What would be the appeady c6e zsvv7.*rance of the Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fleet ird-kg ,6oc8jtn the harbor of Syracuse by focusing the rays of the Sun wo8ck, gj- dr6tith a huge spherical mirror. Is this reasonable?

Although a plane mirror appears to reverse left and rig*)rg -bxoy4x. c rk3mqht, it doesn’t reverse up mqxr )robgy3. -4k* xcand down. Explain.

If a concave mirror pr lz 36:1;,nke*av tjlw8iwjya oduces a real image, is the image necessarily inverted? Explaik1z i6n3w aj;wjly,l:t *8vaen.

An object is placed along the principal axis of a sphe xkepa p.m69a(-zjkr/rical mirror. The magnification of the object is -3.0 Is the image real or virtual, inverted or upright? Is the mirror 96r/-xp(.k akzajmep 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 ofqxw 3 8i39fda), draw r8xwo9f qfdi3 3ay 2 for (Fig. Below b).
(a)
(b)

What is the focal length of a plane mirror? What is the m-69 )9it0rd)w4d8l;mz dr bhxd titqvagnification of a plane -;lr)ht4tdxdzi8)6mib 0qw 9vrdt d9 mirror?

When you look at the Moon’s reflection frpijnp6h0p5/u 6y g1*lj1o pswom a ripply sea, it appears elongated . Explps u1gi n6p5 0/lo*6jhw1yjppain.

What is the angle of refraction when a light ray meets the boundary between tn. 7lmrto+1 aywo materials 1o ay+mt7l.nrperpendicularly?

How might you determine the speed of light in a solid, rectangular, trmsfla*5byx-2yr x3 l(ansparent objectfya (*x -llxsbry 2m53?

When you look down into a swimming6ding n41 1rp0n08xkwkdmk ,x pool or a lake, are you likely to underestimate or overestimate its depth? Explain. Hon x6kd1g mrd4 i,w 008kknpxn1w does the apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to ;c4 9q 3-r1ivxrpnb cjshow why a stick looks bent when part of it is under water (Fig. v9cq;jrnbxi- 3r4cp1 Below).

Your eye looks into an aquarium and views a fish insidbjw8tfrh5r* /b x: 7oee. 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 j5r8wfx bh*t/reo:b7 fish. Briefly justify your answer.

How can you “see” a round drop of water on a table e3 59sln jlc)pry5p*fcucs g47ven though the water is transparent and col snlc*3yc7p4p)5lgfj c5 u9rsorless?

When you look up at an opb :euh7uvff/83ns 2 bbject in air from beneath the surface in a swimming pool, does the object appear to be the same size as when you see it directly u/7fb upvbh:2es 83fn in air? Explain.

How can a spherical mi aak:(vgvj z.-3g 3se1u +utsjrror have a negative object distance?

Light rays from stars (including our Sun) always bend (qfk+j ia-438go lg gdev1y( gtoward the vertical direction as they pass through the Earth-ggo 43l8qf(+ag evgj i1d ky(’s atmosphere.
(a) Why does this make sense?
(b) What can you conclude about the apparent positions of stars as viewed from Earth?

Where must the film be placed if a camera lens e sr+g r md*i lr,g+:j;9wcf(kis to make a sharp image of an object ver,(d;i9 kmer++gj*r s: r gflcwy far away?

What type of mirror is shown in (Fig. Below)? Ex,asn+ *,0m3 gsdfcl hfplain.

A photographer moves closer to his subject and then refocuses. Does gj .8 xz sw.v81kdgg1ldk4qt 8the camera lens move farther from or cl.88xd4k8s.kg vgjqt g1 1dl zwoser to the film? Explain.

Can a diverging lens form a real image under any circumstancek-u btgu;dowc( 5w gy7fg,d)/s? Explain.

Use ray diagrams to show that a real i:qerr -gx7fhnpd*p9 7mage formed by a thin lens is always inverted, whereas a virtual image is always upright if the object ihp *xr 9:prg-nqef 77ds real.

Light rays are said to be “reversible.ae7fxyn1m ug +79s p8fve y,i3” Is this consistent with the thin lens equativ y ua1f,3y987 imnpfx7e+e gson? Explain.

Can real images be projected on a screen? Can virtual /n 1cpl3ikg q ecwag,4x9 ;x-himages? Can either be photograplq/n3; gwh4c -pxgxc9k ei1a, hed? Discuss carefully.

A thin converging lens is moved closerf5)at,kih7s-zqnt *ilm,r x zxq89 j( to a nearby object. Does the real image formed chang,,9rq m-n 7 j)l h*iizak(xf58qzstx te
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material q(tryc07dtn j 0aa z)3with an index of refraction n = 1.30 In air, it is a converging lens. Will it still be a convd0qy7cnrz (a)t3 0j taerging lens if placed in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands facing a converging lens. If the no)-q-bj) aqy21 hf8dstxmh9r*zb:m vnse and the tail are y:)*fq b-8mtn9hh a1qrmz-xdjb vs2) 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 stands facing a converging lens. Under what circ es:rzpx5ade37ygfy3vx g m; t y-h*e .i5w0+eumstances (if any) would the image of the nose be virtual and the image of the tail be real?x5:gfxeyyr7pgd0ayw 3ee+;sihm .3* v -e zt5 Where would the image of the rest of the cat be?

Why, in Example 13, must the c0r6h 0 y/8r7v qyyyeyxonverging lens have a shorter focal length than the 7xh q/60y 0yev8ryr yydiverging lens if the latter’s focal length is to be determined by combining them?

Explain how you could have a virtuald;x9.q uls 1kmwan ;k0 object.

  An unsymmetrical lens (say, planoconvex) forms an i-d odb8k, *h hp5nzt-jmage of a nearby object. Does t8hnktj,*b- d5dp-oh zhe image point change if the lens is turned around? ----待选择----yesno 

The thicker a double convex lens is in the center as cokln1wtkuanj .-7ok 7 *mpared to its edges, the shorter its focal length for a given lens diameter. Expla7la1 wknj.to- k uk7n*in.

Consider two converging lenses s ww0zlu,lzxqe/7 ( ki/kur25.p rrr0 beparated by some distance. An object is placed so that the image from the frlr2i k z,.u/qrebrx7wu 0/( w5zpkl0 irst 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 photolw6 yx 2iz9q7bgraph of yourself as you look at your image in a flat mirror 2.5 m away. For what distance shoub7iyw 2xlq69z ld the camera lens be focused?    m

When you look at yourself in a 60-cm-nuu fe3)5h q01wvq*czbq,zp9 tall plane mirror, you see the same amount of your body whether you are close to the mirror or far away. (Try it and see.) Use ray diagrams to show why this should be tru5cnbuqpf) e3,q*h1 zz 9wv0uq e.

  Two mirrors meet at a .je)- kaws81 n ntf4bcxzjgz4 112pki 135$^{\circ}\,$ angle, (Fig. Below). If light rays strike one mirror at 40$^{\circ}\,$ as shown, at what angle $\phi$ do they leave the second mirror?    $^{\circ}\,$

  A person whose eyes are 1.68 m above the floor stands 2.20 m in front of a vet nd+w1r/i u,grtical 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 can be seen reflected in the mirro g/iwtnu, +1rdr?    cm

  Suppose you are 90 cm from a plane mirror. What arehz dw:7usszbx iq:d,m,)d i;8a of the mirror is used to reflect the rays entering one eye from a point on )dxdwds,8s;,: qhbuiziz :7mthe tip of your nose if your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors meet at a h ,-hpjxs5l-jn 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, focuses the Sun’s rka3ji8f*1 gg4y ux;ys ays 18.0 c1; 3igyx s8ufjy4g*a km in front of the mirror. What is the radius of the spherical surface from which the mirror was made?    cm

  How far from a concave mirrordg6 egfi6/i9n* l ic5l (radius 23.0 cm) must an object be placed if its image is to be at ii9* ilgnlgfie5 6dc/6nfinity?    cm

  If you look at yourself in a shinn5orwsnlh( 1 +y Christmas tree ball with a diameter of 9.0 cm when your face is 30.0 cm away from it,5n+wsnhr1 l(o where is 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 an o2 o-lj6b:k5dln386ik+ qnz fjvns-wupright image of any person who stands 1.4 m in front of it. If the image is three times the person’s height, whatz:j3lf nov6s+k5w-oqd bknj 2li 68n - is the radius of curvature?    cm

  A dentist wants a smallqscpb-f uz /+,w(x54l/ptyit 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 produce images of cars behind you that are smaller thjml e+lx6j r7.k7mj, du*6 dvhan 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× them7, jvrhk. 6e6*x+ljjdd7 lumir normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is pj) -ndk+g f6b6c.fyj -eei6wnlaced 20.0 cm from a convex mirror of radius of curvature 20 j6c6eynkfe -6j-gi+) . bnwfd.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 bmitc*e-te 4 3m from a convex security mirror in a store. You estimate the height of your image to be half of your actual height. Estimate the radius of curvaturtmeict4e3b-* e of the mirror.    m

  (a) Where should an object be placed in front of a concave mirrorx87d v6 evph78/-guzeoo5c ynksey) / so that it produces an image at the same location as the o8u5xncy-yk e)sh7dvo v8pz7g/ /eo6 ebject?
(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 la)m fa ya,9v *7azn8nsmall when viewed in a curved mirror. The image appears to be 18.0 8)nzm*,a7a9 nflya vacm behind the mirror. What kind of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniqv-u9 ,ie l7hfp ew-0pvues,
(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 convex msyv:b+4c(ru: rg 5 zhiirror 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 7avwejc94k7 dconvex mirror as long as f is considered negati7e4 k7av c9wdjve.

  The magnification of a convex mirxd)u*gp0zp0mf7 wg /gror 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 isl5d1 wwyb: p5o6: qiew placed 28 cm in front of a spherical mirror. It is desired to produce a virtual b:w6io1w5y 5d e pwlq: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 face by a fac pkl( 74ote:gctor of 1.33 when your face is place:g( eto4lk 7pcd 20.0 cm in front of it.
(a) What type of mirror is it?  ----待选择----convex mirrorconcave mirror 
(b) Describe the type of image that it makes of your face.
(c) Calculate the required radius of curvature for the mirror. r =    cm

  What is the speed of li4yn- our *erf48hsp 6kght 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 e+e e/v2ts d +tbd*i-cice 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% of its value in water. What is sjj6p6(divvj/12pr jthe index of refraction of this sud1j6i( 26j svvpr/pjjbstance? n =   

  A flashlight beam strikes the surface of a pane of glass (n = 1.58) at gy:fl(j4w1d : hy mucimb7 vz0g(a7:k:zq2 mva 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashlight upward from dawgk. hg. y.0 +djt4mfyy-1xi h27bg beneath the water at a 42.5$^{\circ}\,$ angle to the vertical. At what angle does the light leave the water? $\theta_2$ =    $^{\circ}\,$

  A light beam coming from an underwater spotlight exits the water ) 9i tjndbt7.mat an angle of 66i b9md n7t)jt..0$^{\circ}\,$ to the vertical. At what angle of incidence does it hit the air–water interface from below the surface? $\theta_1$ =    $^{\circ}\,$

  Rays of the Sun are seen to make a 31.*jkybw95b*f wf50 bp/o +ikxl 0$^{\circ}\,$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?    $^{\circ}\,$

  An aquarium filled with water hakk57)me f0ctjf )dy )ds flat glass sides whose index of refraction is 1.52. A beam of light from outside the aquarium strikes the glass at a 43.5° angle to the perpendiculakdyf)) ckm05 )f7etdj r (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 otdfjxb-):t)a +galgq 8bb(: c f a pool at night, a watchman shines a narrow beam of light from his flash(l:)bjfa cb-+ bx:dt tg)8gqalight, 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 equilaterac a ntb8k:m2,l/gaxm 6l 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 shsxl g45,hcc(*i /yeof glass (n = 1.52) and is partially reflected and partia ic5cl*4sxyegh(/h s ,lly 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 uniform layer of transpare4x utmb x9vul6 i2aj/fa 92;xnnt material, as in (Fig. Below), the direction of the emerging beam is parallel to the incident beam, indtx 6 vx9/2aaul2iubf ;xnjm49ependent of the incident angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on a flat piece o/s2oaj3dv4xx6 ,uqt df glass with index of refraction n as in (F, 3 t4a sdvx6/2qjdouxig. Below). Show that if the incident angle $\theta$ is small, the emerging ray is displaced a distance $d=t\theta(n-1)/n$ from the incident ray, where t is the thickness of the glass and $\theta$ is in radians. [Hint: for small $\theta,\sin\theta\approx\tan\theta\approx\theta$ in radians.]

  What is the critical angle for the interface between water and Lucite?8x;t. n4tc bcijz0hd3c 5e - lu:,3px zbzgx,x To be totally internally reflected, the ligh:xtx e n5 tpzi lz.,zxc0cgx4d,cj- 338h bu;bt must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–air surface is 47i4k,u me;d8x-x:gp r y.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 if 8otp ,+dxpbm j od-nj:899xa depth of 62.0 cm. Where must it strike the 9-ndi p9j,mbj+8x dotfp8ox: air–water interface, relative to the spot directly above it, in order that the light does not exit the water?    cm

  A beam of light is emitted 8.0 cm b )7b9-w)p.*/rjuf*x ea mdq.uxji vr eeneath 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 about the index of refraction of the f.m-dqrb )79)xp *x*e.i r /jjeva uuwliquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face of tqswojc/q-*gk.a-4cgi7 r 5 ze-l j*gohe 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 tk04elue vj sa+*xzxjri( c.10he end 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 orjx.siual(04zc0 1x+k*ev e jf refraction is greater than about 1.42. In other words, regardless of the angle the light beam reflects back into the material at point a.

  (a) What is the minimum ind4osi 2gsinomx+.e/ 2olpzon b e7;r+ 3ex of refraction for a glass or plastic prism to be ug x3io ./p+elmi o+s ;o s4b227eznnorsed in binoculars (Fig. Below) so that total internal reflection occurs at 45$^{\circ}\,$? $n_1$ $\geq$   
(b) Will binoculars work if its prisms (assume n=1.50) are immersed in water?  ----待选择----totally reflectingtotally transmitting 
(c) What minimum n is needed if the prisms are immersed in water? $n_1$ $\geq$   

  A sharp image is located 78.0 mm behind a 65.0/y9 ol8c o*nlu1pn /howi 5tmb :f4ov5-mm-focal-length converging lens. Find the object distancn/5hp9b 4c8/mt oo 5yfo w:lunivo*l1 e
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a fzcj , ac+d c2qjf:8 7pa*0v6.l vfxajpoint 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 2.75s2iu* z9f 5 dko*5ijqkg4mse3 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 foce jkkq*45iuos3s*gf iz d52 9mal 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-lengthr3lj3 djd9n8zwot6 *r 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 l+*rw cr-5quy-y.au njength 24 cm to view a stamp 18 cm in front of the-ac+-*yju .5nr rwq yu 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+gtt.bo4odhp8z 2 o)y the position, type, at.+ hoztg 8b po)d4o2ynd height of the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to focus an image on the fiyfgq6i-+x yr)z 8v)c alm of a camera. The maximum distance allowed between theq+yavi8cxg)6 - y zrf) 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 by3 a(pfysll9o- 8y0tn c a factor of 2.5× when a book is placed 8.0 cm behind a lens. 0osyt8(fll- n3y ca9p
(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 9ahe::ptv(wm 07jldvle m m* *if m l(ehvmpa w9ed:*:7tvml*j 0the 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 obu2)7 nm9t9yjv8w el moject be placed to produce a realun7ow v)8 9ytlm m2ej9 image which is the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-nxs;8 vab.2u;;ii ozsp o-doy:nq1 9ulength lens must an object be placed if its image is to be magnified 2.00× and be reai 2uo;ys -oq8s9 nzb.pdv1: ; inxuo;al?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm

  (a) How far from a 50vk4. ij g4aqt4.0-mm-focal-length lens must an object be placed if its image is tk j4gt4q.4 viao be 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 inq964mbr lf+)ztm .bgv sect is 1.20 m from a 135-mm-focal-length lens. Where is the image, how high is it, an)m6vq4rgb bl m9t.zf+d 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 7 3tb1bi 4*pikvycj *4n5-cm-focal-length converging lens if b 4p1 ki4ncbi3tvj*y*the image is 2.5× larger than the object and is real?    m

  A bright object and a vi5 u0fo .zybf-f/h.yk 6ko:;5zxrvy axewing screen are separated by a distance of 66.0 cm. At what location(s) between the object and the screen should a lens of focal length 12.5 cm be placed in order to produce a crisp i x;6y o-.k zvf rh.a505kxo/fybuyz :fmage on the screen? [Hint: first draw a diagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length converging lenses are placed 16.5 cm apa.8 eqw avk;3b,ds, gf3)yb jyqrt. An object is placed 36.0 cm in front of od8).s kyab,q;ewv3 g,qjy3bfne lens. 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 witlp)ls* l3x46fkyx;,r sb .*c xurcw2lh $f=-31.5\mathrm{~cm}$ 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 diverging le( k me3bea/:: zno-xvhns. Parallel light strikes the diverging lens. After passing through the converging lens, the light is again parallel. What is the focal length ofx(oa:k:z v-n3 mhb/ee the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Example 23–12 are now y9vttpp1 ;.e ruuy7n0*zu2( ymdtdr/ placed only 20.0 cm apart. The object is still 60.0 cm in front of the first lens as in (Fig. Below). I2 d0 t7n9 v(;urt1p uumdyzepyy*t. /rn 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 r2u3/xi 7lhys 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 rih23u7l y/ sxthe 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 p .zqyb9sd h- c8zuvlg ;+6i2vqc9 am;to the right of a converging lens with a focal length of 18 cm. An object is placed 33 cm toy;-u+cdg.pm9vbh z2z8s9;a6 qcl iv q 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 lentmzj n:h+sn+a3ja/d/ gth 20.0 cm and one diverging with focal length are placed 25.0 cm apart. An onahmdj :/tn/zj3 + as+bject 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 nexty 63f5*7/cxcyiwwaq mxri0::ckixz 2 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 radii of 34.2 cm and wpoppjq z-;c tp..qo8p3ni8m *1 lgg+23.8 cm. What is the focal length i3nqip qmg8;lp8 j zowp 1cp*-og .tp+.f n = 1.52?    cm

  Both surfaces of a double convex lens have radii of 31.0 cm. If the focal lenm;xa- *8-xn xl 0vt sdrblf(a8gth is 28.9 cm, what is the index of refraction of the lens matemla(rx;td n0fs 8alv8x*- bx-rial?    cm

  A planoconcave lens (n=1.50) has a focal leng.6tut5, fd9 iy/ *lm-grflemrth of -23.4cm. What is the radius of the concave surface9rmlr 6,*lt/- fefig5 duytm.?    cm

  A Lucite planoconcave lens (se lezva9llsw/9bt0 y+2*l0 cboe Fig. Below) has one flat surface and the other has R = -18.4 cm. What islol2c9eb0ll*a09 /+sybt zwv the focal length?    cm

  A symmetric double cno378z n9nn 3feqsc f(xdkhh77*e 7 fnonvex lens with a focal length of 25.0 cm is to be made from glass with an index of refraction of 1.52. What should be 7es*87nnh7efcfk3q9nnxnh 3o f 7dz( the radius of curvature for each surface?    cm

  A prescription for a corrective lens calls for a6mbj2us25 xkwf3:c f+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 tuc fms wk3 xb252:af6jhe other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fig. Below). Yo6qjuj job109w xr),g, k aa/io.js6itu stand 1.5 m away from one of these mirrors and look into it. You will see mjq ,ao6b6jajtrgkwxio0u j .,91 /s) iultiple 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 wipn, h)d4tlcc)b7z b) mth water. We measure the bdhpbczl,))cnm t47) width (x=5.50m) and 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 ce9npaxsa qsb93ad qz ;o3bvd)3 r125lc rtain piece of plastic in air is $\theta_{\mathrm{C}}=37.3^\circ.$ What is the critical angle of the same plastic if it is immersed in water?    $^{\circ}\,$

(a) A plane mirror can be considered a limiting case of /x eq t 4m5*jeab/cdi0a spherical mirror. Specifq45ixj*cmd /a/e b te0y what 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 mirru .ncef*a vhg3h64(xv ors so they form a 90$^{\circ}\,$ angle as in (Fig. Below). When you look into this double mirror, you see yourself as others see you, instead of reversed as in a single mirror. Make a careful ray diagram to show how this occurs.

Show analytically that a diverging lens can never fo ci(+jreueb3: rm a real image of a real object. Can you describe a situation in whi irb+ jc3u(ee:ch a diverging lens can form a real image?

  Each student in a physics lab is assigned to find t *t-nq n pattd,c,ma*4he 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 studatt4 q* d-an,* mpt,ncents complete the assignment at different times using identical equipment, but when they compare notes later, they discover that their answers for the object distance are not the same. Explain why they do not necessarily need to repeat the lab, and justify your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of a prisy;+ gqkpx9)s xy 58hilm is $\phi=72^\circ$ see (Fig. Below), what is the minimum incident angle for a ray if it is to emerge from the opposite side (i.e., not be totally internally reflected), given $\mathrm{n=1.50~?}$ $\theta_1$$\geq$    $^{\circ}\,$

The end faces of a cylindrical glass rodx +mh5wl*q be0 $(n=1.54)$ 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 3de*cgb9jmb1 7t*b. k u3 cm in front 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 cong1e,8g ain oz,t4 f,tfverging lens of focal length f, and a white screen for viewing the image is on the opposite side. The dis1anztt8 f ei,4fgg,, otance $d_T=d_i+d_o$ 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 acts as( *jo vkd,bos. 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 wikso d (v.job*,de, 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 on a sc(xm prqqkz0wmut v/q(/(s 0f4reen 1.80 m by 2.70 m placed 7.50 m from the projector. What focal-length lens should be used if the imageq/v swx4 f(0zukmp0q (/( qmrt is to cover the screen?    cm

Show analytically that the image formed by a conver- )ckfd**pktxz(7viw ging lens is real and inverted if the object is beyond the focalzp )-ftdkxicw (*7 k*v point $(d_0>f),$ and is virtual and upright if the object is within the focal point $(d_0>f),$ Describe the image if the object is itself an image, formed by another lens, so its position is beyond the lens, for which $-d_0>f$, and for which $0$<$-d_0$<$f$.

  A movie star catches a reporter shootin5 a;oucz n83w,2fqsqyqyy8 ;4fhwo6 ig 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.iw4yzcah3s8wfo8;fouy nqy , qq;562 25 mm high on the film, and the focal length of the camera lens was 210 mm. How far away from the subject was the reporter standing?    m

  How large is the image of t,d e)bjp93b:om60o e nf ew9eyhe 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 ch3 6v ja 9z03kgkzuue+m in front of a certain lens is 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 jz+3h ak0kgu v3uz6e9 length? Is the image real or virtual?    cm (diverging)  ----待选择----virtualreal 
(b) If the image were located, instead, 41.5 cm in front of the lens, what type of lens would it be and what focal length would it have?    cm (converging)

  When an object is placed 60.0 cm from a certain converging lens, it fcyv 3. ; hdi)ucaw5gw1orms a real image. When the object is moved to 40.0 cm from the lens, the image .u1;a 3wc)whgvc5d yimoves 10.0 cm farther from the lens. Find the focal length of this lens.    cm