What would be the appearance of the Moon ikt2rj poy0s1+ f it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fleet in t *-5 -hrkcf6s:0 o0jw0jo*hqkn2py neu +x eqyhe harbor of Syracuse by focusing the rays of the Sun with a huge sphxs h eq0*5o6w n00:n*euj2--yyhpk+frjc koq erical mirror. Is this reasonable?

Although a plane mirror appears tv yb dl2m49hwzw(f0o-cq/8b fo reverse left and right, it doesn’t reverse up and 8zw/(9bwlfh02o4vb qyc fd- m down. Explain.

If a concave mirror produc) x:e* t; xbsg0fwlt8 ozb6)x4wi xkde*-y2s ves a real image, is the image necessarily inverted? Ex;xtx 2)ssei6gfo4x)8w**- y lkzb:d0eb xvtw plain.

An object is placed along the principal axis of at4c4 qqk-x6o h spherical mirror. The magnification of the object is -3.0 Is the image real or virtual, inverted or upright? Is the mirror concave or convex? On which side of the mirror is hxc6o q4t4k- qthe image located?

Using the rules for the three rays discussed with refered 3vwovqp5 u0y*:w5)lvmu m p4nce to (Fig. Below a), draw ray 2 f4yu 5 v mvwu0o) vpdml5wqp*3:or (Fig. Below b).
(a)
(b)

What is the focal length of a pbgd* kj7z aow1qk--m, lane mirror? What is the magnification of a plane mirro1badzo7j-k w *,kqgm -r?

When you look at the Moon’s reflection from a ripp 7(qnr 4ni;vpvly sea, it appears elongated . Explavq4 ni;7 pvnr(in.

What is the angle of refraction when a light ray meetsh v7aw;qs(i / q7qmwd: the boundary between two materials perpe7sqw d /:;v(7hi mwqaqndicularly?

How might you determine the speed of light in a solid, rectangular, t;;x9o spsr3-h) j fw 2m cz.k/cxhyhb1ransparent o;y3)chh1xosr/bm9 p-fcx;h zs .2wjkbject?

When you look down into a swimming pool or a lake, are youpj;1rjqlo ,0psf(2u w likely to underestimate or overestimate its depth? Explain. How does the apparent depth vary with (po s;fjrj,p2l0 uqw1 the viewing angle? (Use ray diagrams.)

Draw a ray diagram to sh.1 (mo.hxdr)ui9fws aow why a stick looks bent when part of it is under water (Fig..d. i9ro) 1f(mhuawxs Below).

Your eye looks into an aquarium and views a fish inside. One ray of light :nc3: t +4qv sjw l1uhfdhp*m5that emerges from the tank is shown in (Fig. Below), as well as the apparent position of the fish. In the drawing, indicate the approxim5* f cdn+14qhuh:svj:plm t3wate position of the actual fish. Briefly justify your answer.

How can you “see” a round drop of water on a table even though the water is ,ih i x)qc(gqxi y6,b7transparent and cogi)q h(b ,6iqiy7 ,xcxlorless?

When you look up at an object in air t6+p9d vhnqxt, hoq 108g n7izfu30 lifrom beneath the surface in a swimming pool, does gx 9t8 q, f1v7ip+in 3tdhh0oul06nqz the object appear to be the same size as when you see it directly in air? Explain.

How can a spherical mirror have a negiwsz pvpij0,c.am 5bq: ;02f- 7ln qlgative object distance?

Light rays from stars (includingfd;36t, ccvjc our Sun) always bend toward the vertical direction as they pass through t6cj, c;cvt3dfhe 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 a sharp image of4-al0xvjo d jjdh9r e/g9)ubo g35ig7 an objec9gud0-v hxgjoljgr 9 / b 7d3)ijeoa45t very far away?

What type of mirror is shown in dk t5::tx;fr y(Fig. Below)? Explain.

A photographer moves closer to his subject and tc t5fl(f5ch) khen refocuses. Does the camera lens move farther from or closer to the film? c) f 5tf5hc(klExplain.

Can a diverging lens form a k4s(f2 qi 6gvc1i1*uhy+ykyjreal image under any circumstances? Explain.

Use ray diagrams to show that a real image formed by ah7,c + )j3e7kqoyezrl thin lens is always inverted, whereas a virtual image is always upright if the objecrj 3z),eq7ho7k y+elct is real.

Light rays are said to be “reversible.” Is this consistent with the thin lens zmn9i a+oy /2lequation? Exp/+2a9 lzynoimlain.

Can real images be projected on a sdulhmjaews;;lj .y 6c)8w8)a creen? Can virtual images? Can either be photographed? Discuss carea.l)cml auws)j8w; je 6 ;y8hdfully.

A thin converging lens is moved closer to a nearby ) .)ukl glwr(bobject. Does the real image formed cr)wlubk.( g )lhange
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material witha*7j/u sik8xi.:fzx, zzj xd3 an index of refraction n = 1.30 In air, it is a converging lens. Will it still be a converging lens if placed /f.k:jz, zs auixz7x j3x*i8din water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands facing a convergix; byy(z6fpz0ng lens. If the nose and zx(yy zbf 6;0pthe tail are 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 cxm n6ee8y/ -+ ma 6zonl.,mjleckn-z ,oro*u )onverging lens. Under what circumsta l nrzl-x6)oezma,e m-8ojun*m 6.+cn y,k/o ences (if any) would the image of the nose be virtual and the image of the tail be real? Where would the image of the rest of the cat be?

Why, in Example 13, must the convergb7/h,j )9txe b8elkv ging lens have a shorter focal length than the diverging lens ie/ bgl9 t hj7vbek,8)xf the latter’s focal length is to be determined by combining them?

Explain how you could have a virtual ouw* kf8b0xji2 bject.

  An unsymmetrical lens (say, planoconvex) forms an image of a nearby object. Doans/- fcnsoaxv -g89cg2s45 hes the image point change if the lg4cs8ganv/5f 2nss c-xoa- h9 ens is turned around? ----待选择----yesno 

The thicker a double convex lens is in the center as compared to its edgb87rau)x 9 9 hd +;.bgvnbxmfles, the shorter its focal leng 8vd+ugx hlbm ;7bxb) fra9n9.th for a given lens diameter. Explain.

Consider two converging lenchlbj (dprcjp/:z)cyl;8g,)ses separated by some distance. An object is placed so that the image from the first lens lies exactly at the focal point of the second lens. Will this combination produce an image? If soc/hdc y j))c(lzjppl; :b8r,g, where? If not, why not?

  Suppose that you want to take a photograph of yourself as you loo-ma,i hrf1 *z:v; :mwp ubknv+k at your image in a flat mirror 2.5 m awak;-*p,w:z m rvibf+u:a mvhn1y. For what distance should the camera lens be focused?    m

When you look at yoursel1s) 3phb /wjdlf in a 60-cm-tall plane mirror, you see the same amount of your body whbdl s1p)jw h3/ether you are close to the mirror or far away. (Try it and see.) Use ray diagrams to show why this should be true.

  Two mirrors meet at i/st 3rvo1( q l7pb )c)0+qrg7:wvsquu mshv) 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 1.68/sg nx sk99.ig m above the floor stands 2.20 m in front of a vertical plane mirror whose bottoskx .n/9sigg9 m 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 pl (wr2r 1dk9 u;hyoyzb(ane mirror. What area of the mirror is used to reflect the rays entering one eye from a(2z1uyk w9; r(oyrdbh 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 mee gw;syvn.82l-9ino+ efyq9 not 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 mi b1hl:h5yeg*+l d4xkp rror 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 4h1gpl*yd:5lkxhe +b which the mirror was made?    cm

  How far from a concave mirror (radius 23.0 cm) mutxh4+yp v lu7h yo(78pst an object be placed if its image is to be at iny7 y vh8lu(ohp 7pxt+4finity?    cm

  If you look at yourself in a shiny Christmas tree ball with a diamete atuk;7w3a g6rr of 9.0 cm when your f ktrwg76 aua3;ace is 30.0 cm away 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 showsav g)o3.0fl uw o (tk,chf.p3s an upright image of any person who stands 1.4 m in front of it. If the image is three times thew3lcu po0k .(fsga) 3,hv fot. person’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror thatxbn+ 3x20y wfi, 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:uxd/p yr5to+(; s 8 cfyaowfnihrf557h(l 4z cars behind you that are smaller than they would be if the mirror were flat. Are the mirrors concave or convex? What is a mirror’5wh7 xy o(rh45ud/oczt8nyr s; lip f5f f(a+:s radius of curvature if cars 20.0 m away appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is placed 20.0 ;th3a(kj1pkc . jwizaxmfy 0 705 g,lowkr1e0cm from a convex mirror of radius of curvature .71zak;ga0l,jr ji3m t k(0 pey0xwck5hf1w o20.0 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 br7z3-/o )yu ;v c4ki: v 6zaaeuvlb5zsecurity mirror in a store. You estimate the height of your image to be half;iu 3c5kvbz/z7lae6yo-b a):vzvr4 u of your actual height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an o4dr rar yhj;2tn.+-mmb bt4wlcyt gr/o9+t(*bject be placed in front of a concave mirror so that it produces an image at the same locttt2r*9y4h./m4o bc m r-ty;r+wba n l+jrdg(ation 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 isw 8b,r1n n*rxx virtual and very small when viewed in a curved mirror. The image appears to be 18.0 cm behind the mirror. What kind of mirror is it, and what isxr*rxnb8,nw1 its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniques,xne-dg6d z75j
(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 magnifie)n np+ wy(g1(oqmt+rcation 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–atngmn ; f/;(g2, is valid for a convex mirror as long as f is consideranftn ;mgg(; /ed negative.

  The magnification of a convex mirror e8/wtv14gssa h83i isis $+0.65\times$ 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 sprsd(g ta3 q9 l; 4ylp/m9feutq zvj:80herical mirror. It is desired to produce a virtual image that is dp0;atqgljfu:ezl83yt 9qv (s9r m 4/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 mag mz2/czq u..6gm6 fobznify your face by a factor of 1.33 when your face is plaq6oz mg.zcm b.6zu/f 2ced 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 li, :noz)m-/yhfo9.k7nkinn) .nfir keght 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 iii0ckk2)d :mg(l tf c b4:akl0n ice 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( m*ei toq1muex **kdjs- 7bd1. What is 1 (imu eddo1jx*- bq*k7* msetthe index of refraction of this substance? n =   

  A flashlight beam strikesp8tii0g e4afs rw+n7 0f6(jj m 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 from beneath0k9ar k/k p-g1 ohne4d 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 at an angle of ;mx d6x0fm97v xfv,gsun9ba bq(c**u 66.*7x ucbfafsvn 9g0qxvm(u;b 9d 6m,*x0$^{\circ}\,$ 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 t(w doyp b1;1ehf( d*x31.0$^{\circ}\,$ 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 indexz*7n) 9r6ro9neg3j)lp syv ni of refraction is 1.52. A beam of light from outside the aquarium strikes the glass at a 43.5° angle to th) l7rno96zgni 3ryj )p*sv n9ee 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 p6kn. 8m (d*m,tc i3ndm fkq3yrool at night, a watchman shines a narrow beam of light from his flashlid6 mmknk* (yc3n,qrt8d i.f 3mght, 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 equilatert9ann -ye )+ufmm8fj3b+qzw* al 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 stri+pt4y(w5 t njgkes a slab of glass (n = 1.52) and is partially reflected and partially refracted. Find the angle of jwtn4+ y (p5gtincidence if the angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam incident on a uniformm5aqm5+ lp 5ra layer of transparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the incident beamr5+amal5p 5qm, 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 refraction nov xptu-qql-fsp/imp 9 56t (0 as in (Fig. Below). Show that if thv0-f9o6-it/pxt um5qpqlp( s e 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 betwe19pbl 52yqwoz+d+ bwgen water and Lucite? To be totally internally reflected, t z od 1by+92+qw5lgwbphe light must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–air surface w+zxi)a livrn m1ocq (/y),lf(6)cqhis 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in 0 r7uh7z+rfmpfyt:9d :v oi;.ox3 m pva pool of water from a depth of 62.0 cm. Where must it strike the air–water interface, relative to the spot directly above it, in order that the l+dp:mmpt0 r 7ho3fxio9r u;:fvzv 7 y.ight does not exit the water?    cm

  A beam of light is emitted 8.0 cm beneath the surface of a li l7 xtic3trb49iqutl+jyosb./t7 ,b- quid 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 th,ct7o-lu t+bsl xtyqrj.b b73/it4i 9e liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face of the pri-g 823wndsjwysm 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 (Fig8-;wl9 -8polct gi6ih4caze z. Below). Show that we can guarantee total internal reflectionle9 8zphiztcoi-c4wlg 8 a6 -; 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 :49 oj1gyx1yg 245nkkrgyzfu of refraction for a glass or plastic prism to be used in binoculars (Fig. Below) so that total in5 1kgyj2: u9f1y44gygoz r xknternal 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 .no *y/ivlw7l nc3;lt c2ep7k3zniw: 65.0-mm-focal-length converging lens. Find the olncn eki737pwt2vc*oll .;/yiwn 3z :bject distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.5 cm behind aeydm887 *p e(i.fmd/lgt. llh 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 away as an imagekuk t7z.wim 1( 48.3 cm on the other side of the lens. What type of lens is it and what is its focal length? Is the image tz.17 wkk(mi ureal 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 l weel:77ndou68f61ybi gb;or ens? 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 lengthz v;ja)9 /chg4f/cpif2a7 x ns 24 cm to view a stampgcxi ;n7p92cffaa/4s) h vj/z 18 cm in front of the lens.
(a) Where is the image located?    cm behind the lens (virtual)
(b) What is the magnification? m =   

  A -5.5-D lens is held 14.0 cm from an object 4.0 m/glb 9+mt4 2tswwd -btm high. What are the position, type, and het/4-b ms 9g+d2twlwbtight 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 filmaixw ne0.)jtn i32op j(god hgy *f:4; of a camera. The maximum distance allng(ajht ixwfp)2:i o o g*en 0.;34jdyowed between the lens and the film plane is 120 mm.
(a) How far ahead of the film should the lens be if the object to be photographed is 10.0 m away?    mm
(b) 3.0 m away?    mm
(c) 1.0 m away?    mm
(d) What is the closest object this lens could photograph sharply?    mm

  It is desired to magnify reading material by a factor of 2(zrsh, gv:tyhgm5xz1q 7 k70f 1j:n0q srz)su.5× when a book is placed 8.0 cm bg:sq0r f7g sy)x07uhjqh1 sz:mkv (,5r1z zntehind a lens.
(a) Draw a ray diagram and describe the type of image this would be.  ----待选择----realvirtual 
(b) What type of lens is needed?  ----待选择----converging lensdiverging lens 
(c) What is the power of the lens in diopters? P =    D

  An object is located 1.5 m from an 8.0-D lens. By how much does the image move ifmn6(s 1qg7ruf617mrg( s fnqu the 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 focalbhy:hy./19.8ibi dqmgr c zh+ length of 25 cm should an object be placed to produce a real image which is thezb..+yi h mc b/yqi9hd:8g h1r same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an object be placed if itswgudl lpn9a26-/v (r.kd9 clg image is to be magnified 2.00× and be real?u 9gg k-d walp/nrcl(v6l 92d.    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm

  (a) How far from a 50.0-mm-focal-l;xqu p3/ 5algilnct72 ength lens must an object be placed if its image is to be magnified 2.00× lc /7xua;t2q n 3glip5and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm (formed by some other piece of optics).]

  (a) A 2.00-cm-high insect is 1.20 m from a 135-mm-focal-length lens. Where *g0pr2o.tnmm :+k zzyis the image, how high is it, aorz .y 2k+:mtzgn*p0m nd 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-focght0dc-k/ 2p obn m2*ilt0z 4oal-length converging lens if the image is 2.5× larger than the object and is2hl2io0g-od/ 4mtkp*ct0zb n real?    m

  A bright object and a viewing screen are separated by a distance of7t-.+ox 2s vx3iypr7dec qm d6 66.0 cm. At what location(s) between the object and the dtpr3o +yx m6s-72 .iq7 dxcevscreen 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. 2- okfj5q7 uzk)0yfzvAn object is placed 36.0 cm in front of one lens. Where will the final ik5v)7kou zzqj0y 2f f-mage 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 withrvd oyyla4 , l8s+20tq $f=-31.5\mathrm{~cm}$ 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 l.3 7q6m3swhzx kpc8w d(xpvi8 ens is 21.0 cm behind a diverging lens. Parallel light strikes the diverging lens. After passing through the converging lens, the ligh3xwimxv k88z6.ppd h c7w 3s(qt 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 placed onlvkwefv.ws1m4)dveif8; y xy ,/5f*e hy 20.0 cm apart. The object is still 60.0 cm in front of the wvd)8v51 ff4.m iv/ e *feyehs,;xwk yfirst 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 a0n-w r,aj9+ ouf,d jgfpart. 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 invertedudjnar jfgw9,o +-f ,0 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 placed 12 cm tuxa .zu(;kn*z o the right of a converging lens with a focaz*an uz. uxk(;l length of 18 cm. An object is placed 33 cm to the left of the converging lens.
(a) Where will the final image be located?    cm to the left of the converging lens
(b) Where will the image be if the diverging lens is 38 cm from the converging lens?    cm to the right of the diverging lens

  Two lenses, one converging with focal length 20.0 cm and one diverging with fg hoyg *e// w3wwoz fnx/(j37yocal length are placed 25.0 cm apart. hyxjw*7zo/ /fy(/ wwoeg3ng3An 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 txcc;( ze lk 0d;- :wn8lzsmdj7o 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 )lfvad:( :vd:su4rafy //fjyhas surface radii of 34.2 cm and 23.8 cm. What is the focal length if n /:(u v/r:a sf:dvd) y4jyalff= 1.52?    cm

  Both surfaces of a double convex lens have raq ec7 v4 w1hh+yv8hu )zo6idd)dii of 31.0 cm. If the focal length is 28.9 cm, what is the index of refrdi oedh hyz1c wuv47hq+v68) )action of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm. What is the j2mi gcura60rr(,izpyg* +,o radius o,op ga 2cmjy,*(zugi0r ri6r+ f the concave surface?    cm

  A Lucite planoconcave lens (seegka9qn; g+i16i 6lp0r:js g xe Fig. Below) has one flat surface and the other has R = -18l0gxj;6ei9g6p ig qs+r k n:1a.4 cm. What is the focal length?    cm

  A symmetric double convex lens with a focal length of 25.04+l5ust)cl9dr d)vws cm is to be made from glass with an index of refraction of 1.52. What should be the radius of curvature for each surface? l+94wstl5)du) c vs dr   cm

  A prescription for a corrective lens calls for +1.5ru.g97saga4 h -dq dz2e(t(f g0D. The lensmaker grinds the lens from-9 gdgf r(ud qaat7(hg.se 42z a “blank” with n=1.56 and a preformed convex front surface of radius of curvature of 40.0 cm. What should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apartx:srv25 1fkp0 qsp+y o as in (Fig. Below). You stand 1.5 m away from one of these mirrors and look into it. Yp+ 0yxok 2v:q 5sfpr1sou 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 swukbe6f ),s ku. z2u8kpimming pool filled with water. We measure the width (x=5.50m) and then note that the bottom edge of the p2 ,kf eub.z) uuskkp86ool is just visible at an angle of 14.0$^{\circ}\,$ above the horizontal as shown in (Fig. Below). Calculate the depth of the pool.    m

  The critical angle of a certain piece of plastic in d. u*3 thp:npbair 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. Spv5guc oxwiz;,v0 f f/6ecify what tcwvf,x05; fozi v/6ug his 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 900lq) 1qii irw:71uuoy $^{\circ}\,$ 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 neq8qyu2 *jf1u cver form a real image of a real object. Can you describe a situation in which a diverging lens can form a real ima ucqquyf*j812 ge?

  Each student in a physics lab is assigned to find the locatv:k0luk v(b 17a vvtd(ion where a bright object may be placed in order that a concave mirror with radius of curvature r = 40 c1tu lvvk ad7:vkv(b (0m 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 prism is p3jc-q 9t81 inju-s6gi/v pog $\phi=72^\circ$ 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 cy u79gn+3 ese kuchm0 (4ujnk3clindrical glass rod $(n=1.54)$ are perpendicular to the sides. Show that a light ray entering an end face at any angle will be totally internally reflected inside the rod when the ray strikes the sides. Assume the rod is in air. What if it were in water?

A lighted candle is placed 33 cm in front of a converging lens of focax b4*zebkw h:4;bufj3l 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 fob 0 loc1/nschnh9hf+1cal length f, and a white screen for viewing the image is on the opposite side. Theh n+sc0o9fl1h/hn1cb 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 imfie64bm t5ur2.5dv bqage is projected on a screen (Fig. Below). If a 105-mm-focal-length lens is to project an imagebqdutm b254fev.r i 56 on a screen 8.00 m away, how far from the lens should the slide be? If the slide is 36 mm wide, how wide will the picture be on 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 sct-ui - 8.fbdmnreen 1.80 m by 2.70 m placed 7.50 m from the projector. ndfbm8- u.i t-What focal-length lens should be used if the image is to cover the screen?    cm

Show analytically that the imagaq4p8h t9y a5ge formed by a converging lens is real and inverted if the object is b g 48phytq5a9aeyond 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 pict -rlm 4*p zx0uamg47u()ma 1bcfygs o*ures of her at home. She claims the reporter was trespassing.0z*p o ya7g (lsx)r4u gfmmb1-au 4cm* 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 reporter standing?    m

  How large is the image v6. mwqakwq /.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 ifql3;ishmr *x0 sq74is 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 ir 74iqsfl qx*h m30s;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 fk)sb brvbh.9*y(q+y tv, yz0 srom a certain converging lens, it forms a real image. When the object is moved to 40.0 cm fromybr0v.s,y (v9b)y*qzt hs b+k the lens, the image moves 10.0 cm farther from the lens. Find the focal length of this lens.    cm