What would be the appearance of the Moon if it had y/r fxq771dyis 8 s:ynw2 o*(d7 gaemq
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fmsguydvcv esgo5 w;3z81)5 u1 leet in the harbor of Syracuse by focusing the rays of the Sun with a huge spherical mirror. Is thi v)vuu ezs5y1w5cm1s ;38d oggs reasonable?

Although a plane mirror appears to reverse left and right, it kxo2qq)6ov4 o u 5.xuqdoesn’t reverse up and down. Explaq.ouqov)65 qx4kuo x2in.

If a concave mirror produces a real image, is the image necessarily - **vyrs1(uqu*r qlsn inverted? Explau v -1qql*r*r sy(usn*in.

An object is placed aiyt,:3*t1/ia s lqykglong the principal axis of a spherical mirror. The magnification of the object is -3.0 Is the image real or virtual, inverted1a g*/kqt:t ys,ii3yl or upright? Is the mirror concave or convex? On which side of the mirror is the image located?

Using the rules for the three rays discussed with reference to (Fig. Below a)n+i+s h+ eyc6*99ijcv)2tosa0jfx fp, draw ray 2 for (Fig. p sxy*jsj+)0o9fe+v2c9 ih+ait6f n cBelow b).
(a)
(b)

What is the focal length o rzas4-3qn nq1q xh0z,oa6ax5f a plane mirror? What is the magnification of a plane mirroh 301oq a-6azqn,x z4asq5r xnr?

When you look at the Moon’s reflection from a ripply rc/(3b0e21qv yf;(i6ty/xlmocxfl j sea, it appears elongated . Exf0x;/rf(6iy3yc lvx2c/q( bmj et1loplain.

What is the angle of refraction when a light ray meets the boundary betu:5a t3fbsk)b oy-5yv6gpa i.ween two materia-uaaib g5oy3 )y:f65 p. kstbvls perpendicularly?

How might you determin3po n40*tlon ee the speed of light in a solid, rectangular, transparent oop ne4t*3n0 lobject?

When you look down into a swimming pool or a lake, are you likely to uoa86z 1w2r.aobu( jn gnderestimate or overestimate its depth? .( zw ograab6nu12 oj8Explain. 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 m)/.kc-bbj ec g4y2xiunder water (Fig. Below).)k/c yjbg.ce2mx4bi-

Your eye looks into an aquarium and views a fish in rzc+wcy6m8r7side. One ray of light that emerges from the tank is shown in (Fig. Below), as well as the apparent position of the fish. In the drawing, indicate the approxrymzcc+ rw867 imate 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 is trr 5lo.r2 ,vlfseke dy-i 2p7tfdlr0-/ansparent a il2vy,e7-eddk rs f2ltlf.5r pro/0- nd colorless?

When you look up at an object in qf30g b n q3og6rr(x2f+iuw2t air from beneath the surface in a swimming pool, does the object appear to be the same size as when you see inf 2 ob2rqu6gfgx i3qw(0r+3tt directly in air? Explain.

How can a spherical mirror have a negative obxnoipafr74) v;wxtv8 5 p pfo.18vbe9ject distance?

Light rays from stars (including our Sun) a7ym*1etlfgu4s2r u/ .c rd0lq7y8 wrrlways bend toward the vertical direction as they pass through the Earth’s aturtqms14*2y/rgu07 e.dylwcl f7r r8 mosphere.
(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 bvt /cw1mpfgi476 sx 3is to make a sharp image of an object very far xc/6v i1 p4w3fgsmb7t away?

What type of mirror is shz (8u mohs j6*wss)*ml.o 8jlsown in (Fig. Below)? Explain.

A photographer moves c26qsg(amp 0cgwcy7m)ytn z -v 1 dg8z,loser to his subject and then refocuses. Does the camera lens move farther from or closer to the film? Explain6z1tdgs8(q-gz) a y7 gcmw,vny0 mc2 p.

Can a diverging lens form a real image ugbqtk 3 i2uf8773rx zsncu 1:pnder any circumstances? Explain.

Use ray diagrams to show that a real i)kt4punm z 17ymage formed by a thin lens is always inverted, whereas a virtual image is always upright if the object is real.n14z p7y)mku t

Light rays are said to be “reversible.” Is this consistent with thej jbi.fk,giky;j8x / , thin lens equation? x;g,, jkib.jj/ikf 8y Explain.

Can real images be pr.jes nc4me23p ojected on a screen? Can virtual images? Can either be photographed? D p23c menj4es.iscuss carefully.

A thin converging lens is moved closer to a nearby object. Doefgcj1xs.k1,/q: v e gzs the real image formedfeksj, . qg1v1 c:gz/x change
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of refractiv rye(svb:,;aon n = 1.30 In air, it is a converging lens. Will it still be a converging (:r;,vebva sylens 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 nose and ao(m) er gz4s0nwv0,y4mwszr(e ,00 ygn)o vathe tail are each focused on a screen in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stand:c. ugy4dm)(vi4 r fchs facing a converging lens. Under what circumstances (if any) c( v ri4fu4 gy:hmc)d.would the image of the nose be virtual and the image of the tail be real? Where would the image of the rest of the cat be?

Why, in Example 13, must the converging le9 3l t8uz wa1alvz99;qrnpzj1ns have a shorter focal length than the diverging lens if the latter’s focal length is to be determined by combin 1a wqpj98z 3l1un9r;zt zalv9ing them?

Explain how you could have a virtual obw*ufv-w3o ngjfh. 03cject.

  An unsymmetrical lens (say, planoconvex) forms an image of a nearby objeccpxwt; 6 vn4t0t. Does the image point change if the lens is turned aroux;tn0wct p4 v6nd? ----待选择----yesno 

The thicker a double convex lens is in the center as compared to its oa6:xhnk)-ecyn, k6 yedges, the shorter its focal lengecyak 6hnx 6- )y:n,okth for a given lens diameter. Explain.

Consider two converging lenses separated by 2kn *ezvb,+ knsome distance. An object is placed so that bzk n kn,*ve+2the image from the first lens lies exactly at the focal point of the second lens. Will this combination produce an image? If so, where? If not, why not?

  Suppose that you want to take a photograph of yourself i tb/ .: 4l0pj:j*7znfxtexiqas you look at your image in a flat mirror 2.5 m away. For what.47:n0ix zfi */qxjbpttj e: l distance should the camera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mirror, you ser+fmcjy.u :b,r6. gpb e the same amount of your bod.bu r f6+mycpb.,gj:ry whether you are 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 a 1lv(+:),t zb23icbmv4zpubcn3 pz 4ym 35$^{\circ}\,$ 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 t1ts)pu8vox 4 93ktuzfloor 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 the mirror of the nearest point on the floor that ca tu9tvu81z)ko pstx34n be seen reflected in the mirror?    cm

  Suppose you are 90 cm from a plane mirror. What area of the mirror is xhmv 1xs3+dd.o(a ly .used to reflect the rays entering one eye from a point on th +xmdsl.(dxhyav13. o e 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 angl+ajo 6: /a eyty2qi8tne $\phi$. 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 a.5vc hryg qq+(on/1 4wak m5kyt the Sun, focuses the Sun’s rays 18.0 cm in fvnygr aq4/kwqo+. hy kcm15(5 ront of the mirror. What is the radius of the spherical surface from which the mirror was made?    cm

  How far from a concave mirror (radius 23.0m4br2 g3hcw( p cm) must an object be placed if its imcpw(b4m23hg rage is to be at infinity?    cm

  If you look at yourself in a shiny Christmas tree ball withvg ;xpgb3 u.m .jpe( g /akic,kh:j*(c a diameter of 9.0 cm when your face is 30.0 cm away from it, where is your image? Is it realc j( /j:xgb3 miua.ce(; pp,h.vg*kkg or virtual? Is it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shows an wgld/i +g8,x lupright image of any person who stands 1.4 m in fronw,l i8glx/ gd+t 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 2sigk28; m57irhpfsdf2zoj+k 0n 7 s-(dmp bx ).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 smadqw9ux ,vsj.6t 1r 6wyller than they would be if the mirror were w xdswyv 69, 1qrju6t.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 cmshdtb y/6ga hv*37,0 z6fars q from a convex mirror of radius of curv rhq0 6/g*ta ,fyzv 3bh6s7dasature 20.0 cm.
(a) Show by ray tracing that the image is virtual, and estimate the image distance.    cm
(b) Show that the (negative) image distance can be computed from Eq. 23–2 using a focal length of -10.0cm
(c) Compute the image size, using Eq. 23–3.    mm

  You are standing 3.0 m from a convex security m,onm8a r* pchy. xt/x8irror in a store. You estimate the height of your,8on.cmx8 xhta yp/ r* image to be half of your actual height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object be placed in front of a concave miyi1, tx*8z:lcutx9tc rror so that it produces an image at the sametttyz 8l9xx : ,c1ci*u 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 argedaou b)9+2r-b 6k z curved mirror. The image appears to be 18.0 cm behind th 6or 9-d2ka+ gebrz)ube mirror. What kind of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniqhr(q/ b kn90ek;azi+6b53z rd6 2d)wx wyrumm ues,
(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 theg;;uehjxh,w.n 6d n+4d ej8sw 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 equation, Eq. 23–2, is valid for a g,5kl i9woj(econvex mirror as long as f is considered gw( 5,loj9iek negative.

  The magnification of a convex mirror 7ab,l q8:wb 5cgxx +imis $+0.65\times$ 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 mirrokd c: 8nqeg 7li 73 8akxus3;f*tg:mmur. It is desired to produce a virtual image that is mt8acnmukd7l 83 s7q:g3;gf e:*ux k iupright 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 face by a factor of 1.33 w24 t.c fhkv4sfhen your face is placed 20.0 cm is k.f4t4vc 2hfn 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 fx jhy48)i0tcin
(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 icev2rc5 hs 8ue2a /lit;k 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 89% o v dm29qmqdide 26ip*fa)u20m;ep ke;f its value in water. What is the indexe2pfdq;6u; * e0a ddmv22mqkii9p e )m of refraction of this substance? n =   

  A flashlight beam strikes)p7 r.wn gc/ ru /:te6kolexh9 the surface of a pane of glass (n = 1.58) at a 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashlight upward from beneath the water/ d6b irdyfc899 jdw2l 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 ;t/l qj)4atq5 3xvcbs v6 wck*an underwater spotlight exits the water at an angle of 66.k c 6q*q)tsx/ tc3vlv4wb5;aj0$^{\circ}\,$ 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 t7phu c.s yx+.vo 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 g0xcpp ;(z*a *7m:vycso w/on rlass sides whose index of refraction is 1.52. A beam of light from outside the aquarium strikes the glapmzc7sn:a0 o*wr /c *(opyv;xss 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 shi 0e/rk)dnwu0z nes a narrow beam of light from his flashligk z ue)0n0dr/wht, 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 foot, if the pool is 2.1 m deep?    m

  Light is incident on an equil dejd5c7dar, :ateral glass prism at a 45.0$^{\circ}\,$ angle to one face, (Fig. Below). Calculate the angle at which light emerges from the opposite face. Assume that n = 1.58.    $^{\circ}\,$ from the normal

  A beam of light in air strikes a slab of glass (n = 1.69 7y)xok:hyk:nblkq 52) and is partially reflected and partially refracted. Find the angle of incidence if the angle of reflection is twice the angle of refraction. b :)ykk 9ohqkx6y:ln7    $^{\circ}\,$

Prove in general that for a light beam incident on a u+7i.kf v ewoiptv 5.o4niform layer of transparent material, as in (Fig. Below), the direction of +ivt 5o4keoip.vf7.w 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 refraction n*i9,ti ejy; em as in (Fig. Below). Show that if th itie 9,j;ey*me 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 Lucite? h82a* kv5g qh;;abjwnd4h4 l9m abfn8To be totally internally ref9hhkamq5w4h28 b;4jn;na8lb* adfvg lected, the light must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a md jb 9 v:y*(ecpcs8m;certain liquid–air surface is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in a pool of water from a depthc(r8nhu+;u )vro6omn g9 f7xky;,uqt of 62.0 cm. Where must it strike the air–water interface, relative to the spot dir6qk;f7vmy )u r(nu ho9;c8o ,t+n rguxectly above it, in order that the light does not exit the water?    cm

  A beam of light is emitted.ey(dk(6v ( bsrwyzc5 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 reflection occurs, what can you say adyb5ryk(.ve wz(s6c ( bout the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes tpny47on 06o cjhe left 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 fiber as shown in (Fig. Belo .5w. m+ro p gmgu0gbh.ps;ww0w). 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 reflect.5gphrmggom .wws 0.0+bpuw;s back into the material at point a.

  (a) What is the minimum index of refraction 31)rtqwjh t fgcn2 19kfor a glass or plastic prism to be used in binoculars (Fig. Below) so that totagf1n19qtt c2h k)wjr 3l 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 6prlz4o bt zd.jy .3/z;2 v0mtx5.0-mm-focal-length converging lens. Find trdtxo.zm4;b2v.3l y / jztp0zhe object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point5 ucrpxdd *fx t:/c70v 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:fok2gl mo6mr xzwkz 0z)5t/; .3 cm on the other sidm6 zgw;/otloz5xzf 2 0krk:m)e of the lens. What type of lens is it and what is its focal length? Is the image real or virtual?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the power ofj3bs /:.h: qv/fu bh d sepz3tw(js,zeb*g, *l a 20.5-cm-focal-length lens? P =    D  ----待选择----converging diverging 
(b) What is the focal length of a lens? $f$ =    cm  ----待选择----converging diverging 
(c) Are these lenses converging or diverging?

  A stamp collector uses a converging lens with focal length 24 cm to view a sd wub d/9x-03im-uex*d8 vp jdtamp 18 cm in front of th 0 e j*m9 v3xu8d-di-wdxdpbu/e 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 5b7g 6 iggd,ikhigh. What are the position, type, and height ogg,d b57gkii 6f the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is u8 pxbmxsr1 klvp17npmuu7 31:sed to focus an image on the film of a camera. The maximum distancel :bm 18pp s1mr1npxuk73u v7x 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 reading f)j8o7x3cjg y material by a factor of 2.5× when a book is placed 8.0 cm bgj8c x fy3o7)jehind a lens.
(a) Draw a ray diagram and describe the type of image this would be.  ----待选择----realvirtual 
(b) What type of lens is needed?  ----待选择----converging lensdiverging lens 
(c) What is the power of the lens in diopters? P =    D

  An object is located 1.5 m from a291o q2q lgcotn 8.0-D lens. By how much does the image move if the object is moo2ltoq 29qg1cved
(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 length of 25 cm shou j5nk37.i.a u-myxgreld an object be placed to produce a real im.73xugnyimk . -r aje5age which is the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens must aw.:dkmiu43wwj qg e:/n object be placed if its image is to be ma4/j.w:ik3ugm qwwed:gnified 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 r7wgso poct 5t.5+,qs.0-mm-focal-length lens must an object be placed if its image is to be magnified 2.00×,wsg5osr. c5ttp+ 7oq 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-z5-i47h a z60a bdui hw2ihql5length lens. Where is the image, how high is it, aqu-5 hi i2l4w0a azbh d5hz67ind what type is it?
$d_i$ =    mm (real,behind the lens) $h_1$ =    cm (inverted)
(b) What if $f=-135\mathrm{~mm}$?
$d_i$ =    mm (virtual,in front of the lens)
$h_1$ =    cm (upright)

  How far apart are an object and an image formed by a 75-cm-fpeoa f8b*n8 1uk9)xq kocal-length converging lens if the image is 2.5× larger than the o8obxupe1*aknk89 q) fbject and is real?    m

  A bright object and a viewing screen are separated by a distanc6sa24nnh5v y ee of 66.0 cm. At what location(s) between the object and the screen ne 6a5vsn24yhshould a lens of focal 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 convergf,qkb1 /xgr7skr/( rfa/w- jp2gj4o eing lenses are placed 16.5 cm apart. An object is placed 36.0 cm in front of one lens. Where wi4kxf7bfw(rr,1j j//r qg2 sgk/ e-poall 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 86 be h 6tbrv9ymk6ok($f=-31.5\mathrm{~cm}$ 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 diverntn7qy6 62wyc ovq)y3ging lens. Parallel light strikes the diver )vn7qq3 62ny yocwt6yging 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 diagram.]    cm

  The two converging lenses of Examsk q0:h ib7cr8ple 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). In this case, determihi87sqbc kr :0ne
(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 p a9e*mpj1b zy /cw.6vwlaced 30.0 cm apart. The focal length of the lens on the right is 20.0 cm, and the focal length of the lens on the left is 15.0 cm. An object is placed to the left of the 15.0-cm-focal-length lens. A final image from both lenses is inverted and ea1pj m96vwz b. wy/c*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 gs1wnd+ )r1 0qx,ljvn a focal length of is placed 12 cm to the right of a converging led1lr jx,s w 0nnqv)1g+ns with a focal length of 18 cm. An object is placed 33 cm to the 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 convergpt*:u adt8og+ing with focal length 20.0 cm and one diverging with focal length are placed 25.0 cm apart. An object is placed 60.0 cm in front of the converging lens. Determineg*dt at :o8up+
(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*3fy 9c+ojh a)kplz0w next to a converging lens of 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 radiumr+l,r ; vjg3i of 34.2 cm and 23.8 cm. What is the focal length if n = 1.52mg+ r 3,jlvru;?    cm

  Both surfaces of a double convex ),zho 0h3 axcwlens have radii of 31.0 cm. If the focal length is 28.9 cm, what is the index of r3 z,o)c h0xawhefraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm. Whatraukoko s) 4u 46y(e/b is the radius of the concave surface?o4( eob yk) r64akuus/    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat su4/s+:-8vye t:z-yt w r e7mzaibm4pjjrface and the other has R = -pmv8t4+i :zser-4a yjt/j z:y e7bw-m 18.4 cm. What is the focal length?    cm

  A symmetric double convex lens with a focal length of 25.0 cm is to be made frore 6gudzhnahb +6w 5f+itz0:j l-d,s;m glass with an index of refhzjb0g,z:sthrw+5;fe l d-a+iu6d 6 nraction of 1.52. What should be the radius of curvature for each surface?    cm

  A prescription for a corrective lens c (q;vbocza ,psj8 r8uv u6)d;yalls for +1.50D. The lensmaker grinds the lens from a “blank” with n=1.56 and a preformed convex front surface of radius of curvature of 40.0 cm. What should be the radius of curvature of the u y) rvzu aod;6qj8sb ,v8;c(pother surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as 0e. 4t.5iedmi nwl2sd in (Fig. Below). You stand 1.5 m away from one of these mirrors and look into it. You will see multiple . n2.sedm40 iie twld5images 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. /87b)6itle22bk yi/xff it d fWe measure the width (x=5.50m) and then note that the bottom edge xi6b ittk)yf2 fd7/ /2ebi8flof 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 p r+etxyv:t(;ra- wm6liece 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 ca/-qfwo r,aqy wrv, 9k,se of a spherical mirror. Specify -v, aq/kor w9,r,fqy wwhat this limit is.
(b) Determine an equation that relates the image and object distances in this limit of a plane mirror.
(c) Determine the magnification of a plane mirror in this same limit.
(d) Are your results in parts (b) and (c) consistent with the discussion of Section 23–2 on plane mirrors?

Stand up two plane mirrors so they form;u q2wz jcrx(3 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 real ic; h gtrfg(*lufvu0,90xm rj6mage of a real object. Can you describe a situation in which a divergi t0rg*gc f,f( umrl09uj 6xv;hng lens can form a real image?

  Each student in a physics lab is assigned to find the location where a brigt*fn h* )) mh8f .grs0/8 gm+kjxezltjht 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 theyst*n*80 g )fr+ mj. kghf8mzt eh/jxl) 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 is kzqjk21 p5i;xr;fei (e.u 9lp $\phi=72^\circ$ 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 gls o+j47g9 ayz xmii:u9ass 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 fro,t 3-4)ncte taglnr p*nt of 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 le1yxq m8sj n+5ia iat20ns of focal length f, and a white screen for viewing the image is on the op 2st 8aqa 1jyn5m0iix+posite 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 actslwdflujn5q o /d413h, as the object whose image is projected ofqdh4w o/n1j 5d,l l3un 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, how wide will the picture be on the screen? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (picture size is actuall07t bcy)zxtu 3-qxvv8po9-lfl m/x*ry 24 by 36 mm) is to be projected on a screen 1.80 m by 2.70 m placed 7.50 m 7 0bzpy ftqvo38l/-m-t*xcxu)9l v xrfrom the projector. What focal-length lens should be used if the image is to cover the screen?    cm

Show analytically thcym01oyb1 pm p ;(-z hli.cda8ol bf64at the image formed by a converging lens is real and inverted if the object is beyond the focal point clm 8b0m-bcyfa4ld(.;ho6y 1 ipp1 oz$(d_0>f),$ 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 catches5,+. fh2s*tb akozmas a reporter shooting pictures of her at home. She claims the reporter was trespassing. To prove her point, she gives as evidence the film she seized. Her 1.75-m height is 8.25 mm high on the film, and the focal length of the camera lens was 210 mm. ,za5.*bofmt sk as+2 hHow far away from the subject was the reporter standing?    m

  How large is the image of bbs2ik w zm) 3:f:x:wuthe 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 certain lens is imaged 8. uw.jftt5+l h/20 cm in front of that lens (on the same side as the object). What typuf5l.htwtj/+ e 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)