What would be the appearance of the Moon4n*3bimsgf wc9a 6ev, if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Romanfn8gj0rg ) g)ly j5ys(1nzr1e fleet in the harbor of Syracuse by focusing the rays of the Sun with a huge spherig( 1ngyrj0rsl)je) y85zgnf1cal mirror. Is this reasonable?

Although a plane mirror appears to reverse le. e5hf8a6o42afdv t3ozfax 6 vft and right, it doesn’t reverse up and dow5 xvzetf f.2fvdh6 o4aa6a8o 3n. Explain.

If a concave mirror produces a real image, is the image necessarj.af2b- x lyv.ily inverted? Explainy.f -bxl2.a vj.

An object is placed along the principal axis y4.-z0*xem d/mqh+ dw xd h)vbof a spherical mirror. The magnification of the object is -3.0 Is the image real or virtualm qh0xddm)xz. h4+vb-*y/ ewd, 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 discussed with re vuygafqh8f8( 6zgy ii (oe.n*do2.g*ference to (Fig. Below a), draw ray 2 foro(h f6*gi8 . n2gfyediavog8u .*z(qy (Fig. Below b).
(a)
(b)

What is the focal le*8wtntagm 4 / ewql*)z3i7 nzdngth of a plane mirror? What is the magnification of a plane mi t*z)4 i*anmzdl/ 3w 8twne7qgrror?

When you look at the Moon’s reflection from x oj8 6t4f6ygra ripply sea, it appears elongated . Extrg 68ofj4yx 6plain.

What is the angle of refraction when a light ray meets the boundary between twohil qg zjx4g0:iq3z)jhlmk*e,1 1x :y materials per1iz0g*, 3hyl exmi:gqlqk)x jz:jh14 pendicularly?

How might you determine the speed of light in a solid, 6vp4/w91 qesqhh u0v1gxaao:rectangular, transparent obja01vhwa:61p qe g/u sho49x qvect?

When you look down intok8 0fecp4k: ve a swimming pool or a lake, are you likely to underestimate or overestimate its depth? Explain. How does the apparent depth vary with the viewing angle? (Use rkc ke4p ve80:fay diagrams.)

Draw a ray diagram to show why a stick looks bentiv2bbbb+8qy s8(3 m vi when part of it is under water (Fig. Below). i3bqm(8i82vybb b+ vs

Your eye looks into nit x2ppw3dg) ay :u;-an 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, indp;xig2 :u3-)a dwpnty icate the approximate position of the actual fish. Briefly justify your answer.

How can you “see” a round drop of water on a table p(/hejtmi5:q even though the water is transparent an:tj i5/phme(q d colorless?

When you look up at an object in air from beneath the su h6lso *y)x /gzo/pjq e5ug3 9,vzqa*irface in a swimming pool, does the object appear to be the same size as whe3 ghi g*uq5e/s a jpxoo l/6,q9yz*z)vn you see it directly in air? Explain.

How can a spherical mirror hav+0 l6eo i(dv0vnzfh)se a negative object distance?

Light rays from stars (including our Sun) always bend towaras2 k-tzgp+tiy s39*g d the vertical direction as9s32t * gys -kpi+tgaz they pass through the Earth’s atmosphere.
(a) Why does this make sense?
(b) What can you conclude about the apparent positions of stars as viewed from Earth?

Where must the film be placed if a camera l95snr6 +cz)2fpi1 i8 jo 5buu jh,lovyens is to make a sharp image of an objoyr+lp u5fii h6n2 jvs1 o,)z85ju9b cect very far away?

What type of mirror is shown in (Figch:1sr dfd*qfks.nj .uh89 8z. Below)? Explain.

A photographer moves closer to his subject and then refocusq4abw7 *ivzs:bu ,zrsmv;b.8kuz , a4es. Does the camera lens move farther from or closer to the film? E:a8km,bbs4a;v z7,w4 bqz.r*sv uz uixplain.

Can a diverging lens fol6cl wbykg82q:.2 redrm a real image under any circumstances? Explain.

Use ray diagrams to show that a real image formed by a thin lens is always iqmrpa)upxw 2-ly +5 viboa 3(4nverted, whereas a virtual image is always upright ixmyla i(o45p3p+aw 2-)buvrq f the object is real.

Light rays are said to be “reversible.” Is thu/ot*ccvp ax 3ob*iz: q/c( )gis consistent with the thin lens equat co :a3/)p( *c*ox ubzvctgq/iion? Explain.

Can real images be projected on a screen? Can virtua06zkli wodi;e*km 3is lh.l20l images? Can either be photograwisek2.6lm i* li0zhl do;0k3phed? Discuss carefully.

A thin converging lens is moved closer to a neaedcyk,e7g,3 utj zr(7ia7c;b rby object. Does the real image formed ch,eyz7j;,b tuk7 7caer(di3c gange
(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 9.gqavym dvv/l0)c gci(r,e8(e+ zka1c: twois a converging lens. Will it still be avtc9e8v wmo1 y g,e((ci: d.k l0qcvz)a/+arg converging lens if placed in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands facing a converging lens. If the gu7my2g2j c96d-- iyumx d.fc nose and the tail are each focused -.y9m27 fuc gg imjd-duc 26xyon 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. Uno3f;x*y)u :xo oes*meder what circumstances (if any) would the image of the nose be virtual and uysex :f)*ooxoe3m ;*the image of the tail be real? Where would the image of the rest of the cat be?

Why, in Example 13, must the convergijh7w n)2wtza- ng lens have a shorter focal length than the diverging lens if thw2t az7j n-)whe latter’s focal length is to be determined by combining them?

Explain how you could ht:h u*,8rxf,4gnh cir)ho6 a8cu r,qi ave a virtual object.

  An unsymmetrical lens (say, planoconvex) forms an image of a nearb2dh, l ntj)miv-8vk ;by object. Does the image point change if the lens b)nvmjdv- l,i; 8h2tkis turned around? ----待选择----yesno 

The thicker a double convex lens is in the co7bxzsyj qtx u(k 0tf-+8d-*nenter as compared to its edges, the shorter its focal length for a +8ox-tb 0f skq yxjzdu*-nt(7 given lens diameter. Explain.

Consider two converging lenses separated by some distrkabskk( ch- c6 9bc6:ance. An object is placed so that the image from the first lens lies exactly at the focal po :hcbk kr6skcb-69ca (int of the second lens. Will this combination produce an image? If so, where? If not, why not?

  Suppose that you want t lm z:mux7y2 ysy:+z/vo take a photograph of yourself as you look at your image in a flat mirror 2.5 m away. For what distance should the camera l ymyus2: +xv7z l/zmy:ens be focused?    m

When you look at yourselfqmoke t,d+xq31 hc;7a in a 60-cm-tall plane mirror, you see the same amount of your body whether you are close to the mirror or far awa,+3mxqq;tkcedh17a oy. (Try it and see.) Use ray diagrams to show why this should be true.

  Two mirrors meet at a 1t:s3/b,r7 8 b fsmmrxr35$^{\circ}\,$ 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 3y5f li.+xq)gbxbv-b) vo8x xfloor stands 2.20 m in front of a vertical plane mirror whose bottom edge is 43 cm above the floor, (Fig. Below). What is the horizontal distance x to the base of the wall supporting the mirror of the nearest point on the floor thatxy83)x5ixl q+ vxb)fbbov-g . can be seen reflected in the mirror?    cm

  Suppose you are 90 cm from a plane mirror. What area of the mirror is3reyx )ff0 bpt,/kb*6y/d 9w3f bljol used to reflect the rays entering one eye from a point on the tip of your nose if your pullf 6f9br 3do,/ky 30xbbjp wf*e/)typil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors meet at an angled5m:wnm )og admssxt 31*vk8 ; (jvsm+ $\phi$. 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 l 1lzu0f(vw(6a*k+qhh, ouh/ c o7tr gpointed 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 the mirror was madeq(7 gwh1,o*k0hu t6rf u/hlao+zcl(v?    cm

  How far from a concave mima9j 4 om1cfpjr a+ ;cv5ftnn*i7dj-3rror (radius 23.0 cm) must an object be placed if its image is to be at infpaj-t +ro34v1mm njc;95j*7f cif adninity?    cm

  If you look at yourself in a shiny Christmas tree ball with a dizuseh+pqqo2x5w7 ; *g; kje6gap /0 fiameter 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 upright orwjz;he s*;gpq/6+f x2k7 0eig oq p5ua inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shows an tt/rr jnncd3 -: k7px5upright image of any person who stands 1.4 m in front of it. If the image is three times the person’s height, what is thcrr 3n5dk/ t -n:tx7jpe radius of curvature?    cm

  A dentist wants a small r ,:* gh(cx /id:rnwz/5nsbub mirror that, when 2.20 cm from a tooth, will produce a $\text{4.5×upright}$ image. What kind of mirror must be used and what must its radius of curvature be?
 ----待选择----convexconcave 
r =    m

  Some rearview mirrors produce images of cars behindkc vpm 2)xo:2w,z8wl s 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 ofc8pk)xo zslw :mw,22v 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 cm from a lv.y nlmk:b 2r+jm o)7 +0tmwvconvex mirror of radius of curvaturbv)m+w.2kv my 7nrl+:ot0jm le 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 store. You estimaj0b, nkr5/5w bie+a9mat yh (5x w)hkite the height of your image to be half of your actu(ibw n,r akh et ij+5 xyh5w)05/abkm9al height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object be placed in front of a concave mirror so that itom3r78zstf acp0 j7q1 produces an image at the same location as the obf7qz01t3ca mp7o8 jsrject?
(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 distav;47h*bdox f0:6 w izn:gwsndnt tree is 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 isx n4 d:7;v*wf w6hszi:odng0b it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different tew-m+fz *q*p 0oy bhak;chniques,
(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 d 8pgbyjn:yj5 l0em.oxel, 77magnification 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 m6h)cjhhr g)vajh 2c7 3irror equation, Eq. 23–2, is valid for a convex mirror as long h)h72gchc6jvr3 h) aj as f is considered negative.

  The magnification of a convex mirror i)apv 6e nw:8pwx.s yg,s $+0.65\times$ 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 placec;o yuxsetm0 r9a)hfh *+kh,,d 28 cm in front of a spherical mirror. It is desired to produce a virtual image that is upri ,h*;k 9frht)m a o+xe0cyush,ght 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 magnifcnj wj/4zyg .7gk/wg8oa x,,yy your face by a factor of 1.33 when your facygkg4cj ,j a w8ozg/wn/y7. ,xe is placed 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 li6 6baiqjnwi77ght 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 f pmkbi e0q0.w+fx(;p 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 su5/mz pmvb d05xw(qd /ibstance is 89% of its value in water. What is the index of refraction of this substance?pv5/z bqdw/ id(mm0 5x n =   

  A flashlight beam strp ) spm hwlqx)5.cm9w5ikes 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 beneath the wp xj*( hxj1:l4go, wly)zb3rpater 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 thh /uu24 yulub2g8p p*c5f gqd-e water at an angle of 6*8u h /uqgc4yfp ul gp-b2d52u6.0$^{\circ}\,$ to the vertical. At what angle of incidence does it hit the air–water interface from below the surface? $\theta_1$ =    $^{\circ}\,$

  Rays of the Sun are seen to make a 31.0r;j lvuv.:8rk$^{\circ}\,$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?    $^{\circ}\,$

  An aquarium filled with wate:qic n) a,g1rpr has flat glass sides whose index of refraction is 1.52. A beam of light from outside the aquarium st:apq1, )ic grnrikes 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 watiwhs -sw0 mr6p qfe-( ot/f.2tchman 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 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 de( 0.os -srw-6/fpefmw qtht2iep?    m

  Light is incident on an equilaterl. +kxicmh99 fal 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) andmim mzy9p:j 10caa,g- is partially reflected and partially refracted. Find the angle of incidence if the angle of 1j ,acamm9 mpy:g-0 izreflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam incident on a uniform layer oy+fi 59 (2eb53-c cill ghf j5qs7f0pooeh,wqf transparent material, as in (Fig. Below), the direction of the emerging be(2ic3,fhj7b0 se+woflcglqe55qfh5 iy op9 - am 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 refraction n ak rs+kynwaiejq:zl+/rt,)k * *-t -yfs in (Fig. Below)y ,aj s+zne)i* kf- /k klrt+:-*yrqtw. Show that if the incident angle $\theta$ is small, the emerging ray is displaced a distance $d=t\theta(n-1)/n$ from the incident ray, where t is the thickness of the glass and $\theta$ is in radians. [Hint: for small $\theta,\sin\theta\approx\tan\theta\approx\theta$ in radians.]

  What is the critical angle for the interface between water and Lu4tbixiu:/1iony 9us6cite? To be totally internal/ n:su9iuxo yt61bi4 ily reflected, the light must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liq24b7z trz mgc+uid–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 drkz pb ,u8/+sma;u uy7epth of 62.0 cm. Where must it strike the air–water int8bkyu7 ,+usmruap / z;erface, relative to the spot directly above it, in order that the light does not exit the water?    cm

  A beam of light is emitted 8.0 cm ben o.h.w,ztm/cvzk e8/:m9u0+cwgu mvieath the surface of a liquid and strikes the surface 7.0 cm from the point directly above the source. If total internal reflection occurs, what can8zw.+, c/u0gwe zmv9:c t/kouv i.mhm you say about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes v)o cx63pv-ldthe left face of the prism in (Fig. Below) at 45.0$^{\circ}\,$ as shown, but is totally internally reflected at the opposite side. If the prism apex angle (at the top) is $\phi=75.0^\circ,$ what can you say about the index of refraction of the prism? $n \geq$    (retain three decimal places)

A beam of light enters the end of /kqok0tl, xd2an optic fiber as shown in (Fig. Below). Show that we can guarantee total internal reflection at the side surface of the material (at point a), if the index of refraction is greater than about 1.42. In other words, regardless of the angle the light beam /tqx ,kl2dok 0reflects back into the material at point a.

  (a) What is the minimum index of refraction5-xdbv1f zk,l57 tyhk for a glass or plastic prism to be used in 7zvk1yh f5dlk -5b,txbinoculars (Fig. Below) so that total internal reflection occurs at 45$^{\circ}\,$? $n_1$ $\geq$   
(b) Will binoculars work if its prisms (assume n=1.50) are immersed in water?  ----待选择----totally reflectingtotally transmitting 
(c) What minimum n is needed if the prisms are immersed in water? $n_1$ $\geq$   

  A sharp image is located 78.0 mm behind a dc lr-),pv5 3l d5m tohmb;+yd65.0-mm-focal-length converging lens. Fi dpc 5,5l+o-lmbt)dmr 3hdyv;nd the object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a z+rd0 ytz4 cx1point 18.5 cm behind a lens.
(a) What kind of lens is it?  ----待选择----converging lensdiverging lens 
(b) What is its power in diopters? P =    D

  A certain lens focuses light from an object 2.75 m away as an image 48w:nd+k1qp ux--50utxygr )iy .3 cm on the other t:di )kw+xug5q1n-p-y0yxu r side 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-ztsk0 5ar 8ch6 3g-spsfocal-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 col e3 u,ztc2d:/wd78 v1io l)obim s)ypnverging lens with focal length 24 cm to view a stamp 18mdu2dyl)w)zio8 c t,vpi s7 l :e3o/b1 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 heldl 3/v fki uo.zy/2 mxzd*6zh.g 14.0 cm from an object 4.0 mm high. What are the position, type, and height of thz6d*kg 2xvzo3hul.m /f /z.yie 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 film of a camera. Tp wt82fu6 6gv qgpi/u8he mgv8tiu8 6q6u /ppwg2faximum distance allowed between the lens and the film plane is 120 mm.
(a) How far ahead of the film should the lens be if the object to be photographed is 10.0 m away?    mm
(b) 3.0 m away?    mm
(c) 1.0 m away?    mm
(d) What is the closest object this lens could photograph sharply?    mm

  It is desired to magnify reading material by a factor of 2.5×f hugz b4)-h8/hj:qb v when a book is placed 8.0 cm jv f h8 gh)u/h:zbb-q4behind 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 theu)em*d 9om vhy:dcdw 5t(4w 2z image move if the object tw4 :(u5 dzy2 mwevhod)m*cd9is 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 conve)au)ewyi m6crx8f;znd g5u 26o 3cb ,qrging lens with a focal length of 25 cm should an object be placed to produce a real image which iz;c o)fb6,u)n w xd2 qmua5rgi86e y3cs the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an object be placed:k* amkz q+6. zhfo:tq if its image is to be magnified 2.00× and be hqq6akm :tzo.+ *:zfkreal?    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 a-z8u2z/wa6tnp0n m u lens must an object be placed if its image is to be magnified 2.00 /zn8wa6pt-am z 0unu2× 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 ju*s9yiwvnln9-b)+ l is 1.20 m from a 135-mm-focal-length lens. Where is the i *l-vbuyj l n9)w9+snimage, 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-focalukx2 )ozjsb//nh4o 3x-length converging lens if the image is 2.5× larger than the object and is x4o3/nu/2kzjbos hx) real?    m

  A bright object and a viewing screen are separated by a distanc 9p*q cx1w n,x8y6dms5 mzww9ie of 66.0 cm. At what location(s) between the object and the screen should a lens of focal length 12.5 cm be placed in order to produce a crisp image on the screen? [89xwsqinmxp9 * 5cy1d,wz6 mwHint: 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 o1 8if1w1oc q yxum3q4xbject is placed 36.0 cm wc4 8ixxmo3y1 1q1fq uin 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 withtiyl+o;j6)uv7nd7j j $f=-31.5\mathrm{~cm}$ 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. fn l1xuc6:t4 pParallel light strikes tul nt:6xf c4p1he diverging lens. After passing through the converging lens, the light is again parallel. What is the focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Example 23–12 are now placed only 20.0 cm ap0gdi a.0vstc ,a d;fm)art. The object is still 60.0 cm in front of the fi fsmda cgv .di0)0,;atrst 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 +0qx) xu s(ehaplaced 30.0 cm apart. The focal length of the lens on the right is 20.0 cm, and the focal length of the lens on the left is 15.0 cm. An object is placed to the left of the 15.0-cm-focal-length lens. A final image from both lenses is inverted and located halfway between the two lenses. How far to the left of the 15.0-cm-focal-length lens is the orighu s(qxax+0e )inal object?    cm

  A diverging lens withy9 reozp/z9ng*qvfd//o1. gw 0 9sx to a focal length of is placed 12 cm to the right of a converging lens with a focal length of 18 cm. An objq sz*g.z9or d19xpw toyeg // n/vf9o0ect 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 focd b0+l;21. .nsgc 1 rnpg4*juwc tsnwjal length are placed 25.0 cm apart. An object is placed 60.0 cm in front of +.gls jn.s11npd2*w;nj 4ucb0 wgcrt 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 conq 8j.i56dpkpoo3hev)m hi2 w -verging lens of focal length $f_C$ as in (Fig. Below). If $f_T$ represents the focal length of the combination, show that the focal length of the diverging lens, $f_D$, is given by
$\frac{1}{f_\mathrm{D}}=\frac{1}{f_\mathrm{T}}-\frac{1}{f_\mathrm{C}}.$

  A double concave lens has surface radn/ y5dd123x1au;ue 8npgxeazii of 34.2 cm and 23.8 cm. What is the focal lengtp5a38 d xy de1 z2a/eguxu1;nnh if n = 1.52?    cm

  Both surfaces of a double convex lens have ra (k-amk :5cb0nj- cekvdii of 31.0 cm. If the focal length is 28.9 cm, what is the i vnmkk- cjce 5akb0(:-ndex of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm. What is the q1-fyd(u/qdkctf dv fta/6m q-4x2n; radius ofqtu2q/(1m-dt ;vkf /- x 6dfqynd4caf the concave surface?    cm

  A Lucite planoconcave lens (see Fig. Below) has one flatcz9a3.ty /wmc surface and the other has R = -18.4 cm. What is the focal le wc mt/cya39z.ngth?    cm

  A symmetric double convex lens with a focal length of 25.0 c u:ukc 1o;h+fa4iso g4m is to be made from glass with an index of refraction of 1.52. What:s4oau+ik4 ;ogh cfu 1 should be the radius of curvature for each surface?    cm

  A prescription for a corrective lens calls for +1.50D. The lensmaker gri x ka29itk84einds the lens from a “blank” with n=1.56 and a preformed convex front surface of radius of cur4i2ak9kxte8i vature of 40.0 cm. What should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face eyary3x n3ei)5 libr;4ach other 2.0 m apart as in (Fig. Below). You stand 1.5 m away from one of these mirrors and look into it. Youn;)43a 3r byxriil 5ye 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 pool filled with water. We measure k.8sk g/*esa bthe width (x=5.50m) and then note that the bottom edge of the pool is just visible at an angle of 1 *bkag8ekss /.4.0$^{\circ}\,$ 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 asnox b 5a:ux1emd1* 8m 69wv wz0ye4drir 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 emag:)xp;n dxt q)8uy: wv5 t2case of a spherical mirror. Specifyx 2 5wta:nt)pdqug m)8yx:;ev 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 j-d7/wz drk z+to.ci9 un*e0w 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 lenk+hsxtdjdh , ap029, qs can never form a real image of a real object. Can you describe a situation in which a diverging lens can fo,0jkd th9d2ph ,s aqx+rm a real image?

  Each student in a physics lab is assigned to find the 2mqqy*+smc 2a t /m(um g7cl.t 8yr bsyno0*.ylocation where a bright object may be placed in order that a concave mi tc*nmy mysby m/atuy +l7r8.0osq.gq2( *m2crror 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 prism isi 8o4v;5eznz;v c59qgo pue3r $\phi=72^\circ$ 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 0 wp(rp(mi9 jhglass 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 place roxwf2glo c9tvo.g7b 4.37zrv 8,r/md9rhiud 33 cm in front of a converging lens of focal length $f_1=15\mathrm{~cm},$ which in turn is 55 cm in front of another converging lens of focal length $f_1=15\mathrm{~cm},$ (see Fig. Below).
(a) Draw a ray diagram and estimate the location and the relative size of the final image.
(b) Calculate the position and relative size of the final image.

A bright object is placed on one side of a converging lh3 )mwcbu )rxz d/zux;i(/ (;/ iqhglpens of focal length f, and a white screen for viewing the image is on the opposite side. The dista;/(x)zm/ugw/ i xchldzh( ui )p;qr3bnce $d_T=d_i+d_o$ 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, th 2x0tdqb)* wbfe 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 screen 8.00 m away, hwbq2fx) 0 *bdtow 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 8koz0m.ufa3 -dceo* fbh0.bcby 36 mm) is to be projected on a screen 1.80 m by 2.70 m placed 7.50 m f -.kz0e fhoda.ob bc uc3f*m08rom the projector. What focal-length lens should be used if the image is to cover the screen?    cm

Show analytically that the image formed c:upsq 7 j l57(hgcq5dby a converging lens is real and inverted if the object is beyond the foc:h7j57glq(cu cqsp5 dal 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 1np5wtlgl *g8g):tceher 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 8 ltglg:)cgwe* 1 npt5mm. How far away from the subject was the reporter standing?    m

  How large is the image of the Sun on film userpfbr3sndcnj e9yb 7ka1+ 9/1d 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 oa 61r+ s*m2p:zjrkhv is imaged 8.20 cm in front of that lens (on th6p1* sarvorh:+2m zjke same side as the object). What type of lens is this, 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)

  When an object is placed 60.0 cm from a certain converging lens, it forms +dsd*yjy:jau* 9klcg,, f mem 4 (vhrt2+rfy;a real image. When the object is moved to 40.0 cm from the lens, the image moves 10.0 cm farther from the lens. Find th,,;e uj (kfc+ y drgrvd9y+fj: athlm4**y m2se focal length of this lens.    cm