What would be the appearance of the Moo+iw6 nwcl 8 pxx:m)of1n if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said tl5h mn qb6)meuka/1s1zee :s8 o have burned the whole Roman fleet in the harbor of Syracuse by focusing the rays of the Sun witmunzm5leak1es 6s 1/ )bq:8 ehh a huge spherical mirror. Is this reasonable?

Although a plane mirror appeajvuf 8qww:+zm+wh i*1rs to reverse left and right, it doesn’t reverse up and down. Explain:z fuw+ 1 +v*whwjmi8q.

If a concave mirror produces a real image, is the image necessarily inverted? E0wum1 ,tgi *dpxu*d1 mpt g0iw,plain.

An object is placed along the principal axis oucd,i9zxj gc+ nn/.:oe+u oq-f a spherical mirror. The magnification of the object is -3.0 Is the image real or vio-+: cd9quizcx u.+ gjen/o,nrtual, inverted or upright? Is the mirror concave or convex? On which side of the mirror is the image located?

Using the rules for the three rauhpwg)1sjn-; (9(k-k mj dcw j5:ktzeys discussed with reference to (Fig. Below a), draw ray 2 fokm5kz(:je-g)jduk9sc 1 pwjh;w ( -nt r (Fig. Below b).
(a)
(b)

What is the focal length of a plane mmqw7ba4pu j:o uc00 pxi): qa-gne(4wirror? What is the magnification of a plane mi uq4j gq:p( o7n0)bcwue ia-m0p:4xa wrror?

When you look at the Moon’s reflectiemcl uk6 3;wt0on from a ripply sea, it appears elongated . Explaimktc;l0eu 6w 3n.

What is the angle of refraction when a light ray meets the b( a;6 pwsah;mfoundary between two materials perpendicula 6mh(f;aa;ps wrly?

How might you determine the speed o hr(8, nwogce xq7x5gij(9,cl f light in a solid, rectangular, transparent objexlg9c(wj, nc,5hqr 78e x(gio ct?

When you look down into a swimming pqk* bvlz3;q0s ool or a lake, are you likely to underestimate or overestimate its depth? Explain. How bvql *0q3 s;kzdoes the apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks bent when part t a8l 784ayx7twxgw9.g116;po crvh s) ctq faof it is under water (Fig. Belowwor)p yltxf7g.8 86c tcgh4;7aaqxw v19s 1 ta).

Your eye looks into adt) ;fmhu;442kxd azmn aquarium and views 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 the2xh;madkzm 44ftu) d; approximate position of the actual fish. Briefly justify your answer.

How can you “see” a roui4rk ) v)mo(jxnd drop of water on a table even though the water is transparent and col)rkxjvoi()4 m orless?

When you look up at an ob-p ngybe, 7 1tg,phv.;6 x,mfwg/z wj44dqsdnject in air from beneath the surface in a swimming pool, does the object appear to be the same size d;by7vndfs4- z4/ w,gm1wntpgq.6,ejxg ph ,as when you see it directly in air? Explain.

How can a spherical mirror have a ngbnk.3ze u 5gglp()9yegative object distance?

Light rays from stars (including our Sun)l u94l6v ,sdzqz c*zwp3fx2h1 ijbv:4 always bend toward the vertical direction as they pass tl3 z4 ,9q*6fjz psud x vivz1w:c2b4hlhrough 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 placed if a camera lens is to make tz2cf.)h:vx pa sharp image of an ob)c 2:tpvx f.zhject very far away?

What type of mirror is shown in (Fig. i5 zxot3.3lxj Below)? Explain.

A photographer moves closer to his subject and then refocuses. Does the camegr0n 23-paun xmsge(i s /.-fxra lens move farthinuasnps2x/g(- g.30 f r-e xmer from or closer to the film? Explain.

Can a diverging lens(dxxa7y h -nk7 form a real image under any circumstances? Explain.

Use ray diagrams to show that a real image foy w-c8uga lbw2yo; 9efp;a.8krmed by a thin lens is always inverted, whereas a virtual image is always upright if t f.gp-8b;ckywoey9 ; a8wa u2lhe object is real.

Light rays are said to be “reversible.” Is this conz uu9x*yykog) 7 +nrmddzo)sa6y*/e .sistent with the thin lens equato/y naxyzkud*om s7*rze g+.u)d6) y9ion? Explain.

Can real images be prb4 v*sl.s104ulnl oo;bfyw 0a ojected on a screen? Can virtual images? Can either be photographed? Discu ba4 1nvuo00 l;4lbw.f yo*sslss carefully.

A thin converging lens is moved closer to a nearby obj le, a51.vlupject. Does the real image form.l jpea5v1,ul ed change
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of refraction n = 1.30 In air, it is7 7 hrl0q9zrqs a converging lens. Will it still be a converging lzqr7ql7 srh09 ens if placed in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands facinz(/q etio d0qd jwn9-(g a converging lens. If the nose and the tail are each d(q0-ie/dzt (qonjw9focused 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. Uofey+ qu9 yg38 f1gibe4h*a*b nder what circumstances (if any) would the image of the nose be virtual and the image of the +au8f* biygebg*qfe y 43h1o9 tail be real? Where would the image of the rest of the cat be?

Why, in Example 13, must the converging lens have a shorter focal length than 8i 2g(nt)rugtthe diverging lens if th(unt g8t2 ri)ge latter’s focal length is to be determined by combining them?

Explain how you could hayl 0c-k2otlrh: (6jxuve a virtual object.

  An unsymmetrical lens (say, planoconvex) fqrp:yr .0qs(.yx5jf t orms an image of a nearby object. Does the image point change if the lens is turned around?sjqt rpqyr(:y . x0.f5 ----待选择----yesno 

The thicker a double convex lens is in th28l f4j e45u ho/pdocce center as compared to its edges, the shorter its focal length j54/h4cldf2ou 8ec op for a given lens diameter. Explain.

Consider two converg7s c.mf 3kcaj(ufj.5 fiss(-a ; lmg;jing lenses separated by some distance. An object is placed so that the image from the first lens lies exactly at t3.i7af.j;s kc ;jfc(s(5fmu -j g mlsahe focal point of the second lens. Will this combination produce an image? If so, where? If not, why not?

  Suppose that you want to take a photograph of yourself r(nff +x74 pdz u tht0r-v6fu)as you look at your image in a flat mirror 2.5 m away. For what distance should the tz+u6-0hxtr rv7pff4nu fd )(camera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mirror, you see the same amokf/w71 ,p a-cmqav)qz v1q9g uunt of your body whether you are close to the mirror or far away. (Try it and see.) Use ray diagrams to show why this shoul/w -)zp c1 ga9ukfqqv7qa1,mvd be true.

  Two mirrors meet at a 12 tfqkrc i k.h+vvf.4,35$^{\circ}\,$ angle, (Fig. Below). If light rays strike one mirror at 40$^{\circ}\,$ as shown, at what angle $\phi$ do they leave the second mirror?    $^{\circ}\,$

  A person whose eyes are 1.68 m above the flo 501;-b ckodg:5cqyh epfq hm)or stands 2.20 m in front of a vertical plane mirror whose bottom edge is 43 cm abov1hk5 5emc;-d0)yoc q:gb h pfqe 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 mirror?    cm

  Suppose you are 90 cm from a plane mirror. What area of the mirror z* fcu e*mfzg rwmjwr42:5vpd -v) 7t7is used to reflect the rays entering one eye from a point on the tip of your nose if your pupil diameter -)egwtrm4fm pjdw7r *uvf:vz5*z 7c2is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors meet at an angle k xod*cm/;6)jbbtj)( tsdn.f$\phi$. 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, focusebfk)c /fkq, j rkr 8hirn2+99js the Sun’s rays 18.0 cm in fc, /j kij9kn2)rb rfqk+ rfh98ront of the mirror. What is the radius of the spherical surface from which the mirror was made?    cm

  How far from a concave mirror (radius 23.0 cm) must an object be placed if itu:ii4zwy- g 5es image is to:-gw yue5 izi4 be at infinity?    cm

  If you look at yourself in a shiny Christmas tree ball wiik s1 wam*w f513qihs,th a diameter of 9.0 cm when your face is 30.0 cm away from it, where is your image? Is it real or virtual? Is it upfs1i kaw s1hq w*35im,right or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shows an upright image of any per9ymiw5faao; d5j(0x b x:kt g e-o2mj,son who stands 1.4 m in front of it. If the image is three times the person’s height, what is the radius of cutjowxm a5afgdo0 m,5ji9( y;eb2x:-krvature?    cm

  A dentist wants a small mirror that, whe oxm idfdcy 383041liqlvb/(kn 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 yo:ivg vr.*w* xru 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 av . vr:iwxg*r*ppear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0wbazr(s2 /qaaxas- /o few/7 ) mm high is placed 20.0 cm from a convex mirror of radius of curvature/r aqaze/axsbas- fw)2(7w/ o 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 secu 23gy0 u2pblydrity mirror in a store. You estimate the height of your image to be half of your actual height. Estimate the radius plg b32yu0d2 yof curvature of the mirror.    m

  (a) Where should an object be placed in front of a concps6*btj w*e*3sg- qjv+8 u qbvave mirror so that it prod3vqbj* upq +j8g-* tsw 6*vesbuces an image at the same location as the object?
(b) Is the image real or virtual?  ----待选择----realvirtual 
(c) Is the image inverted or upright?  ----待选择----invertedupright 
(d) What is the magnification of the image?   

  The image of a distant a rsv;p4lbv-7tree is virtual and very small when viewed in a curved mirror. The image appears to be 18.0 cm behind the mirror.vsr-7l4 bp;av What kind of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniques, - o b2ew 8h8ycu-x1jibv8qo8 k
(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 *m3r.s78 zwm 6w m omeppt6wa/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–r+v.3z bwjib e7m /5lnwd70 le2, is valid for a convex mirror as lone.5wi7l +rzw /b j3nldb07v emg as f is considered negative.

  The magnification of a convex mirror ic*,p(-nb5q ( gwl1+toy sxanus $+0.65\times$ for objects 2.2 m from the mirror. What is the focal length of this mirror? $\theta_2$ =    $^{\circ}\,$

  A 4.5-cm-tall object is placed 28 cm in front of a spherical mirror. It is oa-i.m3vja t9desired to produce a virtual9 ivaa. 3j-tmo 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 fac5n yd7r0mx5.* zekfqw-y u sh8e by a factor of 1.33 when your face is pw07dfn k5z 5 y8myu*r.esh-qxlaced 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 lighxv: njl3 i)7vedp q5e7t 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 g,k gw2jzf b wwu4i+.*is $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain si-h a xco qqf:j1a3)+gubstance is 89% of its value in water. What is the index of a gcho )f- jx+:qiaq31refraction of this substance? n =   

  A flashlight beam strikes the surface of a pane of glass (n = 1.58) at a 63 vzr ((c-kqbfgjnhfr;ejv cb,e(u05 7 g67q/h$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashlight upward from beneath the water at a:n:z:cnrf8 pa 42.5$^{\circ}\,$ angle to the vertical. At what angle does the light leave the water? $\theta_2$ =    $^{\circ}\,$

  A light beam coming frt6ja zpni rerabd;kf lq214d /:.9c3aom an underwater spotlight exits the water at an angle of 66.er1 ti36pbka9qn 4fz:; cd2ajl/ dar. 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 c:+6-aaw:vxo9 j orgaa 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 flatyk5t :dbz51 kkioh0e* glass sides whose index of refraction is 1.52. A beam of light from outside the aquaydh15 kbeik otk0*5z:rium strikes the glass at a 43.5° angle to the perpendicular (Fig. Below). What is the angle of this light ray when it enters
(a) the glass, $\theta_2$ =    $^{\circ}\,$
(b) the water? $\theta_3$ =    $^{\circ}\,$
(c) What would be the refracted angle if the ray entered the water directly? $\theta_3'$ =    $^{\circ}\,$

  In searching the bottom of a pool u-w98qyqmgx up5m3 m 1at 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 5uq3gx u m-98mmyq p1wof 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 equilateran w8 dn4ku*r3gl glass prism at a 45.0$^{\circ}\,$ angle to one face, (Fig. Below). Calculate the angle at which light emerges from the opposite face. Assume that n = 1.58.    $^{\circ}\,$ from the normal

  A beam of light in air strikes a slab of glass (n = 1.52) ac 5 zxp o+dqd66sad:4vdkt/ u)nd is partially reflected and partially refracted. Find the angle of incidence if the angl d5 td6)a4pkqxd + /ozud:s6cve of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam incident on a uniform layer of traw 3a brfsxb.w( s3l2h5h f2b:rnsparent material, as in (Fig. Below), the direction of the emerginab3.5 32bwrb f:rx(hss h2fl wg beam is parallel to the incident beam, independent of the incident angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on a flat piece of glass with index of rv )kvuikl7fyq/c;s v .7 -zdx/efraction n as in (Fig. Below).7)v/7vkq.ld -czk ;fuix s /yv 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 interface2j7zga 3mwd55, iuma;rzd; fe between water and Lucite? To be totally internally reflected, the 5 afme j,z37ai5 md2uzrg;w; dlight must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liqubkql cha4)s 6i9h2rmt e2fzjs-( 4)esid–air surface is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in a pool of water from a depth nbr3l*z n+uwb4re: 2l of 62.0 cm. Where must it strike the air–water interface, relative to the spot directly above it,*r: lbe2z3n+rl bun4w in order that the light does not exit the water?    cm

  A beam of light is emitted 8.0 cm beneath the surfx 6/o(llpe6 3bk(qut tace of a liquid and strikes the surface 7.0 cm from the pointl ox(/btt u6epk36q( l 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 pris7*hbd 2kj+czg m in (Fig. Below) at 45.0$^{\circ}\,$ as shown, but is totally internally reflected at the opposite side. If the prism apex angle (at the top) is $\phi=75.0^\circ,$ what can you say about the index of refraction of the prism? $n \geq$    (retain three decimal places)

A beam of light enters the end of an optic fiber a)rt( *rv tyhm;s shown in (Fig. Below). Show that we can guarantee total internar*t(mr;)h yv tl reflection at the side surface of the material (at point a), if the index of refraction is greater than about 1.42. In other words, regardless of the angle the light beam reflects back into the material at point a.

  (a) What is the minimum index of refraction for a hvnboj2 d5v7.glass or plastic prism to be used in binoculars (Fig. Below) so that total internal reflection o nvhd.bj725v 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 converging ns.a g lg3h7o4lens. o 74 an3ghlsg.Find the object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.p3/6dttuw+t i- ik3i-vy0yum 5 cm behind a lens.
(a) What kind of lens is it?  ----待选择----converging lensdiverging lens 
(b) What is its power in diopters? P =    D

  A certain lens focuses light from an object 2.75 m awjhv ,s;6 vq0chek+um.ay as an image 48.3 cm on the other side of the lens. What type of lens is it and c .u+0qkhe6 ;vhm,vjs 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 20z 7r8+5j qpxkf.5-cm-focal-length lens? P =    D  ----待选择----converging diverging 
(b) What is the focal length of a lens? $f$ =    cm  ----待选择----converging diverging 
(c) Are these lenses converging or diverging?

  A stamp collector uses a converging lens with focal leng kp4nr)z 4z5 0er0qfhgth 24 cm to view a stamp 18 cm in front of the lens. f4z)qz4hprk 500eng r
(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 , v+1texj8xqp-6k fi i:sv+ky 4.0 mm high. What are the position, type, and height of vxy86xepjt+i+s if ,- :q1v kkthe image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to focusvfkj9)wpq9* qg-b m 4q an image on the film of a camera. The maximum distance allowed between the lens and the film planej*-qq b9wfm gpv9)kq4 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 materzqr wc l/.u2 vb*p7vq3ial by a factor of 2.5× when a book is plav u 7v zbqc.l/r2*qpw3ced 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 wde5n)ct* 9wu m from an 8.0-D lens. By how much does the image move if the object is movetn9wdc ue*w 5)d
(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 wi ogk7hr797 cz ro1h6yrth a focal length of 25 cm should an object be placed to prod1hrzk rorc97o6hg 77 yuce a real image which is the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an object be placed xt mb6u7 8:4g al,qujnif its image is to beb 4j m8gtu6xquln,a 7: magnified 2.00× and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm

  (a) How far from a 50.0-mm-focal-length lens must an object bei2p39wo6+fk5u 9 lsvt k)bq xd placed if its imag659)sb ofv tqp3u9l kwi kd2+xe is to 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 insect is 1.20 m from a 135-mm t1)dxx5h:ibe -focal-length lens. Where is the image, how high is it, and dh 1tx):bie5 xwhat 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 a 6momlg:ct: ,yn image formed by a 75-cm-focal-length converging lens if the image is 2.5× larger than the object aglcmm ,to :y:6nd is real?    m

  A bright object and a viewing screen are separated by a distance of 66z0z/qigog- m, .0 cm. At what location(s) between the object and the screen should a lens of focal length 12.5 cm be placed in order to produce a crisp image on the screen? [Hint: first draw a diagramg-i0zmgoz/ ,q.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length converging lenses are placed 164 e-yg/iqbbljlp,)8 p.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 lp/jpgiy8bb4,l-e )q total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens wit xr0 cv587yvbpla*j-s h $f=-31.5\mathrm{~cm}$ 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 convenwi5 viq+uq+5 rging lens is 21.0 cm behind a diverging lens. Parallel light strikes the diverging lens. After passing through the conve +q+5i 5qwuvnirging lens, the light is again parallel. What is the focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Example 23–12 are now placbk* 6ev: xsp p/y:c:zaed only 20.0 cm apart. The object is still 60.0 cm ib ::* ky/ep sc:pxva6zn 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 are pl1tgk9ibx eg *ftia79s1 dcz ./aced 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-length1 9ibsga/i gz1tctf7d.k* xe9 lens. A final image from both lenses is inverted and located halfway between the two lenses. How far to the left of the 15.0-cm-focal-length lens is the original object?    cm

  A diverging lens with a focal length of is p)q aqx()+ ipw;ec wb/glaced 12 cm to the right of a converging lens with a focal length of 18 cm. An objectwx(; iq)pc)+bwqe ga / 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 divegvheg83:(2 wj(g eqqb rging with focal length are placed 25.0 cm apart. q(geqe vgb:2(j8g 3wh 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 converging lens of focal length 8 : +lifmy 4uql s00;371vhamcueil qb$f_C$ 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 surz4ne l9u)pl8 eface radii of 34.2 cm and 23.8 cm. What is the focal length if n = 1.52e4z lln8)peu9 ?    cm

  Both surfaces of a double convex lens have radii of 31.0 cm. If the focvv sw-wi4/1 ykhba5/yhbbb ;wwp* +(oal length is 28.9 cm, what is +ihv abyvw s/b pw( wh/5bok;w*4-by 1the index of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has+c2trpp l0 0vhd7 v- 92d;bd ss.wlyoj a focal length of -23.4cm. What is the radius of the concave surfaces-bwjy+0ddprv2s0c9l d7l2 h. pv ;t o?    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat surface and the otheqe 358rf. a9ggs bs/kzr has R = -18. 5/ekfzg .rq9s3sa8 bg4 cm. What is the focal length?    cm

  A symmetric double convex lens with a focal h -p) fse-xnlx43,ei blength of 25.0 cm is to be made from glass with an index of refraction of 1.52. What should b,s- bfhexpi x-n3)l4 ee the radius of curvature for each surface?    cm

  A prescription for a corrective lens calls for +1.50D. The lensmaker gri.es jqjn /xz41lp5n:1fo gc95 ru b+gends the lens from a “blank” with n=1.56 and a preformed convex front surface of radius ofe +4xj.1/q:nju5s1lorn5g gcbp e 9fz curvature of 40.0 cm. What should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 .lbur0,68nj d nci5ay m apart as in (Fig. Below). You stand 1.5 m away from one of these mirrors and look into it. You will see multiple images .806c,bj ulydn niar5 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 deph:k2/uoxyx cm q4 v( xok4g02rth of a swimming pool filled with water. We measure the width (x=5.50m) and then note that the bottom edge of the pool is just visible at an angg4mc(ok2x4uk vxoy 2r h0q /x:le 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 fg91f7 rdj f0u2h sp+me .5dwgpiece 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 +pmh8+f2l8svap5 g ziof a spherical mirror. Spec am8p2 g5pl8zs++fv hiify 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 mirrors so they form a 9r.wxry(86 t6z gjfz( e0$^{\circ}\,$ 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 nevtv 3.ez2yh 8soi c)f,xer form a real image of a real object. Canso3 yxi8z.f2ec h,tv) you describe a situation in which a diverging lens can form a real image?

  Each student in a ph2mui/gc)ee g 1ysics lab is assigned to find the location where a bright object may beu 2)me1 cgig/e placed in order that a concave mirror with radius of curvature r = 40 cm will produce an image three times the size of the object. Two students complete the assignment at different times using identical equipment, but when 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 t m+y2u xas o3wn uyzlyphc 509u8*0o/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 cylindrical glass rol6 tp 44+okkvjd $(n=1.54)$ 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 5bgrqo( jcjc.ix9z-8cm 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 co2eo7 yod 3xc)onverging lens of focal length f, and a white screen for viewing the image is on the opp)3y7oex o 2cdoosite 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, t:n5te1mkgm8 qhe 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 screeg8 m1mk5e :tqnn 8.00 m away, how far from the lens should the slide be? If the slide is 36 mm wide, how wide will the picture be on the screen? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (picture size is actually 24 by 36 mm) is to be projected on fb2c9yu ok n u l2bm1ra-g2kp/ c30s/aa screen 1.80 m by 2.70 m placed 7.50 m from the projector. What focal-length l s a pnukg9ocbk/cb2 1 my-raf2lu2/03ens should be used if the image is to cover the screen?    cm

Show analytically that the image formed by a converging le-uo5gu 1 ng0dd w8(cwins is real and inverted if the object is bei 8o ggdw wun5dcu(-10yond the focal 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;o3w+uet5 nwypi8;cw reporter shooting pictures of her at home. She claims the reporter was trespassing. To prove her point, she gives as evidence the film she seized. Her 1.75-m height is 8.25 mm high on the film, and the focal length of the camera lens was 210 mm. How far 5;+cp8eiw t yno u;w3waway from the subject was the reporter standing?    m

  How large is the imat(+vo17o.n,atbtd ea ge of the Sun on film used in a camera with
(a) a 28-mm-focal-length lens,    mm
(b) a 50-mm-focal-length lens,    mm
(c) a 135-mm-focal-length lens?    mm
(d) If the 50-mm lens is considered normal for this camera, what relative magnification does each of the other two lenses provide? The Sun has diameter $1.4\times10^6\mathrm{~km},$ and it is $1.5\times10^8\mathrm{~km}$ away.    for the 28 mm lens    for the 135 mm lens.

  (a) An object 34.5 cm in front of a certain lens is imaged 8.q *bw+*s b6-lufpv;jr20 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 qrl**bs;p fj +ubv 6-wthe 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)