What would be the appe8b pz,5r)2hd 7rx fzatarance of the Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Romavmi58fi*orfr tmt 7,.y- z5vsx: (hsbn fleet in the harbor of Syracuse by focusing the rays of the Sun t5-fi, .rfst xvm : *ih7(by8 sr5zomvwith a huge spherical mirror. Is this reasonable?

Although a plane mirror appears to reverse left and right, icqbgje:: (;u1yn ok je jh;t.0t doesn’t reverse up a:on1etu:j(yg qj0 h ; ;kcjbe.nd down. Explain.

If a concave mirror produces a real image, is the image necessarily inverte)ri(sl.+q nabd? Explai( l.sbrq ia+n)n.

An object is placed along the principal axis of a sd7ydesaekoe+l: 6 e( xyo(* y2pherical mirror. The magnification of the object is -3.0 Is the image real or vir7e +ds y2oxeey(e*d 6(l:koya tual, 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 an -67/jq+moub+t ba2pp bp7yreference to (Fig. Below a), draw ray 2 for (Fig. Below b7p+ y/bo tpn ba6pu ab-+7q2mj).
(a)
(b)

What is the focal length of a plane mirror?e25 ybpxd(s3oa 2ugehd2 r95q What is the magnification of a plane mirr3bhedg2s2(rd5xp ya 92e5uq oor?

When you look at the Moon’s 8 n.sg91l x, orw5jijkd/l9( b-zrcnnreflection from a ripply sea, it appears elongated . Exp,dox /rin9 n jrcngkl s wb.z5-(jl198lain.

What is the angle of ref,rj)pn,fdn8k5sn0l nraction when a light ray meets the boundary between two materials perpendir,k)d, 0jnnn 5 8nflspcularly?

How might you determine th1z h v)pp ;n,48jkfcgle speed of light in a solid, rectangular, transparent ofgpc;vph1 ) 48z,jnklbject?

When you look down into a swimming pool or a lake, adl3*rr/j kaa 8re you likely to underestimate or overestimate its depth? Explain. How does the apparent depth vary with the viewing angle3d j/ 8aalrr*k? (Use ray diagrams.)

Draw a ray diagram to show why s7v-c7) 71yx acbv qv2q9qqria stick looks bent when part of it is under water (Fiy7 b9c7c vq)rv7-1siq qq2 xavg. Below).

Your eye looks into an aquarium and views a fish insgr9evm4qrm- wmpw39 .ide. 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, indic 9r-vrmw mw.93meqg4pate the approximate 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 .6t saqfrb6b /transparent and colorler6bq6a.s fbt/ss?

When you look up at an object in ai3 ik538p,nu.terdln jr from beneath the surface in a swimming pool, doej i3en5u,kr dlpt.83 ns the object appear to be the same size as when you see it directly in air? Explain.

How can a spherical mirror have a negative object distance?p ;+39fw6 1pcwuwphf2)kj; ut4q*vk iaxb2 lo

Light rays from stars (including our Sun) always bend toward the vertical directa-5j sxzs7sh5t rd0k4o )n au2ion as they pass through the Earth’s atmosp z02a )dsushosknt557r-ax4jhere.
(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 len e lmyag+/5ym7ab52kdh.h y0rs is to make a sharp image of an obje dmr/hm.a ae+yyk2y5 0bg7lh 5ct very far away?

What type of mirror is shown in (Fi/zn*zr9v 4s,k rnvzg(g. Below)? Explain.

A photographer moves closer to his subject andv9u, zgy7 -wnx then refocuses. Does the camera lens movuw gxv,zy7 n9-e farther from or closer to the film? Explain.

Can a diverging lens form a real image under any circumstancn,zde.,q xvp--b h5vie )8uvlv5j (vn es? Explain.

Use ray diagrams to show that a real image formed by a thin 7ogf ,j44l2t4 2 s9uejfd:iqrhyv z k*lens is always inverted, whereas a virtual image is always upright if the object is :oyu4eg7,kt i4v2 2dhsq 9 ffzjl*rj4 real.

Light rays are said to be “reversible.” Is this consistent g u, ,sqweiqm2 r9y-li8 4d1kcwith the thin lens equacls1 yi - qkm4qu298iw eg,dr,tion? Explain.

Can real images be projected on a screen? Can virtual images? Can either be pjg q 9,iq;,vv (fsjx(nhotographed? Discuss carefully. ;j, (,gnqivx fqjs9v(

A thin converging lens is moved closer to a nearby object. 5 hqttue q74(bDoes the real image formth4qqeu5(7b t ed change
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an8rceesisr*cha .a33h,d,*x m index of refraction n = 1.30 In air, it is a converging lens. Will it still b eemis*, 3 hhdc38r,* carax.se a 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 conver*u*,f.c8hzbl8 q.3pl wqe:a jbnjbc *ging lens. If the nose and the tail are each focused on a screen in turn, which will have the lue., j*pf b38 wzc 8ljhqa*:bnqc.b* greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facing a converging lens.jx:-bar )(r w76re,s;ixwxkx Under what circumstances (if any) would the image of the nose be virtual and the image of the tail be real? Where w:(rx;,xrrs kixej)wb 7wx -6aould the image of the rest of the cat be?

Why, in Example 13, mus2 ubl )zurrs;4t the converging lens have a shorter focal length than the diverging lens if the latter’s focal length is to be determil2)bu zusr;r 4ned by combining them?

Explain how you could ha 6fl8n,;ldlyb n d-ajbxqjv-3 79vhw +ve a virtual object.

  An unsymmetrical lenx8e/2wce z2f rw/mlc3s (say, planoconvex) forms an image of a nearby object. Does the image pointfrwc32m z8 2lx /wcee/ change if the lens is turned around? ----待选择----yesno 

The thicker a double conv;w.y rd3*l3e5yac igrex lens is in the center as compared to its edges, the shorter its focal length for a gy3cw.3r ;d yirae *lg5iven lens diameter. Explain.

Consider two converging lensef q2xtmd. k;mz2v 03uus separated by some distance. An object is placed so that the image from the first lens lies exactly at the focal poinzu.;mud3 mv2xfq2k0 t t of the second lens. Will this combination produce an image? If so, where? If not, why not?

  Suppose that you want to take a photcm7n4fg x9z *-;vkeai ograph of yourself as you look at your image in a flat mirror 2.5 m away. For what distance should the camera lens v -4igxckm9n7f *a; zebe focused?    m

When you look at yourself in a4w2 46oz8h. eg0jgakj hw3tzu 60-cm-tall plane mirror, you see the same amount of your body whether you are close to the mirror or far away. (Try i .k 8egj2waz4jg4 whht 6ouz03t and see.) Use ray diagrams to show why this should be true.

  Two mirrors meet at ;x nb/s9.8 bafpxv 7ora 135$^{\circ}\,$ angle, (Fig. Below). If light rays strike one mirror at 40$^{\circ}\,$ as shown, at what angle $\phi$ do they leave the second mirror?    $^{\circ}\,$

  A person whose eyes are 1.68 m above the floor stands 2.20 m in froht5*9qm* wheg b;t jk3nt of a vertical plane mirror whose bottom edge is 43 cm above the floor, (Fig. Below). What ke gjh*tw*mhtb;3 9 q5is 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 at9wvu)xi.+ x(8 mgaje;baizn+ ,db fa+2 ;t tx plane mirror. What area of the mirror is used to reflect the rays entering one eye from a point on the tip of your nose ifxzat+x;djiugba + fnt 9,x)vi2(;.tmb+a we 8 your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors meet at a,gb71ft p 4ixei:qnz2 w) tka.n 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 +rsm lwr-pgjzl+6f;2/(leeo 6 nnqkn n2y -+la concave mirror 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 frolln sw6-+opmeg k 2rnzllr j e-( 6/;+q+2nnfym which the mirror was made?    cm

  How far from a concave mirror (radius 23.0 cm) must an object be placed if1wnj m. t*1evf its image is to be at infin w1ef1 .jn*mtvity?    cm

  If you look at yourself in fu4ktp* .:b 26brdoy ca shiny Christmas tree ball with a diameter of 9.0 cm when your face is 30.0 cm away from it, where is your image? Is it r y u*tb 4b.pokf26rd:ceal or virtual? Is it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement parkngl n9qckt1uk1:*xzz c oh( 4b (bd:i; shows an upright image of any person who stands 1.4 m in front of it. Ig(;o kuqic kn:x:czz9bhtdl11*4(bnf the image is three times the person’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror that, when 2.20 cm from a tooth, will pr/f)wi b12b)7a l9ad qw6er ylqoduce 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 imagsw mmwx0+q 25les of 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’s radius of curvature if cars 20.0 m away appear 0.33× their normal size?2m 5xl0qmw+s w
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is placed*( qe+uv*5 g.dftabp 0)(x4x xl,st ffyie4 eg 20.0 cm from a convex mirror of radius of curvature 20.0 cm. af4gv(+ ,q)lgt.*pe xxy etid ff54xb0 *se(u
(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 y zo2 m5-thgj5l.)xrta convex security mirror in a store. You estimate the height of your image to be half of yol j2 . gm5x)tzr5hy-tour actual height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object be placed in front owd(obo,/; jbn ohm /9gf a concave mirror so that it produces an image at the same location aoo/9gn /dh( jb;owb,m s 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 ani:)2w;xn ny uyd very small when viewed in a curved mirror. The image appears to be 18.0 cm behind the mirror. What kind of mirror ;i2yn: nx uyw)is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniqueszu uxd ;47ros9,
(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 mirror6 97zcsh.eada 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 equal qpp6w7b 3rs/l:sazs*b9k+b tion, Eq. 23–2, is valid for a convex mirror as long as f is considered negat96 /l7awbs+qsbr*ksb plz :3pive.

  The magnification of a conv,llc:27i xshlex mirror is $+0.65\times$ for objects 2.2 m from the mirror. What is the focal length of this mirror? $\theta_2$ =    $^{\circ}\,$

  A 4.5-cm-tall object is placed 28 cm in front of a spherical mirror. It is desinu61q/mwc nkc u6gq3 w:a740 zxjr3pzred to3krujn4 7/pxu6gzq6m ww0 1c3qn: azc produce a virtual image that is upright and 3.5 cm tall.
(a) What type of mirror should be used?  ----待选择----convex mirrorconcave mirror 
(b) Where is the image located?    cm behind the surface
(c) What is the focal length of the mirror? $f$ =    cm
(d) What is the radius of curvature of the mirror? r =    cm

  A shaving/makeup mirror is designg :vtxs; zzr*um2 +0nced to magnify your face by a factor of 1.33 when your face is placed 20.0 cm in fro ur+zg * mt2xsc:;zv0nnt 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 v 77f/i.qyylap9 cn6qn
(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 icxc1 kevi 4g6 ;mmchn746l) pwne 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 i s)1zjw.p o+jxts value in water. What is the index of refraction of this substance? n =xs+ jjz) wop1.   

  A flashlight beam strikes the suruf( t))i*:a3ku hnrk fj5slo1face 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 :hy*(7+(rru st;g8: uxk9cf haefo qzfrom beneath the water at a 42.5$^{\circ}\,$ angle to the vertical. At what angle does the light leave the water? $\theta_2$ =    $^{\circ}\,$

  A light beam coming from an underwater spotlight exits the water a 5rfed-d2t;+ 7kgu sh3*wy84 ctagsiet an angle of fh+ -tw usi2yaecrd *s g354dke8tg 7;66.0$^{\circ}\,$ 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 toif8-f)he qds5+twfeuv ow y9d(z+k/2 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 gl w nd;2fk*m2wyass sides whose index of refraction is 1.52. A beam of light from outside the aquarium strikes the glass at a 43.5° angle to the p 22*; wnywkmdferpendicular (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 (jqsxc *ezt/e 2 l.b3fnight, a watchman shines a narrow beam of light from his flashlight, 1.3 m above the water level, on 3bzs*e cxe.j (/l2tfqto 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 equilateral glass prism at a 4jkoy9 .39-bfok7u xws5.0$^{\circ}\,$ 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 is pca:apq+ yv7 2qartially reflected and partially refracted. Find cp+7a :v qq2yathe angle of incidence if the angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam incident on a uniform lay 7*l* y3uupykrer of transparent material, as in (Fig. Below), **p 7lkuy3y ruthe 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 piece of glass8vz;o e xhkib6-n.m *w with index of refraction n as in (Fig. Below). Show that .zwiho enm6*;bxk 8v- 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 L l cynk6lr)2- stb4v qyx:f/y qe/..jyucite? To be totally internally reflected, the light must start in which maty-lyy2 ev sn 4.rc)jl:kqf/xq.t/b6 yerial?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle fooljosu(*gpy a;b .ek ty4a,17r a certain liquid–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+jtejl mz.6 tr7oo//k depth of 62.0 cm. Where must it strike the air–water interface, relative to the spot directly above it, in order that the light does not exit the water?o rl7oj//m6+ kjet .zt    cm

  A beam of light is emitted 8.0 cm beneath the surface of a liquid and m mbyonog:t.2 .h8:2fkbrlk 3strikes the surface 7.0 cm from the point directly above the source. If total inter:.o3ymkmn2f lt .hbbkor2:8 gnal reflection occurs, what can you say about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the pf.68op9.n 6huhh uf:c5 oanfleft 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 an optic fiber as shown in (Fig. Below)ow cl1:k q0 )hmw1b*ct/d*kug . 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 a* )1*0kgu1 c/ tdlokwcm:wqbhbout 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 ofh k, 2x;bng8-ogg pyu* refraction for a glass or plastic prism to be used in binoculars (Fig. Below) so that total k2-;gop,xbu*g yngh8 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 locw ruv*37l m -cl -lbt+h.pys:sated 78.0 mm behind a 65.0-mm-focal-length converging lens. Find the object distvyscs:hl-lr *mb.l7-putw + 3ance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed xat.or /y*h tqwr3qu45f;4 otto focus at a point 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 25 -q udji ng 8d(myw4+ *qni6ws1n9izt.75 m away as an image 48.3 cm on the other side of the lens. What type of lens is it and what is its foc(dy 1 9-8sz nmw+46i jqnu*n 5dgtiwiqal 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-0h4sah n/ggv3ryg2v2) 1 o,xhvf l0btlength lens? P =    D  ----待选择----converging diverging 
(b) What is the focal length of a lens? $f$ =    cm  ----待选择----converging diverging 
(c) Are these lenses converging or diverging?

  A stamp collector uses a converging lens wypjr5c kjqlc8 p,: .af.zzf9h(j, 7jqith focal length 24 cm to view a stamp 18q9j,jyq: rhf c(f.5,z ajlp8z7pcj.k 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 mm high. What are the posito (sa3kce4nk 0ion, type,0n(se coka43k and height of the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to focus an image on the film of a rumxe31*/)rx umo o 1bcamera. The maximum distance allowed between the lmrruo e131x ou)*m bx/ens 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× when a book v;zs ccxp,)1nis placesv p)zxc,;nc1 d 8.0 cm behind a lens.
(a) Draw a ray diagram and describe the type of image this would be.  ----待选择----realvirtual 
(b) What type of lens is needed?  ----待选择----converging lensdiverging lens 
(c) What is the power of the lens in diopters? P =    D

  An object is located 1.5 m from an 8.3rdf;z2* z f.cmy r+le0-D lens. By how much does the image move if the object is moy3z+f*l.cmd;e2rz frved
(a) 1.0 m closer to the lens,    cm away from the lens
(b) 1.0 m farther from the lens?    cm cm toward the lens

  How far from a converging lens with a focal length of (;tm::p 1.epqsh szdf25 cm should an object be placed to produce a real image which is the same size as th:f( 1dp:q ezs;hsmt.pe object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an objecsdq:r 038eup g(dq6zz +wdm,yt be placed if its image is to be ma,(z wp8u+d 0r:me qq6 dgs3yzdgnified 2.00× and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm

  (a) How far from a 50.0-mm-focal-length lens must an object be plat umj:9 yn f;/+zzzt.g-i t+jaced if its image is to be magnified 2.00× and be real? i.a+zt -mfytj zjgun;+t:/9z   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-i(5ihr+y lp .sfocal-length lens. Where is the image, how high is it, and(py +i hlr5si. 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-length conver1j crxxql;-+m:q ky/hging lens if the image is 2.5× larger than the ojmk/yc;- x l:rh1q +xqbject and is real?    m

  A bright object and a viewing screen are separated by a distance of 66.0 cm. nm:vvw s03 3vbAt what location(s) between the object and the screen should a lens of focal length 12.5 cm be placed in orde3wv0v snb3 v:mr 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 ob5slew-psbc 4;lwuu 1r *rz41 nject is placed 36.0 cm in front of one lens. Where will the final image formed by the second lens be located? What is the total mal14rpe rsznb14 c 5swulw-u*; gnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens withep8f6g80x jdsxa6d6e +q t- sp $f=-31.5\mathrm{~cm}$ 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-lengthw;zk6l15oudf converging lens is 21.0 cm behind a diverging lens. Parallel light strikes the dif 5kl6;dw1ouz verging 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 aparl s0f9y f,s6ugt. The object is still 60.0 cm in front of the first lens as in (Fig. Below). In this case, dete u9g6syf, f0lsrmine
(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. Tagq ucr-v1swk2-u6d /he 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 inverq-/ ru6 gdvu1sa-2kcwted 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 i * rmqht5, q y(/-ehzxm/tltc5ig.6va focal length of is placed 12 cm to the right of a converging lens with a focal length of 18 it6.qryie(*-c / lt t m 5qh/hmvgxz,5cm. 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 dit 88npa6;h 4pu+l yrd fh dag-)tu0e-iverging with focal length are placed 25.0 cm apart. y-dahtnfue8 4+ d l;rit 0)8pgauph6- 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 ;jn nlpox z6(tz:k72m a converging lens of focal length $f_C$ as in (Fig. Below). If $f_T$ represents the focal length of the combination, show that the focal length of the diverging lens, $f_D$, is given by
$\frac{1}{f_\mathrm{D}}=\frac{1}{f_\mathrm{T}}-\frac{1}{f_\mathrm{C}}.$

  A double concave lens has surface radii of 34.2 cm and 23.8 cm. What is4wgj 0o4tbu,r the focal length if n = 1.52? r 4u w,o0gj4bt   cm

  Both surfaces of a double convex lens have cz;bq68 se 4byradii of 31.0 cm. If the focal length is 26z8y cbs4;q be8.9 cm, what is the index of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm. Wr0(s 0l9ugzik hat is the radius of the concri slu(0z0 kg9ave surface?    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat su2 d+4zchb79 y-ayxpcyrface and the other has R = -18.4 cm.acb2ypy 47 - xzd+hy9c What is the focal length?    cm

  A symmetric double convex lens with a f,hjg 1os3j, tfocal length of 25.0 cm is to be made from glass with an index of refraction of 1.52. What shouo ,j,thf 1g3jsld be the radius of curvature for each surface?    cm

  A prescription for a corrective lens calls for +1.50D. The lensmaker gri2gi+g amo5ev /3o / r47 rlz/drbotzfgs7f +)bnds the lens from a “blank” with n=1.56 and a preformed convex ffd 4/7f+t ezrv+r5/mb2)aboorgi z3s 7l/ gog ront 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 eachnm0;y q5 -3fna )mdujn other 2.0 m apart as in (Fig. Below). You stand 1.5 m away from one of these mirrors and look i mm3);dqn-ufj na5yn 0nto 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 depda5 asmjnb9yh; ht;l)*o4 a6vth of a swimming pool filled with water. We measure the width (x=5.50m) and then note that the bottom edge of the pool is jubala h h4*oayd 5n;m)9v jst;6st 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 pil7m4jyumg1;*ue8 q v ns:ri k7ece 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 sphericuyl:wy ( zb7tf:m2m.4+lj:gecez a q( al mirror. Specify what this limit is g:c bmzm.t :y ll72 +qeufa(y:z4wj(e.
(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 mrehdlqya 1eoh*3 a*ty520z (hirrors so they form a 90$^{\circ}\,$ angle as in (Fig. Below). When you look into this double mirror, you see yourself as others see you, instead of reversed as in a single mirror. Make a careful ray diagram to show how this occurs.

Show analytically that a diverging lens can never form a h1 dvvl:d8z: ..iuw(xg uli 2preal image of a real object. Can you describe 1 :8zp2i:wuuldh vxi(.dvg l. a situation in which a diverging lens can form a real image?

  Each student in a physics lab is assigned q tf4qbs5/ s z6dd89c.x*lokhto 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 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 whzk.c8*fx/d l 6ssqbh ot945 dqy 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 k9ygekx7gx9ali*98 i 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 l7b, -x6nlajeyh37knglass 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( e53y 2xdysek 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 lep5)i((qz dhyq ns of focal length f, and a white screen for viewing the image is on the opposite side. Th5(h qzdpi)q(ye 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 pg f)zqlv8,5ql rojected on a screen (Fig. Below). If a 105-mm-focal-length lens is to project an image on a screen 8.00 m away, how far from the lens should t q)vl8l fz,q5ghe 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 v .*gwteaeo*vx61 ku0by 36 mm) is to be projected on a screen 1.80 m by 2.70 m placed 7.50 m from the projector. What focal-length lens should be used if the image is to cover the screex*0k*eoweat.uvv 61 gn?    cm

Show analytically that the image formed by a converging lens is real andbpckp- 7t.ztdc9 l8 :o inverted if the object pt d:.o8l7kz bp-t9 ccis 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 her at ho4:o d)yo6za2vd,f,yr .y mwxt me. 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 .yom:d,,vxwy 2 r4f)zotyd6a lens was 210 mm. How far away from the subject was the reporter standing?    m

  How large is the image of the Sunb4e8u:eeo.d u 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 f.;tbgpj7mx al*.gk4 of a certain lens is imaged 8.20 cm in front of that lens (on the same s l7.4katgfm.p ;*gjb xide 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)