai-wkn4t7p tn angle of 66t+ tn2 h+ -b:awy4n 7aki4nsyp.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 ,(+xd jkgwb-z make a 31.0$^{\circ}\,$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?    $^{\circ}\,$

  An aquarium filled with water has flat glass sides hmyx7v0h2dafnub8 d bk;b37.xkn 2,twhose index of refraction is 1.;3t72damhb.8x2nufb 7xh, 0kkbn yd v52. A beam of light from outside the aquarium strikes the glass at a 43.5° angle to the perpendicular (Fig. Below). What is the angle of this light ray when it enters
(a) the glass, $\theta_2$ =    $^{\circ}\,$
(b) the water? $\theta_3$ =    $^{\circ}\,$
(c) What would be the refracted angle if the ray entered the water directly? $\theta_3'$ =    $^{\circ}\,$

  In searching the bottom of a pool at night, a watchman shinespl6adc ,gw 66s a narrow beam of light from his flashlight, 1.3 m abowg6p 6sadlc,6ve the water level, onto the surface of the water at a point 2.7 m from the edge of the pool (Fig. Below). Where does the spot of light hit the bottom of the pool, measured from the wall beneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equilateral g30s wm.amnr;e/akfz9p h 6:dy2 o7afdlass 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 strikes a slab of glass (n = 1.52) and is partially refle, xhl2pk0ox2/t ub vn2cted and partially refracted. Find tbo/0 2kt22vxux, nlph he angle of incidence if the angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam incident on a uniform layedaehfr p8 9q,ah-; y gdd7a+:ur of transparent material, as in (Fig. Below),gpd8daarhh:a+;fd y-e97u q , 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 pbe2 ;-u fz:0/cjbhiuh iece of glass with index of refraction n as in (Fig. Below)./ buf; uei-2zc 0:hhjb 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 between water and 16wc 9w;s0a+nh7tzz qnwd p (tLucite? To be totally internally qzsa97 c+n(hw1;n0wdw6 ttzp reflected, the light must start in which material?
$\theta$ =    $^{\circ}\,$
 ----待选择----waterLucite 

  The critical angle for a certainsgnv w.x o tek )t()*/rm+de)c 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 62.0 cm. Where 4f*.jxq4bmp cc n) s3omust it strike the air–water interface, relative to the spot directly above it, in order that3. fx sbpn*4m)qjcoc4 the light does not exit the water?    cm

  A beam of light is emitte ir es(zxw8 n7az.a9j5d 8.0 cm beneath the surface of a liquid and strikes the surface 7.0 cm from the point directly above the source. If total internal reflec5x esjra( 7 .za9ni8wztion 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. Below) a4xw4+jg7v14 fzw zanci* qyf 1t 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. Below)bpz+x ,xxuxw z8pusvh,op7 (4+rc0(a. 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 wor,r+zp ,b+0uv ( howc48pspzax7xu(xx ds, regardless of the angle the light beam reflects back into the material at point a.

  (a) What is the minimum index of refn i8ke-d9e1lh 0pr jel3su/t)raction for a glass or plastic prism to be used in binoculars (Fig. Below) so that total internal u1 r-edtje9s lnh i/pl380)kereflection 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-l7:x y)k1d94 t tz(wf kdrcq/sht-gen /sr*s.length converging lens. Find txf9de rt/s/shzrg 4-kycs7 lt (t:* 1w.d)kqnhe object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to p-q1u:ej zdngp31dj.0 *gqs kfocus 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 adq tt 76xrdevi 3d50/yway as an image 48.3 cm on the other side of the lens. What type of lens is it and what is its focal length? Is the image real or virtual7 50/ddtevy r6q3dxti ?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the power of aoig6 fr)0b.nv 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 stamp 0wj( kc-+hpf 8ini8fh 18 cm in front of8ipj(w ich08n fh-f +k 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 objef8 az.28yd-oklg )y nect 4.0 mm high. What are the position, type, and heizeyy-fo8)d2gn8 l. kaght 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 9mj,ejwokv kb8- / +ra,ho1qv film of a camera. The maximum distance allowed betweerjb 9hkq 8+ akw/o ojevv,1m,-n 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 reading material by a factor oce6/ w31*y0 owqfdlx ff 2.5× when a book is placed 8.0 cm behind a lens w3o1 c6deffw0 l/*xyq.
(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 a0uo s)-xkybozv r93:)j;f v -jkqhh v;n 8.0-D lens. By how much does the image move if the ;f9b- ozyo vj 3 0vkq)h rkv:);uxs-jhobject 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 foc7a 4b p9xqg8di-+xduk al length of 25 cm should an object be placed to produce a real image which is the same size as the object? p 9udx8+qdgaik7xb -4   cm

  (a) How far from a 50.0-mm-focal-l;jfixa zsie)y008 w5si 6qmy5ength lens must an object be placed if its image is to be m06jwxmfsa y)si5 ze58y; qii 0agnified 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 lens must an dbn/od9e:ys6n7a2a mobject be placed if its image is to be magnified 2.00× a /y 2nd osb6emd97:naand 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-m2ga9fs/a 6 kihm-focal-length lens. Where is the image, how higk/ ga69afhis2 h 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* ideuk/7 l 3r42ja y:bexcg8a and an image formed by a 75-cm-focal-length convergi4e*3bcal/yjaxd u :r 872 gkieng lens if the image is 2.5× larger than the object and is real?    m

  A bright object and a viewing screen are separa)oz x)/6wd7rq nqr l)csj.d r -0)rljzted 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: first draw a ddd )lorcjz rswxz6qr/) n q)rlj-).70iagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length converging lenses are placed 16.5 cm i o3km (i)jke0w acyd ))iu8k-p5 r*wsapart. 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 magnification? 3o5a(*k-ym d))prk0eiwu js8wiic k)
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens withj 6n35qij ftpnn:sb *8 $f=-31.5\mathrm{~cm}$ 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 2kwn:g6v(a .xr 1.0 cm behind a diverging lens. Parallel light strikes the diverging lens. After passing through the converging lens, the light is again parallel. What is t xag6k :rw(.vnhe focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Examplpb(*hdamj ,lz)0 cb66t j- cqjuj,n 8me 23–12 are now placed only 20.0 cm apart. The object is still 60.0 cm in front of the firstmb,ha-p ( zju dm6*bn86jjq jc0)c,lt 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 l,d *d u )yadfwv;g s b0m0bl7yu,ms8i(eu i0z-ength 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 th(s 0 )0ew;d-,g7yu bdai0zvs,byum u *ld8 fime 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 c(ks1 n7ufrm6z mpvmx1 x45j(mk7 8we 12 cm to the right of a converging lens with a focal length of 18 cm. An object is placed 33 cm to the left of the con8kpe(m6mxvwr u1 77mc1s(4znkmjxf5 verging lens.
(a) Where will the final image be located?    cm to the left of the converging lens
(b) Where will the image be if the diverging lens is 38 cm from the converging lens?    cm to the right of the diverging lens

  Two lenses, one converging with focal length 20.0 cm and one divmuy +lj 6nnu9 zya-1x -d8cki(erging with focal length are placed 25.0 cm apart. An object is pla+1l(n dk -ua89cyj znu -xyim6ced 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 fir0us63ora-z q )0kv )grfzt )ocal 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 34.3vadl j95up szo+.fog (v (6;(mk f.jhzi gk6l2 cm and 23.8 cm. What is the focal length if n = 1.52azuhz l3 ( mffo.jv6d;i9 lo(k+vp5s.(j g6kg?    cm

  Both surfaces of a double convex lehb,gel1 n8gi7xxthuh(s -f( v74 nop3ns have radii of 31.0 cm. If the focal length is 28.9 cm, what is the index of refraction e, tg-h bl41fo7ins3vh xup7h g8n(x( of the lens material?    cm

  A planoconcave lens (n=1.50) has a fosggi-a4 e,v gzd6pz 6;cal length of -23.4cm. What is the radius of the concave surface? 4g zp-v;66agi ,g dezs    cm

  A Lucite planoconcave lens (see Fig. Below) has b/3 ejsjs.vq4 y(pgn)7dyn99br -(mv*buy s o one flat surface and the other has R = -18.4 cm79nb)y ms9sv jegqb.j(3do/(4b nrsu p*yyv -. What is the focal length?    cm

  A symmetric double convex lens with a focal length of 25.0ouc+ ,i - y/uchg+fz* 6yfo2bc cm is to be made from glass with an index +g2,cyf-ou z uioc b6 hcf/*y+of refraction of 1.52. What should be the radius of curvature for each surface?    cm

  A prescription for a corrective lens calls for +1.50D. The lensmaker ey.yirt iv9u-6k 9h8wgrinds the lens from a “blank” with n=1.56 and a preformed convex front surface of radius of curvature of 40.uty.iwehy - rv8 69k9i0 cm. What should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.6 5:97h4 l1*zyemc4 -tmnzj2uabku9 rjp ro us0 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 images of yourself. m5r7h9eucu4jz j-:sla926 ork1uty bnm*pz 4
(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 w3qt;i (g.,q. suinz//2mdx 0 ujwlbh qith water. We measure the width (x=5.50m) and then note tut3 0b l;qius,.g (j h/dmxwqnz.qi /2hat the bottom edge of the pool is just visible at an angle of 14.0$^{\circ}\,$ above the horizontal as shown in (Fig. Below). Calculate the depth of the pool.    m

  The critical angle of v5p avrcb2l xe ,213ara certain piece of 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 considered a limiting case of a 0aff/ uxe p,7lp9j(zc/ fi,*na,lu yw spherical mirror. Specify what this limit is. af upc/7 e/,9(xw0 *,nyiauj, llpfzf
(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 mirro3 f8sjamz i wpwanhk.1v 47n,gm .bh,-rs so they form a 90$^{\circ}\,$ angle as in (Fig. Below). When you look into this double mirror, you see yourself as others see you, instead of reversed as in a single mirror. Make a careful ray diagram to show how this occurs.

Show analytically that a diverging lens can never fo(eltn l 8t0 o(xxj23zucid x)*rm a real image of a real object. Can you describe a situat xt oxd8nzeicl(tl 3 0j)x*u(2ion in which a diverging lens can form a real image?

  Each student in a physics lab is assigned to find the location wny6aym4bt4z 5gp e*w (here 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 z(met4yp4 a*5byngw6 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 pripc1gdc ;xg5og. rn +i z44jh)ssm 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 cylindr6,.r8v , w ag,4zsqk iau,yahgical 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 o)ph)vmd5uvq7w a. m3lens of focal length $f_1=15\mathrm{~cm},$ which in turn is 55 cm in front of another converging lens of focal length $f_1=15\mathrm{~cm},$ (see Fig. Below).
(a) Draw a ray diagram and estimate the location and the relative size of the final image.
(b) Calculate the position and relative size of the final image.

A bright object is placed on one side of a converging lens of focal le p 9*ob6lfy1uxngth f, and a whiteyfpx l1u ob69* 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 fily ; p1eppv8a rhw .2p*v 7n*,nmyvky3tm acts as the object whose image is projected on a7pvty*np wv;8v ya yr,em1.n*2 kpph3 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 proju6 z;v;zz22ymtl j9qc ected on a screen 1.80 m by 2.70 m placed 7.50 m from the projector. What focal-length lens should be2mlc tz qzy2u j;9z;6v used if the image is to cover the screen?    cm

Show analytically that the image formed by a converging lens is real andmvvyzs 2jd mgtcd9+89s2c86 f inverted if the object is beyond the yc89s82+2 v6fc z9dmtj gsmvdfocal 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 pictu7u.,vz xk*z3 fq3qbrqbz6 0ycres 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 oxvq3 qz 0qzr b zcb,3*6yuf7.kn 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 imagdk 892mbpout7b *kq8ce of the Sun on film used in a camera with
(a) a 28-mm-focal-length lens,    mm
(b) a 50-mm-focal-length lens,    mm
(c) a 135-mm-focal-length lens?    mm
(d) If the 50-mm lens is considered normal for this camera, what relative magnification does each of the other two lenses provide? The Sun has diameter $1.4\times10^6\mathrm{~km},$ and it is $1.5\times10^8\mathrm{~km}$ away.    for the 28 mm lens    for the 135 mm lens.

  (a) An object 34.5 cm in front of a czx)9) mz ,p vnnuy,t7sq6t 2gu.v-xriertain lens is imaged 8.20 cm in front of that lens (on the same side as the object).vzu7tn .sg, ,)vy6ux nmxz)-t29qpir 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)

  When an object is placed 60.0 cm froaim8b4l2c4pa c d)y m-m a certain converging lens, it forms a real image. When the object is moved to 40.) 2m4-b4 a8iam ldcpyc0 cm from the lens, the image moves 10.0 cm farther from the lens. Find the focal length of this lens.    cm