What would be the appearance of the Moon if it ha a*lh s)*vbr*rd
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Romanafh/hq 7 h //lbo2kzy)di9erxa0 z63d fleet in the harbor of Syracuse by focusing the rays of thf/ 9eoah7r0/3yh2h b) iaz 6kd/ldqxze Sun with a huge spherical mirror. Is this reasonable?

Although a plane mirror appears to reverse left and riq +j7- -fa tl.ptc7ybyght, it doesn’t reverse up and dowfapbq.7cyt- y-7 tl+ jn. Explain.

If a concave mirror produces a real ima/-ed.p d lrpv6ge, is the image necessarily inverted? Explain.-v. l edp6/rpd

An object is placed along the principal axis of a spherical mirr9d +yc8hbq+mt or. The magnification of the object is -3.0 c9q8tm+by+hd Is the image real or virtual, inverted or upright? Is the mirror concave or convex? On which side of the mirror is the image located?

Using the rules for cq3,c xy rx2z2the three rays discussed with reference to (Fig. Below a), draw ray 2 foc2x3 z,qc ryx2r (Fig. Below b).
(a)
(b)

What is the focal length of a plane mirror? What is the magnification of e4 :do6xkok5 m4z4dfc a plane mird ofz d4x56ck4e4om k:ror?

When you look at the Moon’s reflection from a r3/ko mhh2 g)yxipply sea, it appears elongated . Explaigh3/)k 2x omyhn.

What is the angle of refraction when a li doy-3)dfba+j jb8fk ,q4gi(k ght ray meets the boundary between two materials perpendicul-b8bd4+ )gqkjfj3 oyak ,f (diarly?

How might you determine the speed of light in a solid, recmqjoyc b+,x *2tangular, transparent +2 yqb*j o,mxcobject?

When you look down into a swimming pool or a lake, are you likely sc 08u9 1iw4b h)qkfkmto underestimate o01h 8msc) wubq9fk4ikr overestimate its depth? Explain. How does the apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stickr6cm57,jurk e looks bent when part of it is under water (Fig. 7 5ek,m urj6crBelow).

Your eye looks into an aquarium and 2jrvwexbfnv y)v8i n5z /7 d,(ys-w1eviews 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 the actual fiy 71xeji(5f-n2 y)ezwb r vsvnw/v d8,sh. Briefly justify your answer.

How can you “see” a round drop of water on a table even though tf,3(;ay ovn*f1*hbsu e .wenthe water is transparent as;w1f* nh.etyfvu be3*ao,n(nd colorless?

When you look up at an object in aexfmr7r m0 -,mhw4f, cwlj 9-si;7 hbhir from beneath the surface in a swimming pool, does the object appear to be the same size as when fj7,m9rl4fwcwrm;xhhb 7hie,- s-0 m you see it directly in air? Explain.

How can a spherical m/1pgvgb6*n)ehy . 0 tz x+rbdiirror have a negative object distance?

Light rays from stars (incl6q 63m:q nkg)potmbn5u 9c n4 d0* saotoaf/)nuding our Sun) always bend toward the vertical directio *:)nqn m3koo0u6 nst /d5q4 tgna bmp6of9)acn as they pass through the Earth’s atmosphere.
(a) Why does this make sense?
(b) What can you conclude about the apparent positions of stars as viewed from Earth?

Where must the film be place(yh;xo zq x.qhjc58e9d if a camera lens is to make a sharp image of an object very ; z. 9 qeoxycqh5xhj8(far away?

What type of mirror is shown in (Fig. Below)? Explan5 ;rws(v)mpn z o:8vmin.

A photographer moves closer to his subject and then refocus.: x4s:ebg(1vxr nk qyes. Does the camera lens move farther from or closer to the film? Explain rx.v1gy(xq4s:k:e bn.

Can a diverging lens form a reafk2g)w a6xw+fohi 5 2ul image under any circumstances? Explain.

Use ray diagrams to show that a real image formed by a thin lens is alwa2oxwl p+/ pgg1ys inverted, whereas a virtual image is always upright ifpwl/p o x2g1+g the object is real.

Light rays are said to be “reversible.” Is xgs4, z48v svxthis consistent with the thin lens equav,8z x4s4gvxs tion? Explain.

Can real images be projec 9bb:9n 1ypqscy;7w 09gdsu xl0 zlg7xted on a screen? Can virtual images? Can either be photographed1bp90n9 gxy csbyls7 9gz7qudlw: 0x; ? Discuss carefully.

A thin converging lens is movedsgj u(m2s(7zdya)- dp closer to a nearby object. Does the real image formed d 7jz)puma-ssg2(( ydchange
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a mk7zr: 69 wrz6e 6iqcbuaterial with an index of refraction n = 1.30 In air, it is a converging lens. Will it still be a coeq6: r 7w6rzz6ck9iu bnverging 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 convegy luc9zb1,hwrd)t5ad 0sz; /-qonm ,rging lens. If the nose and the tail are each focused on a screen9dgw1tr5s0 y a bzdhmqn) z/-c,u;, lo in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air staauqo+j .r.rk/nds facing a converging 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 rek qa ou.r/+.jrst of the cat be?

Why, in Example 13, must the converging lens have a shorter z-i9*r,a xt; har2*mgze: qrz focal length than the diverging lens if the lattezqt h ra-rer zz:am*,;x29i*gr’s focal length is to be determined by combining them?

Explain how you could have a virmjkp b414akh;,.w l)hiq1f jytual object.

  An unsymmetrical lens (say, planoconvex) forms an image of amr vrnm0 531fgtd r/)e nearby object. Does the image point change if the lens is turned around0 mv1tg3r5r drn)em/f? ----待选择----yesno 

The thicker a double convex lens is in the center8x ds6oz ybzg +8-ye-9kyvo*re7y o;z as compared to its edges, the shorter its focal leng xkg*8- 8z9z6 vy yy- eodo;7rozys+beth for a given lens diameter. Explain.

Consider two converging lenses separated by some distance. An object is placed sgny; 2r32 t hb:uj) n.f shkaeay9+7h-h uvmj;o that the 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 notbsv+jkjhn-m rah.yun9;2;ag2he :hfty)u 3 7 ?

  Suppose that you want to ta 8r,qz( y fmfjd(qxnxw1 t m:p:1hlu.3ke a photograph of yourself as you look at your image in a flat mirror 2.5 m away. For what distance should the camera lens b mqxhp:1 ql1(yntwf m.3jx(,d8 z:f ure focused?    m

When you look at yourself in a 60-cm-tall plblq; 4-ygog) akc12s9ihj tg*ane mirror, you see the same amount of your body whether you are close to the mirror o42yt1hkj )li*9gas q gbgo- c;r far away. (Try it and see.) Use ray diagrams to show why this should be true.

  Two mirrors meet at a f8c ebk*5ens-135$^{\circ}\,$ angle, (Fig. Below). If light rays strike one mirror at 40$^{\circ}\,$ as shown, at what angle $\phi$ do they leave the second mirror?    $^{\circ}\,$

  A person whose eyes are 1.68 m above the floor stands 2.an3q3*(yciwy8s v mez11fa6 a-oz)mg20 m in front of a vertical plane mirror whose bottom edge is 43 cm above the f3 yq1 m1iz6)3a* owe zac8v (as-ygnmfloor, (Fig. Below). What is the horizontal distance x to the base of the wall supporting the mirror of the nearest point on the floor that can be seen reflected in the mirror?    cm

  Suppose you are 90 cm from a plane mir3knps4e:;y. z ;tdo,urlay*o ga2ig(ror. What area of the mirror is used to reflect the rays entering one eye from a point on the tip of your 4,kaepa*2 yd;z;.lts3o( u y ni :rgognose if your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors m no+/ 03tlzgo jat5k)ol(xm+leet 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 concave mirror pointed at the Sun, focusesi6 oh/ar4 uwy6w r3vg2 the Sun’s rays 18.0 cm in front of the mirror. What is the radius of the spherical surf6/hr 36goa 2rui 4wywvace from which the mirror was made?    cm

  How far from a concave mirror (radius 23.0 ndk;q f/e-snfpg xy */*y 4v5xcm) must an object be placed if its image is to be at i y5nn;/ffe y k px4*-/v*sdqgxnfinity?    cm

  If you look at yourself in a shiny Christmas tree ball with a diameter uo /e1xv-.juk of 9.0 cm when your face is 30.0 cm away from it, where j/x uk -1u.eovis your image? Is it real or virtual? Is it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shows .xqli5;x-w+u g j6 wazesssb5m pt+76 an upright image of any person who stands 1.4 m in front of it. If the image is three times the perss;65 tssugbw-wp xx67e+5a qj+l. zimon’s height, what is the radius of curvature?    cm

  A dentist wants a small 7a3icat,+ rbd mirror that, when 2.20 cm from a tooth, will produce a $\text{4.5×upright}$ image. What kind of mirror must be used and what must its radius of curvature be?
 ----待选择----convexconcave 
r =    m

  Some rearview mirrors pro qxab4a*2 5palm0fyi b2jw-d5 duce images of cars behind you that are smaller than they would be if the mirror were flat. Are the mirrors concave or convex? What is a mirror’s radius of curvature if cars 20.0 m away appear 0.33× their normal s abl2fa45w52 -jx qp*dbmy0aiize?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is placed 20.0 cm from a convex mirror q lwkbc;g0lbqi2d31 3:tgk9 jof radius of curvature qql g d ;bl32kjiw3gctb1:9k0 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 s pl8, * 8pvdx4vdkjrcz fy:/5o9rkbx 5tore. You estimate the height of your image to be half of your actual height. Est5 p*ldbk8vkc 5d,xo 4pjf y98/:zrvrximate the radius of curvature of the mirror.    m

  (a) Where should an object be placed in front of a concave mirrorclx r/+ jjq(d2 so that it produces an image at the same lj q2rdlc /x(j+ocation 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 +i;7xmi6cu:z9ftmkx )vjo4xm*+ qxnvirtual and very small when viewed in a curved mirror. The image appears to be 18.0 cm behind the mirror. What kind of mirror is it, and w t7; x9v6+*c mu:ofxqnx i +mjk)izmx4hat is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniqu 1w/v;b0)vl:5+od sh)n7birgsw5 hldjtsv (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 3 :8 nq1)clcrhatt ic:the magnification m of a convex mirror is $m=-d_\mathrm{i}/d_\mathrm{o},$ just as for a concave mirror. [Hint: consider a ray from the top of the object that reflects at the center of the mirror.]

Use ray diagrams to show that the mirror equation, Eq. 23–2, ffib*(z0gk gl(q,8lm.. efsl j g4hx:is valid for a convex mirror al :4j(zgi.gllg( b.s *0xq ,f kfmhfe8s long as f is considered negative.

  The magnification of a convexlk d3*xip;w .y5fqqw9 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 spher 6j8/zpv6 lgul2r0bcyical mirror. It is desired to produce a virtual imag0p2zjblu8 gvcy/l 6 6re 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 magnifydq-ezjsho21 / your face by a factor of 1.33 when your face is placed 20.0 cm iohez/jqs -2d1 n 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 lq)p0d 56dhydt-y wd a,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 ice 10 b 4xijvjwuxr 3h oj98whe-:o5ash: is $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a cert phn ;wn8efy0q: 6w /gd(bt:yk bs8uz4ain substance is 89% of its value in water. What is the index of refraction ot/6qes(hby0k :f :bwyup8 gz48dnw n;f this substance? n =   

  A flashlight beam strikes the surface of a pane of g zydn,s(*d2 talass (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 at s-wxv0,ko-b w00muy q-szy d5 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 8nyr8vl3s,jhi8e- ozwater at an angle of 6683hvi8- ,z8jenr ysol.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 topajs9)hm9b7v*whqqv i pt*8 4 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 whose index of refracql; p 5dvqpm881y -whl0eofx; tion is 1.52. 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 wh 185qf ;o;m8vpqyhl-lp wx d0een 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 shines a narrow beam of l8kl9lg m9tr9a ight 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 9tlmg9r 9a8kl hit the bottom of the pool, measured from the wall beneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equilateral glass p nqc,yl1)5oi dy7rxu; rism 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 reflin1khmqhagq99, xv 3v8 l:d*bected and pn1v kq qhl99di gh*v:m,3xb8aartially refracted. 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 unifo87uj er. u.huh7 v,rk qu.ui.brm layer of transparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the incident beam, independent of the incident ang.h.7u rj.uke iu7 buqr.,hvu 8le $\theta$. Assume air on both sides of the glass.

A light ray is incident on a flatf miu/.pg.*lij0-njsk .l f7oo;dm +(mqc yy9 piece of glass with index of refraction n as in (Fig. Below). Show that if the lmfj oid kul0i( -;/mgy m..so9pcnj . q*f+y7incident 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 anp6 c82chm q.**ecp ljsgle for the interface between water and Lucite? To be totally internally reflected, the light must sta8p62lqh ccs*c* ep.jmrt in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquick -x+; uz1;i 62uvygqa 85kp0maivj fd–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 pbiw 1(3wtjag5l-9ql 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 doeslj51i3aq- p9w( tbwlg not exit the water?    cm

  A beam of light is emitted 8.0 cm beneath t hmcy.;grn4(9b3oafu he surface of a liquid and strikes the surface 7.0 cm from the point directly above the source. If total internal reflection occurs, mahro3;ngyc. f4b 9( uwhat can you say about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face of the 9q 8lo9g 2 t l:h+volgmpcvm(;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 rewr sgv;)/s; 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 other words, regardless of the angle the light beas ;w/seg r;)vrm reflects back into the material at point a.

  (a) What is the minimum index of rezm;szijt495ds* /n y, csecd2fraction for a glass or plastic prism to be used in binoculars (Fig. Below) so that ntczjy2 4;/si dsdz*ms,c 9e5total internal reflection occurs at 45$^{\circ}\,$? $n_1$ $\geq$   
(b) Will binoculars work if its prisms (assume n=1.50) are immersed in water?  ----待选择----totally reflectingtotally transmitting 
(c) What minimum n is needed if the prisms are immersed in water? $n_1$ $\geq$   

  A sharp image is located 78.0 mm behind a 65.0-mm-focal-length convergic-iam6sb2u 6u7v gn0lng lens. Fign06b72svc ul6 um -aind the object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.5 cm behind ac s7a0qj9jw6 d 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 20iw4mfup.,4nlhtlx 9 .75 m away as an image 48.3 cm on the other side of the len0it4hx4w pnum.llf,9s. 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 of a 20.5-cm-focal-length lens? P = mzecj31vm n(z2 d +ed3s j+x-f   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 sebti9rr 3k.5 ntamp t5rkbe.i3 9 nr18 cm in 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 3gn f7)/u4jl96b- mpmn)jgfd )x abda14.0 cm from an object 4.0 mm high. What are the position, ty 3n)fb)uafx/nlm46-pd mjg9b da)7j gpe, and height of the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to focus an img;2hj k4rmkqe ,3o+ibage on the film of a camera. The maximum , m4kq2ok r3;jbe+hgidistance 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 material by a factor of c:2nwx*s*q qg2.5× when a book is placed nq2qxs* g *w:c8.0 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 how much does the image move n*mid e7eiu y81.2c1qq84y 0lhz wzkqif the object is moved iz nklycweyeuqhq4m0i 81*d.8q 127 z
(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 bc n1y mzi;(r5ze placed to produce a real image which is th ycn5r(im 1;zze same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an z4 ,re-i vs;f)a6jysfobject be placed if its image is to be magnified 2.00× andyr;6 f4i)fe,vjsas -z 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 object be pu1o3 j,s za)1qmin 6dolaced if its image is to be magnified 2.00× and be real?3,6qnms oi adu1z )1jo    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 if n8p3c dwas0)nsect is 1.20 m from a 135-mm-focal-length lens. Where is the image, how high dafp )cn0w38s is it, and what type is it?
$d_i$ =    mm (real,behind the lens) $h_1$ =    cm (inverted)
(b) What if $f=-135\mathrm{~mm}$?
$d_i$ =    mm (virtual,in front of the lens)
$h_1$ =    cm (upright)

  How far apart are an object and an image for26oe4-pg b0ixddz;cyiwb ,unfs8:w*med by a 75-cm-focal-length converging lens iffu sypd4zcwxdb2bi n8i : woe;,-60*g the image is 2.5× larger than the object and is real?    m

  A bright object and a viewi m2qsolvio:e3182x csng screen are separated by a distance of 66.0 cm. At what loxs2 ove8s:qicm12l3 ocation(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 diagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-lednk9 3gn0e ,yto rwz25ngth converging lenses are placed 16.5 cm apart. An object is placed 36.0 cm in front of one lens. Where will the final image formed by the second lens be located? What is the total magntog5w3r9z dnk 0n2ye,ification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens withx: n4b j f8c;;or *efub+jo6fj $f=-31.5\mathrm{~cm}$ 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-lengte. ct02u,kn bth converging lens is 21.0 cm behind a diverging lens. Parallel light strikes the diverging lens. After passing through the converging lens, the light is again parallel. What is the focal length of the diverging lens? [Hint: first draw a ray di.uk n,t20 betcagram.]    cm

  The two converging lenses of Example 23–12 are now n.; 2,zd jzdkria83jiplaced only 20.0 cm apart. The object is still 60.0 cm i zajj;i83,d.2 zi nkdrn front of the first 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 aregww :9x-fj1v 7lats8j;uzv a+ placed 30.0 cm apart. The focal length of the lens on the right is 20.0 cm, and the focal length of the lens on the left is 15.0 cm. An object is placed to the left of the 15.0-cm-focal-length lens. A final image from both lenses is inverted and located halfway between the two lenses. How far to the left of the 1- ;wa +1 azvj 8lutg79v:xwsfj5.0-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 conv+yyfu+, 0w5* m)t9rv b 3u wyvflzd6bcerging lens tyd) uw9f* vuv63m0b5l+ybc +ryw z, fwith 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 converging with focal length 20.0 cm and one diverging witkl uva ,fgq4r(jx- -t(h focal length are plac gtlj-kr,f 4q(v (x-uaed 25.0 cm apart. An object is placed 60.0 cm in front of the converging lens. Determine
(a) the position    cm to the right of the diverging lens
(b) the magnification of the final image formed.   
(c) Sketch a ray diagram for this system.

A diverging lens is placed next to a col7 bub3r:of6;lj f+o ;le- n,8kxkxgenverging 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 surfa29p xhxhzm)mu )gw5,a ce radii of 34.2 cm and 23.8 cm. What is the foca hmzpu, xh)x5g2m )9awl length if n = 1.52?    cm

  Both surfaces of a double convex lens have rbrx qj,w 7pm(9adii of 31.0 cm. If the focal length is 28.9 cm, what is the index of refraction of the lens matwpmq , 97b(xrjerial?    cm

  A planoconcave lens (n=1.50) has a focal leng; i l6ludr*dep9g;r .vth of -23.4cm. What is the radius of thl9;.6elv gu pr*;rid de concave surface?    cm

  A Lucite planoconcave4:. 1kgi1nnjimi(jgq: q 3 cvn lens (see Fig. Below) has one flat surface and the other has R = -18.4 cm. What is the focal lengthi3gc j(4 q1migq.nn1inv:j:k?    cm

  A symmetric double convex lens with a focal length of 25.0 cm is b w -db: z.2hgkqjosynt5d1e:/d6hw hm1x1d: to be made from glass with an index of refraction of 1.52. What should be the radius of curvatureghhkd1.dwd xb dnqbe:h om:1s 5yw6zt:/2j - 1 for each surface?    cm

  A prescription for a corrective lens calls for +1.50D. The lensmaker gpbrs4))zmvm5 qjs .t.9ue 1q yrinds 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 m.zyt rqv5sqju)9eb1s .p4m) other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fig. Belst)gl b)c.zjmn i2 r7xo8ff,e /g)c+oow). You stand 1.5 m away from onezon)ge+rt o glcx sb/)f, 2c8mjf.7)i 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 a94k( wq1ouu5 mftg b is)5r;sk, 1/sdsvpc,za swimming pool filled with water. We measure the width (x=5.50m) and then note that the bottom edge of the s1 p)419cwmba,zu dq,/ssg;5roksu 5vt(kf ipool is just visible at an angle of 14.0$^{\circ}\,$ above the horizontal as shown in (Fig. Below). Calculate the depth of the pool.    m

  The critical angle of a certain piece of plaar v5hc;e5n/, voz3d xstic 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 consi l+nd/6y y y1j/gy/im4or(nj3 1 hlt wctkt,c8dered a limiting case of a spherical mirror. Specify what this limit is.tc4k,tyhd/g(8 +n6/ tl yo 1ijc1ylwy/ nj mr3
(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 grm7);npuh0y 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 divergin+k ) 6ejnr n.w r8t(dng hc-0s-rbv6skg lens can never form a real image of a real object. Can you describe a si60sr.r+t nsc dh gr(enkb-v w8nj6)-ktuation in which a diverging lens can form a real image?

  Each student in a physics lab is assigned to find the location where a bright o5olj1m(bwu.d9 z5d -2fbq t nsbject 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 equi2t-m(wdu ldb.b 9f 1n s55ojzqpment, but when they compare notes later, they discover that their answers for the object distance are not the same. Explain why they do not necessarily need to repeat the lab, and justify your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of a prism isb*ik8 y,;z kdc $\phi=72^\circ$ 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 cylindricatq rl80l+m2a al 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 lens 9rq2*vz:+br fkkl p-.m b7jpt+ z k3itof 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 le 3j-fb*tmfdy g0a0 ir os7np4soz206sns of focal length f, and a white screen for viewing the image isds tb 0rif7a2*sop4ns0 0f zgjmy36o- on the opposite side. The distance $d_T=d_i+d_o$ between the object and the screen is kept fixed, but the lens can be moved.
(a) Show that if $d_{\mathrm{T}}>4f,$ there will be two positions where the lens can be placed and a sharp image will be produced on the screen.$d_T$>4$f$
(b) If $d_{\mathrm{T}}>4f,$ show that there will be no lens position where a sharp image is formed.
(c) Determine a formula for the distance between the two lens positions in part (a), and the ratio of the image sizes.

  In a slide or movie projector, the film actm8. ;to3fi ypj0e5j uws 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 away8;jimf5 0eopjtyw u.3, 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 projected o k+mu43po3o ncn a screen 1.80 m by 2.70 m placed 7.50 m from the projector. What focal-length lens should be used if the image is to cover th3no c +4pmk3oue screen?    cm

Show analytically that the image formed by a converging lens is real and rs1 00y3v:qn s/bjrdcbq 78jhinverted if the object is beyond the fjbq/vrd8sjq31s 0b0: cyhn r 7ocal 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 reporte+cgi3pfo0jo 4r 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 onoj g+3f0c4o pi the film, and the focal length of the camera lens was 210 mm. How far away from the subject was the reporter standing?    m

  How large is the image of the Sun on fib(km1 -yj 8cqc*bai,xlm 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 i3a by6w5ah 4qks imaged 8.20 cm in front of that lens (on the same side as the object). What type of lens is this, and what is its focal length? Is the image real k5h643wa y abqor 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)