What would be the ap57f: bd zks w(tkvxmd .5ir--ypearance 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 in the ha.hdk1n+ah5o1m wgwyf m; ,0wy 9t a3varbor of Syracuse by focusing the rays of the Sun with a huge sphericao;13yad w1vkmwh t +n mg,w5.fy0h9aal mirror. Is this reasonable?

Although a plane mirror appears to reverse left and right, it doesn’tt) sgsc1z ,ygy7 p* zkk3- -6 gdtm9;bt9jqfeu reverse up at3bp6 dgce *- -kz9k s)z 9su1tgq7 f,jgym;tynd down. Explain.

If a concave mirror produces a real image, is the image necessarily i yhulg.qs1xp ()0(pgunverted? Explain.y(u1p upqg. s0g)h(lx

An object is placed along the principal axena3: ov5f8/o qb .ftbyqx6i.is of a spherical mirror. The magnification of the object is -3.0 Is the image rea e:obvqtnfi5.fqxya. 6o/b8 3 l 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 the three rays d 6h:v v2qzzhb1iscussed with reference to (Fig. Below a), draw r:16hv bqv2zh zay 2 for (Fig. Below b).
(a)
(b)

What is the focal leo6,wuhpd 0x/v la;ie. ngth of a plane mirror? What is the magnification of a plane mirroro6i /aew0;v.dlx ,uph ?

When you look at the Moon’s reflection from a ripply sefg/1k: j 8q4:8h rsj2l uvw3abe0wrvka, it appears elongated . Explaa kwk:g0/bs1v 8jr328 eqj4uhrl v:f win.

What is the angle of refraction when a light ray meetskjahas sv7w+.6)m*u((q yj sc the boundary between two materials perpenay7.ss k)jv((c j+m qa*6u wshdicularly?

How might you determine the speed of light in a solid, rectangular, transparenad n .4qtm pk9+vufj*ca (yaw5z,2ciwbcf.//t ob(j4+ack 5pif wdu c*wfvc/an.zm.ta, 2q/b y9 ject?

When you look down into a swimming pool or a lake, are you likely to underestima* vk0isjk1 4g8bg1l tjte or overestimate its depth? Explain. How g1b8klkjg*04tj v1 s idoes the apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks bent when part of itl 9 i4vowtp42c is under water (Fig. Bewlc24o 4 vtpi9low).

Your eye looks into an aquari;e;,,pb f- 6g (lwrzg,vmbqoe um and views a fish inside. One ray of light that emerges from te-f; vg;6o mbzp,e(wb,q,grl he 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 fish. Briefly justify your answer.

How can you “see” a round drop of water on9whzrmip m ak*6b)bova ek4 u1.vu1r9a2uw,, a table even though the water is transparent and colorlessa1m,9wraeki6b v* bokz umu) r,42vu.wa9 p h1?

When you look up at an object in air froud t1u1epl4u( m beneath the surface in a swimming pool, does the object appear to be the same size as when you see it directly in air? Explain.1 1(u4ul puted

How can a spherical mirror ha.)kd zdzvm p8..c m7 e8cehtf7e k2v:cve a negative object distance?

Light rays from stars (including our Sun) always bend towarduc0 47xuh 4my*sokk7 b the vertical direction as they pass through the Earth’s atmyo7ks4mu*kc4 7xb0 huosphere.
(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 m9ngucmn+)eujx, 1 x* be placed if a camera lens is to make a sharp image of an object very far,xge u*)un +mm xnc19j away?

What type of mirror is shown in (zetp yc9 q/*w5o/+he fFig. Below)? Explain.

A photographer moves closer to his subject and then refok(qu- ,i:x rdrf;*o , ymypj(ocuses. Does the camera lens move farther from orjqr(,fuko p-(:y,xom y; idr* closer to the film? Explain.

Can a diverging lens form a reap r0q,:ivt /gb 6qk9pnl image under any circumstances? Explain.

Use ray diagrams to show that a real image formed by a thin lens is a 6ssl 8 cq9p.t89koncny54rdhlways inverted, whereas a virtc46.sr9po89t nks8nqhy lcd 5ual image is always upright if the object is real.

Light rays are said to be “reversible.” Is this consistent with thef;1 *y8hydzz, f e0f yzv*rq*x thin lens equatiyz; fv ffhd zr 1**80*eyzq,yxon? Explain.

Can real images be projected on a screen? Can virtual images? Can either be phot s 4vl1w)luy a7h2 kqe*tmp:b3ographed? Discuss care)py*kv qm1l be ts4w23 hual:7fully.

A thin converging lens is moved closer to a nwx).s ag*l a-cearby object. Does the real image formed ax.as *wcl- )gchange
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of refi paw ;qmh y9k,,fvg6ras5-g6raction n = 1.30 In air, it is a converging lens. Will it still be a converging lenaav wks9hi,5 6-m;p g6fqgy,r s 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 noseo,qsn wibswmjbr /m fb//19- w/t8lo, and the tail are each focused on a screen in turn, which will have t,s -fq on,w8 bw1sboimw/r/l//9bjmthe greater magnification? ----待选择----nosetail 

A cat with its tail inb(*e*q0hxt +(bt+c /.osk9t pkwz dqb the air stands facing a converging lens. Under what circumstances (if any) would the image of the nose be virtuttp+9qko e(t z.kx/s(c+ 0bdq *bb wh*al and the image of the tail be real? Where would the image of the rest of the cat be?

Why, in Example 13, must the converging lens have a shorter focal5fp x e7/w yjuhn3zir;w 8d/3t length than the diverging lens if the latter’s focal l/rfhz wpy7ue3t/5dx;8wn j 3iength is to be determined by combining them?

Explain how you could hav36tkh 78ahdxve a virtual object.

  An unsymmetrical lens (sro2e1k/q*h o uay, planoconvex) forms an image of a nearby object. Does the image point change if the lens is2 uhrq 1/keo*o turned around? ----待选择----yesno 

The thicker a double convex lens is in the center as compared t0t h4z6t3uukgo its edges, the shorter its focal length for a given lens diameter.th6 t4 3kuz0ug Explain.

Consider two converging lenses 1:tuhdb/da:-e ,clsz 9q: csn separated by some distance. An object is placed so that the image from the first lens lies exact:csdz t a/b:dl1qucn-,9s h e:ly 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 taka16ds;:sq8h 4r cy yyfe a photograph of yourself as you look at your image in a flat mirror 2.5 m adqhs:sy ay;y c 4186rfway. For what distance should the camera lens be focused?    m

When you look at yourself in a-xo,en.qu.pwk5to 5 m 60-cm-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 t- tm .up,.nqo5 oxke5wrue.

  Two mirrors meet at e.,n2c-ojwp7p9nki,e5 fhsa a 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 1.88 e8c.bq.he2d fiznu 68 m above the floor stands 2.20 m in front of a vertical plane mirror e8e2bnd.hcfz i88qu. 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 mirror?    cm

  Suppose you are 90 cm from a plane mirt*xxl f //ivyj 3yod,;ror. What area of the mirror is used to refl3xd f/l,y vyjx*o /i;tect the rays entering one eye from a point on the tip of your nose if your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors meehn0r- ,r vts) y4ym avn5:fl/wt 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 mirrot1hz eq8mld2/r pointed at the Sun, focuses the Sun’s rays 18.0 cm in front of the mirror. What is the radius of the spherical surface from which tm q/1t2lhzed8he mirror was made?    cm

  How far from a concave mirror (radius 23.0 cm) must an ob/+apf :d6src zject be placed if its image is c:afds 6rp/+ zto be at infinity?    cm

  If you look at yoursel* -u pat3c1qoyf in a shiny Christmas tree ball with a diameter of 9.0 cm when your face is 30.0 cm awayayc1t p3oq -*u from it, 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 upr-6z u/ yfagg t.8f-h74exetxi ight image of any person who stands 1.4 m in front of it. If the image is three times thga6y- .e gz ix tefx7h8t/4-fue person’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror that, when 2.20 c ng7 qn8t7z:5a b;u ,0del9g4slgdyqpm 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 behindd-1.wkfejh :d 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 size? -k1d ej:fwhd .
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is placed 20.0 cm from a convex mirror of r70dv1on)ls tdvnc -i dv4-7er adius of curvadcvo i1n vsre4d7lt7--v n)d0 ture 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: dz hg l(ycnzlxoc2ux0)2a,8 store. You estimate the height of your image to be half of your actual height. Estimate the radius of curvature of the m yg:z nc)hu,dzoa08l2x2 x (clirror.    m

  (a) Where should an object be placed in kqh.+fsti3 vx* 9 jl4wfront of a concave mirror so that it produces an image at txlihwsk 3*tvfj 9+ q.4he 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 tree is virtual and very small when viewed in a )zg zmnj*u:0 7o6pde+ 8bov dpcurved mirror. The image appears to be 18.0 cm behind the mirror. What kind of mirror is it, and what is its radius of curvadom pn 8 zg+)zjvo0p6u:7*bdeture?
 ----待选择----convexconcave 
r =    cm

Use two different technihe7q 3e;ygmt. ques,
(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 mirr tj6:yewq3 b x/a5ibq o7bp)v7or 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 equationm9 rm5 ae9+z.k eppb+w, Eq. 23–2, is valid for a convex mirror as long as f isek9mp 59a+rzepbm. w+ considered negative.

  The magnification of a convex mirror jve *hdvax57/y , u qlrg)-(qpis $+0.65\times$ 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 pl)qzwup4ihw em p* +1tjj-ux. 1aced 28 cm in front of a spherical mirror. It is desired to produce a virtual image that is uh4 p)t u-1xm1+wiwp qu jezj.*pright 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 faxzdzh 1d0; ;oo-xg8fbctor of 1.33 when your face is placed 20.0 cm i-0d8x1 zf;b ;gzhd xoon front of it.
(a) What type of mirror is it?  ----待选择----convex mirrorconcave mirror 
(b) Describe the type of image that it makes of your face.
(c) Calculate the required radius of curvature for the mirror. r =    cm

  What is the speed of light i+ vtnezv6;ct-v r8j h2n
(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 isri dz 9 qze(n*wo.vh1m.g(0fn $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a u,pccvxbf j z36g(up p:b.j3;certain substance is 89% of its value in water. What is the index of refraction of this substance? n j p3fv:zupp3;(u.cbbjc x g,6=   

  A flashlight beam stq8trr tovf(i 3.l*m0i+rx a- irikes the surface of a pane of glass (n = 1.58) at a 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashlight upward fromy1y *ylg0rg:(w stc3s 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 spotlig,v7ixq,omu o:n16y swht exits the water at an angle of ,ovuyi1 msq6xo :w7, n66.0$^{\circ}\,$ 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 kzk 2ysb3id() 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 2gqa8d9lc:bj9x u+r. akrf k+of refraction is 1.52. A beam of light from outside the aquariumjbx u8.+kdg rrc l2 akq+f9:a9 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 at night, a watchman shrwvey.e1 d( j8 7qm5ugines a narrow beam of light from his flashlight, 1.3 m above the water level, onto the surface of the water at a point 2.7 m from the edge of the pool (Fig. Below). Where does the spot of light hit the bottom of the pool, measured from the wall beneath his foot, if the poolywmrgj(eq1u 8 evd7.5 is 2.1 m deep?    m

  Light is incident on aos1jro gipa(c16;;ek n equilateral 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) and iylf/simk/x* o.xd.o 9s partially reflected and partially refracted. Find the angle of incik/i oy9 l dsx.xf/.mo*dence 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 t.q30kuy c.0smmc 9f aj6x4jsoransparent fo.. 6cj c0jxs 0muas 34m9ykqmaterial, as in (Fig. Below), the direction of the emerging beam is parallel to the incident beam, independent of the incident angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on a flat piecea ( *mbypia1l tant5+-z1j jvf-k bu6n,ay7 (x of glass with index of refraction n as in (Fig. Below). Show that if the inciden(*j6 p 1lnai + 5ufnj1zkb,bxtyta-7v (-a mayt 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 watct nhfzx) +.i;ppp7jqdox ;;r0 qkqo1rn06e (er and Lucite? To be totally internally reflected, the light must start in which material? )xjoq(r0q.1d;0 hnep xpk oic ;r6p+ ;7nqztf
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–air surk az:2/dka2a sn hk:k:face 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 fmbd1 cpy-mu;f f3k s rer s //bmu6ag+zg1/;n*rom a depth of 62.0 cm. Where must it strike the air–water interface, relative to the spot direc *1r+b /as cfmgzu/b-nf6um;dg /3 kr;ms1eyptly above it, in order that the light does not exit the water?    cm

  A beam of light is emitted 8.0 cm beneath the surface of a l4mz*1l u7prcbn*:t cwiquid and strikes the surface 7.0 cm from the point directly above the source. If total internal reflection ot7n* c 4r:zwb*c1mlpuccurs, what can you say about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face of the pri ebkamg.d*ih4 nxy5aftt6 28 5sm in (Fig. Below) at 45.0$^{\circ}\,$ as shown, but is totally internally reflected at the opposite side. If the prism apex angle (at the top) is $\phi=75.0^\circ,$ what can you say about the index of refraction of the prism? $n \geq$    (retain three decimal places)

A beam of light enters the end of an optic fiber as shown in (Fig. Below). rvmcd.l wan4n p4o:r7.d)r6 eShow that we can guarantee total internal reflection at the side surface of the material (ma4ndrr):d w erv4col7p .6n.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 glass or plad51 tai8zrd6p jo),o xstic prism to be used in binoculars (Fig. Below) so that total internal reflection occurs at 468ipj5 a,d1rxdzo ot) 5$^{\circ}\,$? $n_1$ $\geq$   
(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 conver:kp61+ m rnfgh4 he8lzging lens. Find the object dhe1pl+m fr:hz86 4g nkistance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.5 cm behind a lens.3 71ovem9ehl v
(a) What kind of lens is it?  ----待选择----converging lensdiverging lens 
(b) What is its power in diopters? P =    D

  A certain lens focuses light from an object 2.75 m away as an image 48.3 cm l p98rfpzgt( 3on the other side3p98 frl pz(gt of the lens. What type of lens is it and what is its focal length? Is the image real or virtual?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the power of a 20.5-cm-focal-length khrx :uc,, wc z0q(y7w l.0rci- rwp)fgy1y(glens? P =    D  ----待选择----converging diverging 
(b) What is the focal length of a lens? $f$ =    cm  ----待选择----converging diverging 
(c) Are these lenses converging or diverging?

  A stamp collector uses a converging lens with focal length 24 cm to vi hfv5v6d9-d cwo ,hc5few a stamp 18 cm in front od5h9dho 5f-6 vwvcf,cf the lens.
(a) Where is the image located?    cm behind the lens (virtual)
(b) What is the magnification? m =   

  A -5.5-D lens is held 14.0 cm from an object 4.0 mm high. What are the d6w 6 :tiuvsapgwsul-) fr:4 (lmq07 sposition, type, and height of thtpgfswwm sal( du i-)6q: sul0:vr467e image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length len.kkthx *d (6dbs is used to focus an image on the film of a camera. The maximum distance allowed between the lens adk6 .(b* tdhxknd 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 *cwn5q; mo ip)factor of 2.5× when a book is placed 8.0 cm behind *iw o;q) cmp5na 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 frv7r2f sh pwxe ctx.9,u. 7m0eaom an 8.0-D lens. By how much does the image move if the2 9,te rm.pxfvs0ec7 axuh7.w 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 l mg : :be2di,gtr-m5iiength of 25 cm should an object be placed to produce a real image which is i:igi tgr -2:dmm,5eb the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an object be placed c)2v:a. nguc6 b gke(jx-5) j m*vijooif its image isa:cx5igo *))g2j6j-v v(jmcoue n k.b to be 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 508mj k- 5new*yydy+7g-xnv 4te .0-mm-focal-length lens must an object be placed if its image is to be magnified 2.00× an ex 5yky+n7j-y*v d -mt4w8engd 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 a 9 cy)kvdja(-,n p/fjmpdh cy(7*ts7135-mm-focal-length lens. Where is the ima mf9*yd7 v 7das)(tpa/ jjpyc-hcn k(,ge, how high 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 formed by a 75-cm-focal-leng2k.pr/ w80n zttyyc f2th converging lens if the image is 2.5× larger than the object anw2nzy/8f tyrt kc0 2.pd is real?    m

  A bright object and a viewing screen are separated by a disey/zj4d1 9pc ;l 9. z)dnyjoyqkew+-ctance of 66.0 cm. At what locat+k wedc yyqyj l nze-p9j)oz ;49d/.1cion(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-length converging lenses are placed 16.5 cm apart. An objhjdpn-c64yeu,dti86xo4u *v ect is placed 36.0 cm p6utd64xi4 yu cev8,o*nh -jdin front of one 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 withh 2( h w4w1-trwrps(au $f=-31.5\mathrm{~cm}$ 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 lens. Par1;lr:*c0x.n ypmbf49q kwpkxallel 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 drawybpw9k.xm :l n1pxrf ;0 kq4*c a ray diagram.]    cm

  The two converging lenses of Example 23–12 are now pq*vfoz blfj; z:i1n4eg/t /v2laced only 20.0 cm apart. The object is still 60.0 cm ini 2j: fvgl z/tzvn /e;*f4boq1 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 placed 30.0 cm apart. The focal length of the lens fc6sh.j(xio/,cq (g t8u7wy fon 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 lohcgcj.t/x 7, w6qo ify8s(fu( cated halfway between the two lenses. How far to the left of the 15.0-cm-focal-length lens is the original object?    cm

  A diverging lens with a focal length of is placed 12o igzellzcxn -*6)c 3a(.y9w c cm to the right of a converging lensz.na )*zwc36ol(gxie 9c-c y l with a focal length of 18 cm. An object is placed 33 cm to the left of the converging lens.
(a) Where will the final image be located?    cm to the left of the converging lens
(b) Where will the image be if the diverging lens is 38 cm from the converging lens?    cm to the right of the diverging lens

  Two lenses, one converging with focaft )gvj 89u 25woq,s u(7 qe0nq.kgmbul length 20.0 cm and one diverging with focal length are placed 25.v ,u.ekg8mugo 5s02qfun(j7 btwq) 9q0 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 converging lgb**l+a j1eq eens 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 348)qvccq-xg4i 6llqgww j n2.( 2h mcb+.2 cm and 23.8 cm. What is the focal lggl)(qim v qxc.q2+bh -8ncw 42jc wl6ength if n = 1.52?    cm

  Both surfaces of a double convex lens have radii of 31.0 cm. If the focal z9xz,8 f g.cpdto0xo,length is 28.9 cm, what is.xc o,gf0zd pxtz8o, 9 the index of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm. y4 mifrzz.i;v bo+i8*What is the radius of the concave surfr+4mvi .bzoz8*y;if iace?    cm

  A Lucite planoconcave lens (seepu u rsiw6 q quo92 m6qeorz57+vg87v; Fig. Below) has one flat surface and the other has R = -18.4 cm. What is 5qserqwoi68 ;vuz2rop9m+u 7ug q67v the focal length?    cm

  A symmetric double convex len)kf6 tnx8fb pkp7xi ..s with a focal length of 25.0 cm is to be made from glass with an index of refracf. p6bi7pkxk x .)tfn8tion of 1.52. What should be the radius of curvature for each surface?    cm

  A prescription for a corrective lens callin*zf 7ja8f4vz n .o2bs for +1.50D. The lensmaker grinds the lens from a “blank” with n=1.56 and a preformed convex front surface of radiusn*bz.o zf a4 ifvj782n of 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 m apart as in (Fig. Below). You stand 1.5 6us4vjt)2gabtauq1rby 6 *8 n m6a1y) b8g s a* qb6u4rvnut2tj away from one of these mirrors and look into it. You will see multiple images of yourself.
(a) How far away from you are the first three images in the mirror in front of you?
$d_1$ =    m
$d_2$ =    m
$d_3$ =    m
(b) Are these first three images facing toward you or away from you?
the first image is facing  ----待选择----toward youaway from you ;
the second image is facing  ----待选择----toward youaway from you ;
the third image is facing  ----待选择----toward youaway from you .

  We wish to determine the depth of a swimming poolvpx rn1qmx(1gp:4wj:c j5 15r7 hqyco 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 angle ncrjwr x147hx(5qj v pp:gqm11y5 :coof 14.0$^{\circ}\,$ above the horizontal as shown in (Fig. Below). Calculate the depth of the pool.    m

  The critical angle of a certain pi tjajok)la 2-mhjx(1c6key1/b le p89ece of plastic in air is $\theta_{\mathrm{C}}=37.3^\circ.$ What is the critical angle of the same plastic if it is immersed in water?    $^{\circ}\,$

(a) A plane mirror can be considered a limiting case of a spherical mirror. Spen9 dbttov/ q+0l 4l3o xast)8jcify what4jta 3so t qlb0)lto8+vn9x/d 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 q 8n,q22bf l,wp;;z adyg6pucform 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 bfz3,m:y m-*tlnf9kii9hur5rm a real image of a real object. Can you describe a situation in which a diverging lens can form a real image?m*935i lt:mnu ,r fk-z byf9ih

  Each student in a physicssk2b*:gjst u4 j nagc4.;vs(znwc8j , lab is assigned to find the location where a bright object may be placed in order that a concave mirror with radius of curvature r = 40 cm will produce an image three times the s; s8v*s2j cg4u:s,.t acgk nzwjbj(n4ize 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 1do7bm vt8kxaq jo )yji*pm4b:8).pna 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 *m(g2jbu m zl8glass 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 of i3j0bygj n(utaye: 3,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 lens of fo q,y e 0+ta jw;iz,s1vvic60bocal length f, and a white screejy,; cvw 0+bsa,o6vt 0eq zi1in for viewing the image is 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 acts as the object whose image is proje-j t)7e9x mt qawzdr9/cted on a screen (Fig. Below). If a 105-mm-focal-length lens is to project an image on a se7 wtd9t/)x zmar9-qjcreen 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 beuws). 3ft3n sn y8t23nikff-e projected on a screen 1.80 m by 2.70 fk3yfe s3i ) 8f3u.-nntw2nts m placed 7.50 m from the projector. What focal-length lens should be used if the image is to cover the screen?    cm

Show analytically that the image h 64f(ysmy17ja0 v8jito9k dyformed by a converging lens is real and inverted if vdy8o9ya(74j0sk1ijhy 6 tfm the object is beyond 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 reporter shooting pictures of he89xbfa/l*dwqjmup v2pkd x37h 4e;6 nr 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 away from the subject was the repj 9f4bp8/a um76qpx;ehnd 2 dvxkl3w*orter standing?    m

  How large is the image of the Sun on film usfjjdy*, k/jl37)fos r fmp-x 9ed 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 le zhp3 k 2+k,fggq3vi:rns is imaged 8.20 cm in front of that lens (on the same side as the object). What type of lens is this,rh k3 2zgv 3qig:,kf+p and what is its focal length? Is the image real or virtual?    cm (diverging)  ----待选择----virtualreal 
(b) If the image were located, instead, 41.5 cm in front of the lens, what type of lens would it be and what focal length would it have?    cm (converging)