What would be the appearance of the Moon if 4t 5dfrum f;e7it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fleet in the hj +zkg/ l u o55lb5,g;qsqa3miarbor of Syracuse by focusing the rays of the Sun with a huge spherical mirr3zm 5 qi5o/gu lblg;jq +s5,akor. Is this reasonable?

Although a plane mirror z,6 2v:wm kov9saym8uappears to reverse left and right, it doesn’t reverse up,:9okuz2ym6 a mw8vvs and down. Explain.

If a concave mirror produces a real ima4q-7m x.w yrghge, is the image necessarily inverted? Explain.mywx7h-.g4r q

An object is placed along the principal axis of a sphericy et o:;ybpr/z/cw.;nal mirror. The magnification of the object is -3.0 Is the image real or virtual, inverted or upright?wz/:cob/e;n. yry tp; 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 re8yud ha.whk1 ;ference to (Fig. Below a), draw ray 2 for (Fig. Below uw18hk.a;dy h b).
(a)
(b)

What is the focal length of a plane mirror? What is the magnification of a cr.+fzqfsb; :plane mifcb+r f:.zs;q rror?

When you look at the Mo 3owgtkg m+.- mjm9ey + 4t;2dv-iqlbton’s reflection from a ripply sea, it appears elongated . E.+bmvlg+m y9m ;wo2 i-qt-jt3tk g4edxplain.

What is the angle of refraction when a light ray meets the boundary betweentk3ga*px(r/f 3mc1 yj two materials pepfkyj/ 13*ar(c xm3tgrpendicularly?

How might you determine the sth2tv o,b 9.sapeed of light in a solid, rectangular, transparent obtv.soh29 , abtject?

When you look down into a swimming pool or a lake, are yonv6b xe6u13/ oignj sgp6tw5 oi,m+* zu likely to underestimate or overestimate its depth? Explain. How does the apparent depth vary with the viewing angle? (Use *w,+o6bu /j6soe6v3mtigxi n 1ng zp5ray diagrams.)

Draw a ray diagram to show why a stick looks k.k 2:e4fxh g mma*a t(p9dd.isj:*bm bent when part of it is under water (Fi9f:s4a(.kj2mae *it.b *kgdm: mxhpd g. Below).

Your eye looks into an aquarium and vic gzdjzdct , 022*q)ocews a fish inside. One ray of light that emerges from the tank is shown in (Fig. Below), as well as the apparent position of the fish. In the drawing, indicate the approximate position of d )gj czccqt2z2do,*0the actual fish. Briefly justify your answer.

How can you “see” a round drop of water on a table even x3e*taslto/3qz1./ qidrp5n though the water is transparent andq * eaxt //s5dinolz13q3rt.p colorless?

When you look up at an object in air from beneath the surfmqc-b 75fv 9 qfallf8-ace in a swimming pool, does the object appear to be the same size 5 8cq-a7flf -vb9lf qmas when you see it directly in air? Explain.

How can a spherical mirror have a negative object distanhbrf/ prga2+;ce?

Light rays from stars (including our Sun) always bf8d+,o*mnp2 . d nhrgcend toward the vertical direction as they pass through the Earth’s atmosphere. r dm*god .n2ch8,f+pn
(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 cwsx8w a9gb0 5;1zalm+ nlj. lzamera lens is to make a sharp image of an object very far .m1 5lslw9zwaal08z b ;g njx+away?

What type of mirror is shown in (Fig. Be hr o*y1jd -p klwbdzu+zt613-low)? Explain.

A photographer moves closer to his subject and then refocuses. Does pdqnfd -;i43 zrv3j;q the camera lens move farther from pf;;nq zd r4dqi-33j vor closer to the film? Explain.

Can a diverging lens form a real image under any circumstances? Ezq 3m2oldo b:1xplain.

Use ray diagrams to show that a real imaggr hx n)23ciu v6 nb8k4c7uv8ee formed by a thin lens is always inverted, whereas u38 v6ki2c nx)4hneg7vcu8b ra virtual image is always upright if the object is real.

Light rays are said to be “reversible.” Is this consijy9.s hx;/fd:jvbx t0stent with the thin lens equh9jj; b/ yv x0sxdf.:tation? Explain.

Can real images be projected on a screen? Can virtual images? Can eitherml7m 2log0hf 7 be photographed? Discuss carefull0gl2mlm7 7f ohy.

A thin converging lens is moved closer to a nearby object. Dog+ v yp0vf,bi9es the real image formed chanifp9by, vg 0v+ge
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material wiq0aj*ru m4aj ba8be2fka + x5(th an index of refraction n = 1.30 In air, it is a converging lens. Will it still be a converging lens if placed in5me(x8raa4ba *j+a 0fk u2jbq water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands facing a converging lens9;o5:anod l2wb1 0d iehga(gl. If the nose and the tail are each focus 1ld2:9wdg loe5ia ;g(bo0ahned on a screen in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facing a converging lens. Uns-5t g0g-xsu c, uz)ycder 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 the cat bez5scsg g)c0--ytx u,u?

Why, in Example 13, muskm.sk lh ,c,) 47beb gxg4:lmht the converging lens have a shorter focal length than the diverg4egc,g4) mhx bsl ,.7k l:bmhking lens if the latter’s focal length is to be determined by combining them?

Explain how you could hav eb*jjg9d )iu7q*g;vybfs- 0q e a virtual object.

  An unsymmetrical lens (say, planoconvex) forms an image of a nearby object. Doe)dqux69j yh k6s the image point chang)qydxh 9u6k 6je if the lens is turned around? ----待选择----yesno 

The thicker a double convex lens is in the center a an(b8z 3pwtc1s compared to its edges, the shortew3 ztnpcab 8(1r its focal length for a given lens diameter. Explain.

Consider two converging lenses separated by some distance. An object is placj9 hxfmk9/l556av*mvsri - v aed so that the image from the first lens lies exactly at the focal point of the secondfh xav/mlm6v559a* kjvi9r-s lens. Will this combination produce an image? If so, where? If not, why not?

  Suppose that you want to take a photograph of 59 ml5y4)m x:1w7glcu ngxles+7; 8wla hcwyoyourself as you look at your image in a flat mih 9+5:w174 mx7 xysla wgcloe8; nlc)5ugwmylrror 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 see the same amys*zwa he )b-1ount of your body whether you are a wse1-)* yzbhclose 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 1 wk:rhoor 5c(, pri*s)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 ar. ktw:.f7idse e 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 the horizontal distance x to the base of the wall supporting the mirror of the nearest point on the fltwe7 i kf:..sdoor that can be seen reflected in the mirror?    cm

  Suppose you are 90 cm from a plane mirror. What area of the mirror is usead da q9)l 4scxle42-tgl*w9xd to reflect the aeqs4 l gtx924-acl*9dwx)d lrays entering one eye from a point on the tip of your nose if your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors meet atf0po 7.iyhx0 ro 4szq6aa8 gf1 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 concave mirror po0 .w3mtu rom0 *fdni4winted 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 t34 o 0f.inmm0*rdwuwmirror was made?    cm

  How far from a concave mirror (radius 23.0 cm) my. ixhan,sba+x f: 45e3 ljz; ;i(phewust an object be placed if its image is to be at infini 5;4e;ln fixzai p(hsxa.j+3e :y,hwb ty?    cm

  If you look at yourself in a shiny Chrisa9lj 7:p5z e emi7nw9gtmas tree ball with a diameter of 9.0 cm when your face is 30.0 cm away from it, where is your imae newz5pg ai77j99:mlge? 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 image0b e n4 by;ct*yz7liw8 of any person who stands 1.4 m in front of it. If the image is three tie7yb0b4nz *liw;y8tcmes the person’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror that, when 2.20 c cztjn+tigq vltq(yv363m3(:m 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 l *yq0jz q e2o/oh+b5zare smaller than they would be if the mirror were flat. Are the mirrors concave or convex? What is hb0 y/+2*z5o qlozjeqa 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 convs:lj rd/ms i5g7 xo7/jex mirror of radius olx: 7imdso sr57j//gjf curvature 20.0 cm.
(a) Show by ray tracing that the image is virtual, and estimate the image distance.    cm
(b) Show that the (negative) image distance can be computed from Eq. 23–2 using a focal length of -10.0cm
(c) Compute the image size, using Eq. 23–3.    mm

  You are standing 3.0 m from a convex security mirror in a stor+7kf uyej; t9d+6 bkt(d 5fjnpe. You estimate the height of your image to be half of yo9jnd; yt +fpfj65+deb 7u(kk tur actual height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object be placed in front o+i9.h-zlx gz of a concave mirror so that it produces an image at the same location as the obje-zo.9zg xl+ih ct?
(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 viewedit;5gp 2e + ptvg,l*n/l4u cfvrrj)) b in a curved mirror. The image appears to be 18.0 cm behind i)btv,4 j5lpp;/r)vgcunltr +ef g2*the mirror. What kind of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different tect-: jaapm.y8 shniques,
(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 of a coq /gzio 0z qp( dl4u*mib0ep1)nvex 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 valim01f.jcrx7j,og -lf 5xin r7kd for a convex mirror as long ik .jn50-cl,j7f xf grx1omr7 as f is considered negative.

  The magnification ofj1 ggi ctr87)f a 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. Ie /c/.l*9j at l,fkg8ogjn+tet is desired to produce. e+nglo t/flgc/kj,ja t98*e 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 your fyd6h25rt373ws j9u1upm y2:ne* h sl8vmjx xdace by a factor of 1.33 when your face is placed 20.0 cm i 3d us*xxv89h 12 euhd nyy672j :w5l3tpsmmjrn 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 l-pu)rll- ojfvz gs.5 ,ight in
(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 ic26lwvh85 w.4thm lve u o+aq :m+za1nie 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% ofg- 4jz,nmuq 4o ewf9*l its value in water. What is the index of l 9*-u,jqz44n efgmworefraction of this substance? n =   

  A flashlight beam strikes the surface of a pane of glass (n = 1.58) v8(gb9b p1kdowex:9r26jav)bsz n8 q 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 lb a3d/ lw4l-x(g db.dwater 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 an angle of,hv9 obnrea3ssor43 ; 66.0r sa43rv9n o3ob ;s,eh$^{\circ}\,$ 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.;2, wdqyzqg* t0$^{\circ}\,$ 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 whose index of refraction is 8 uw8cxaeg .0x)d)3n6ub dm(it*zu k1hn8fad1.52. A beam of light from outside the aquarium strikes the glass at a 43.5° angle t t8uh.d13 u86nmfwezcx)bk0)*g8 u aa( dni xdo 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 bottn90vi z/lqynb q7)ti0om of a pool at night, a watchman 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)qqn7t/ zvli0b9 yn 0i the wall beneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equilateral glass pris2lq*5j4a vua/tkl bp5m 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 gla9dbv vw8kk /j-4* qnstg*x82eu lmi0dss (n = 1.52) and is partially reflected and partially refl4t-jis8mu2**/dk 8 nvxk0wqbg ve d 9racted. Find the 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 lx5p:9 ev 8v , *tbn70sgcvwutvayer of transparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the incident beam,t * s5u n8,vtv c7w0:evb9gxpv 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 ofpn2xj6si7lgk i)v /**dwtaj + refraction n as in (Fig. Below). Show that if th /naj w 6l*j72gkiv*)+pdtis xe 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 bet k7gk7ncuy 5kqkq-41,ojy7x y ween water and Lucite? To be totally internall q okqn,g1y5jkck477yk x-yu 7y reflected, the light must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for .-b)ijqkn riby i5i1z3+v6 pca certain liquid–air surface is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitt8uzy34d lpae3h dxost1-7x,n ed in a pool of water from a depth of 62.0 cm. Where must it strike the air–water interface, relative to the spot directly above it, in order that the light does not exit the wx3y,zeon3u4-xd hp7 l8sd1at ater?    cm

  A beam of light is emitter 0pxso3ns /n5/fecuat46/ xy d 8.0 cm beneath the surface of a liquid and strikes the surface 7.0 /e t6sonnu a04sy 3/rp/xf5xccm from the point directly above the source. If total internal reflection occurs, what can you say about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face of the prism in (Fig. Belo 6 84szzh1:dcq9tf yayw) 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 jxmhlp epxd *8vop,x,+2u( ryc(8 ;qqend of an optic 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 otho,(ue(8rvpjlmhp pdxx,xc8q+2y q *; er words, regardless of the angle the light beam reflects back into the material at point a.

  (a) What is the minimum index of refraction for a glass o7 0mi /2uh5:mgh77 htcj qfkfgr plastic prism to be used in binoculars (Fig. Below) so that to : i7ucf7m h7gkjh05hmqf2/gttal 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 be73ze6bjvjng8td v h1p6ux7p 8hind a 65.0-mm-focal-length converging lens. Find the otpjzbhj 78deu v8vnp3 1xg667bject distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.wz r+chfbtx;,1er)z;)p g sm 75 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 l f bgmo 0 -r-spoxr:; p)3ytds/mec 51heb;fo(ight from an object 2.75 m away 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 viy-eeb13-5 bp r ;cg)fmofo(t/; ds: ohsxpm 0rrtual?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the power of a 20.5-cm-focal-len;;30ym;llb ) o1:ooakithbi bgth 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 sta/1 ocu i5:;j wp knhhmck5me5 mu+d0+wmp 18 cm injcmuncd+ko k ;w +whpm5he5 i:m/0u 51 front of the lens.
(a) Where is the image located?    cm behind the lens (virtual)
(b) What is the magnification? m =   

  A -5.5-D lens is held 14.0 cm from an object 4.0 mm high. What are the position) +a9b5x7uoqtd n .uyf, type, and height of the imtnbuo ud+7) 5 yxqa.f9age?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is us+ymlfdo- pf cq ux;iuu:d-/vw (8:p meko,8g7ed to focus an image on the film of a camera. The maximum distance allowed between the lens and the film pm,pom-/7 ;k88(f::y wuoqid u-d f xg+pecvlu lane 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 of 2.5× when *r zhzzh-g 4mk /+w1uca book is plahkcrz w/z1z h+4mg-*u ced 8.0 cm behind a lens.
(a) Draw a ray diagram and describe the type of image this would be.  ----待选择----realvirtual 
(b) What type of lens is needed?  ----待选择----converging lensdiverging lens 
(c) What is the power of the lens in diopters? P =    D

  An object is located 1.5 m from an 8.0-D lens. By ho*9 tyz f;afx*jw much does the image move if the; jfz 9tya*fx* 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 length of 25 cm should an object bebgz9yi+dju) lk fw687 placed to produg b+j ifld u7)kz6y9w8ce a real image which is the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-lewb w6jj x:fj86/t:od3 lalvk8 ngth lens must an object be placed if its image is to be magnified 2.00× and be re 8t6jk3oxbd fljww 6a8:vl/j :al?    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 object be plac ,pk7ujacqc m) /jtr3voaw) (:ed if its image is to beo,jvj )7:kacwu(a)3 c m tqp/r magnified 2.00× and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm (formed by some other piece of optics).]

  (a) A 2.00-cm-high insect is 1.20 m from a 135-mm-focal-length lens. Where i)r p pb8oz4*q6oh(llhs the image, how high is it,)(*l8oo p4 h hbqp6rlz and what type is it?
$d_i$ =    mm (real,behind the lens) $h_1$ =    cm (inverted)
(b) What if $f=-135\mathrm{~mm}$?
$d_i$ =    mm (virtual,in front of the lens)
$h_1$ =    cm (upright)

  How far apart are an object and an image formed by a 75-cm-focal-length converg5)zs5oqg w9k jing lens if the image is 2.5× larger than tg5 w jkqsoz5)9he object and is real?    m

  A bright object and a viewing screen are separated by a distance ofl-ard)vs, nwo ji;up7+0a8uyp6wf4f 66.0 cm. At what location(s) between the object any s8r,+;)w-4 0olfin 7 6vauaj fpwdupd 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 diagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length 0lwqsgcp0lf xkf n5 ) 355f7iwconverging lenses are placed 16.5 cm apart. An object is placed 36.0 cm in front of one 5cqg )ww 5f0n 3pfxs5ill0k7flens. Where will the final image formed by the second lens be located? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens with g6lrre /r5 -da$f=-31.5\mathrm{~cm}$ 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 d a:k8giyq f*-riverging 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 lryg-: ia*8 fkqens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Example 23–12 are now placed only 20.0 cm acu3uxz.f*av )5p jec am2-qr)part. The object is still 60.0 cm in front of the first lensxa)u.crc)*3-mv5j fu 2a q pze 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 focalm k,t a;a (y klwbe.9.g+a-vjb 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 locat.e lak +t(ajb;-yw kmvg ,.ba9ed halfway between the two lenses. How far to the left of the 15.0-cm-focal-length lens is the original object?    cm

  A diverging lens with a focal length of is placed 12 cm to the right of a/v8 tpfu*puld-lt9 7g9m,/niglrukq 8o)- tu converging lens with a focal length of 18 cm. An object is placed 33 cm to t ug,ll u8tf)79p 9q m-p/*nt/rukvol-tuigd8he 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 l((tvbc9d s5o 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 converginlbsv d9 o5c((tg 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 convergi p2z450vzngdh ng 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 radii of 34.2ey 2xoss 8o lw.wl9g -l3l xb8km631ng4bs;fh cm and 23.8 cm. What is the focal length if n = 1yohbl21g.8lnxbs 4 8x69mkwo 3g3; wfl-ssel.52?    cm

  Both surfaces of a double cojkkxe e kj9y r9:7x7+uxfwushso+ ;68nvex lens have radii of 31.0 cm. If the focal length is 28.9 cm, what is the index of refraction of the lens mk kjxuosy h7+ x+9eu; 8w:x69k7fsrej aterial?    cm

  A planoconcave lens (n=1.50) has (q0ap.js,nr a7lphj( a focal length of -23.4cm. What is the radius of,aq nrppjlahj7 ((s.0 the concave surface?    cm

  A Lucite planoconcave lens (see 1, gub4+ogrw 7u2/r2gdufyn e Fig. Below) has one flat surface and the other has R = -18.4 cm. What is the focal length? /+2gnd roeggu2yu w4ru1 ,bf7    cm

  A symmetric double convex lens.g4ytg i 2cdl c2ct6ik:*wp .d with a focal length of 25.0 cm is to be made from glass with an index o2 p2.i tdk4lidygcg*: .c6cw tf refraction of 1.52. What should be the radius of curvature for each surface?    cm

  A prescription for a corrective lens calls for +1.5 ggks;h;u 3alu1 t4(ki0D. 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 other surfakl;4huta g(g; i k3su1ce?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fig. Below). Yo4pj,q )qzhq.kc4+ chuu stand 1.5 m away f.+ cqqh 4qp)u4k,jhzcrom one of these 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 swimming pool filled with wat. mq.zv219lvs hpf9jker. We measure the width (x=5.50m) andj 19 .q.mp shkl9zvv2f then note that 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 a certain pieh;5 qgw-u*u s+yk/,pknr.yruz (jk /rl.7m dfce 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 spherical mirrzm (idrhp/ ,6pm*6gd oor. Specify what i/od zp,hpg*6rd 6mm(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 a srj :xsnc(9n 2,k,tuk 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 image ofwvx*oti(wa3i t9t(li 6it7- x y2i/qf a real object. Can you describe a situation -(*3otwly t7/(q6 fi ivi2tx9t iwxiain which a diverging lens can form a real image?

  Each student in a physics lab is assigned toksvk- r52pi4 8jyvol6b)t666z s e.urj5yjjo 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 5uj ei6-r sr otovp2s 6 zy6j46jv kybl.5j8)kequipment, 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 /p+:wvph0t p.zxo7ou a prism 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 cylit)l jfxfiq.83ndrical 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 ( ;1ogd +)2m6xnjv*gkeltkuuex3 w 4sof 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 pz;mbaa d/zt- 4laced on one side of a converging lens of focal length f, and a white screen for viewing the image is on the opposite si a4d ambzz;t-/de. 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 pro8w nwmc . *ef6cb*3vmm2vh9bv jector, the film acts as the object whose image is projected on a screen (Fig. Below). If a 105-mm-focal-length lens is to project an image on a screen 8.00 m away, how far from the lens should the slide be? If the slide is 36 mm wide, how wide will the picture be on w*b2em n h3 9cb*mfv.6cv8wvmthe screen? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (picture size is actually 24 by 36 mm) is to be projaw 0fozlui*q0 hm3 7 tzd*j-s;ected on a screen 1.80 m by 2.70 m placed 7.50 m3oqazht-s0 w*f7j *; iz0m udl from the projector. What focal-length lens should be used if the image is to cover the screen?    cm

Show analytically that the image formed by a converging lens is real anu2v cfan 1v-v u4-rf)yd inverted if the object is beyond the focal poiufy -v14 c- )2uvvfnarnt $(d_0>f),$ and is virtual and upright if the object is within the focal point $(d_0>f),$ Describe the image if the object is itself an image, formed by another lens, so its position is beyond the lens, for which $-d_0>f$, and for which $0$<$-d_0$<$f$.

  A movie star catches a reporter shooting pictures of her at home. She claimsyqj :w**xk1ks1/ v nbic6qtd*n35ft d 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 21*t3kidtvf* xdnwb15 1 cq*y:sk j q6/n0 mm. How far away from the subject was the reporter standing?    m

  How large is the image of the Sun on film used in a camj g5d4b+oxnr: era 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 8.20 cm in frooo nxd, o5(rr 7+v6phmzzy p85b c3+eto9k cl3nt of that lens (on the same side as the object). What type of lens is this,,o67lbzrhrm3te+ypocz9 5o 8p5 (v+nd oxc 3 k 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)