What would be the appearance of t qkll s9:nnw,2he Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fleet in the hrh6 uqu ,f/c7x ltgc45jf s(4darbor of Syracuse by focusing the rays of the Sun with a huge spherical mirror. Is this reasonablq f6/sudrlccu xg57 jtfh (44,e?

Although a plane mirror appears to reverse left and right, it doe; j*(wbr2tp5( gk cg5 twg3xvzsn’t reverse up and down. pg 5 3c;v( zt*2bxjwwrktg5( gExplain.

If a concave mirror produces a real image, is the image necessarily iu:lla bhp y-r)iv8+:cnverted? Explaia:p ul):- 8bhyvrl+c in.

An object is placed along the principal gttn71a7cxxc )uqr 8+axis of a spherical mirror. The magnification of the object is -3.0 Is the image real or virtual, inverted or upright? Is the mirror concave or cox +1xnu gcq )7ra7c8ttnvex? On which side of the mirror is the image located?

Using the rules for the three rays discussed with reference to (Fig.f y-t9 u)svt0kw)xr3i Below a), dt9)u)-03vrk wtsxf iyraw ray 2 for (Fig. Below b).
(a)
(b)

What is the focal length of a plane mirror? What is the magnification of a planecm9;hcn 6 rviyqe f,1c3: q2s8zvjbi3 mirrov:qh f,8q icen2vzj6;cs33ryi1 b9mcr?

When you look at the Moon’s reflection from a ripply sea, it appears elongated .nk v ;,lg49j nyyf7k;z Explz4v,n; kyknj7; yg 9flain.

What is the angle of refraction when a light ray meets the boundary betw5*zlnbz g (xc.y l vz)(oxgusda6*6+9fe 1a wfeen two materials perpendiculabo (*cz)ef9 1vxxa6lnwy*(zz f+d a sg5ul6.grly?

How might you determine the speedm,n))w1,e mfmb;mcup q/0 rdj of light in a solid, rectangular, transparent object?f0 ,)pm qw,bmcr ) ;nmu/1dmej

When you look down into a swimming pool or a lake, ab5l1hyxr*u n2re you likely to underestimate or overestimate its depth? Explain. How does the apparent depth vary with the viewing angley1ul2hr5*nxb ? (Use ray diagrams.)

Draw a ray diagram to show why a df4pd s( *vh ynz:q,p 83p/ zm+rwrry5stick looks bent when part of it is under water (Fig. Below5v fwyq: ps,rrm pprhd*34z(8yn/+zd).

Your eye looks into an aquarium and vi0 ze(3iq cl9dzews a fish inside. One ray of light that emerges from the tank is shown in (Fig. Below), as well as the apparent position of the fish. In the drawing, indicate the approximate position of the actual cdl0eizq9 ( z3fish. Briefly justify your answer.

How can you “see” a round drop of water on a table even though the:exdnq6 6 .ij vbrt--b water is transparent andi -r:btxn6ejbq d -6v. colorless?

When you look up at an object in air from be; - .(;ydee prr:yx0vw, dxkgic(,a jqneath the surface in a swimming pool, does the object appear to be the same size;pg,j(c:iwxva( ded,x 0.-rkey;y r q as when you see it directly in air? Explain.

How can a spherical mirror have a negative object distand+2w o8i m h.:e,p1ckyoe* *ihwroil+ce?

Light rays from stars (including our Sun) always bend )s+4 gjud5u c6e (84zn(wgnz blqudh +toward the vertical direction as tn)4e(uqzcl (gbj5n+dz6hs+d4 wug8u hey 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 lens is to make a sharp image(2x(bupehk-3npcv4 m of an object vue4 bc-phxmk2( n 3(pvery far away?

What type of mirror is shown in (Fig. Beli3 4 f9fk7qw 8w7wv/hv nvo8tqow)? Explain.

A photographer moves6q36f rx,cau; lpxotf pn,*1;mbk9nu closer to his subject and then refocuses. Does the camera lens move farther from or closer to the fk6 ,;ftnql *,x1uf9 cm; pn3xa6oupbrilm? Explain.

Can a diverging lens9jn- ccjc bw1rvq, h-8 form a real image under any circumstances? Explain.

Use ray diagrams to show that a rea o1nar2f/t kn3 *k5s vj tnqfln97bc1,l image formed by a thin lens is always inverted, whereas a virtual image is always upright if the object i*j1fnq2 9/7v s1l3tnbako t r5ncknf,s real.

Light rays are said to be “reversible.” Is this consistent with theb(ou zn-p w qeg6oe0p. ;vg6/g thin lens equati6g / gn0;zpwvee6bo ( uoq.-gpon? Explain.

Can real images be projected on;.ke egj+ b3xw a screen? Can virtual images? Can either be photokg3+wxejbe ;. graphed? Discuss carefully.

A thin converging lens is mov-v t)79: jm5swygskwdfo )7 mked closer to a nearby object. Does the real image formed change jgf-k 5mk7w9syod vt :)) 7mws
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index ot qd oqdp93tw*lp vo5b(y,6)sf refraction n = 1.30 In air, it is a converging lens. Will it stidvo 6 l(ptsq)w5y3o b*9dqp,tll be a converging lens if placed in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the (eh2f/oyi(vgmfcm*l9+w0i w c0wv 3 wair stands facing a converging lens. If the nose and the tail are each focused on a sw/yv+fw(0vhl 2ecwiw0 f93mg ico* (mcreen in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facing ax2 vsmu- rgnw*.:sjtv -35t pl converging lens. Under what circumstances (if any) would the image of the nose be virtual and the image of the tail be real? Where would the image of th vl*j2t 5-.sswnp-3um gx vr:te rest of the cat be?

Why, in Example 13, must l khzq;pkzl1 8n rzh26:cpe6,the converging lens have a shorter focal length than the diverging lens if the latter’s focal ,k 1k;zeh r8zcq :6ll2hznpp6 length is to be determined by combining them?

Explain how you could have a virtual objeo02 vw*th-apvt ck- 1zct.

  An unsymmetrical lens (say, planoconvex) forms an ik ,r pwzxfp+ py)6+syh6rk5s7mage of a nearby object. Does the image poih p, zrsx+p wy)y675fksk+r6pnt change if the lens is turned around? ----待选择----yesno 

The thicker a double convex lens is k4pk2yj3q*c/ up rb.y in the center as compared to its edges, the shorter iqk.k24 jyrpupcb3 y/* ts focal length for a given lens diameter. Explain.

Consider two converging lenses separated by some distanj utwx2*-*m dtce. An object is placed so that the image from the first lens ltt*2uwjm*d -xies exactly at the focal point of the second lens. Will this combination produce an image? If so, where? If not, why not?

  Suppose that you want to take a photograph of yourself as you look at v kq,70h-hn fbyour image in a flat mirror 2.5 m away. For what distance shof7vh b0-q ,nkhuld the camera lens be focused?    m

When you look at youmo71 3tb 2aondrself in a 60-cm-tall plane mirror, you see the same amount of your body whether you are close to the mirror or far away. (Try it and see.) Use ray diago3m on1tbd 72arams to show why this should be true.

  Two mirrors meet at a 9/(ret cq mq1tjp1 -vq135$^{\circ}\,$ 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 eu(qk3q d*t0cf d5-pek:bd -ifront of a vertical plane mirror whose bottom edge is 43 cm above the floor, (Fig. Below). What is 3ceikqk bd t:-f* pq( ed-d5u0the horizontal distance x to the base of the wall supporting the mirror of the nearest point on the floor that can be seen reflected in the mirror?    cm

  Suppose you are 90 cm from a plane mirror. Whg ez9*-pz21-(ugx u6bt fjwot6aw zcn; h*g.sat area of the mirror is used to reflect the rays entering one eye from a poinf6p.*(x6zt;w-gnbz2outw -* e1g jh9 uas zcg t on the tip of your nose if your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors meet at an anglee+e ,v.r/l.tb .ersct $\phi$. a single ray reflected successively from both mirrors is deflected through an angle of $2\phi$ independent of the incident angle. Assume $\phi<90^{\circ}$ and that only two reflections, one from each mirror, take place.

  A solar cooker, really a concave mirror pointed at th*hyk fda e5k6,e Sun, focuses the Sun’s rays 18.0 cm in front of the mirror. What is the radius of the spheri*kd56a y ,efkhcal surface from which the mirror was made?    cm

  How far from a concave mirror (radius 23.0 cm) must an j4ps6 7gpzy53gs gkbq-r-mh7 object be placed if its image is to be at infinity? gmyb65g7s7rgs-q4hpp 3- zjk    cm

  If you look at yourself in a shiny Christmas tree ball with a d n :qhjbvgu3a)0zyw1j p j3vs zgo,5:0iameter 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 or invsz:qgn5,: zjpyo gjj w3uv1hb00v)3aerted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shows an upright image of any 4kgfo ,pnjl)62+sbc q jpa8(,j r s0rbperson who stands 1.4 m in front of it. If the image is three tim f)brpqsr bgp6kl,n0 s,+cj2a o (jj84es the person’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror thatb0iquakb b k/a:;p6fz) dh v+g/+b5hs, 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 f -yyu+:gjkh)r hc9l -images 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 9 -:chuk )jgl h-y+fyrof curvature if cars 20.0 m away appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.px 3r /gnx1c64uhnu2+k czq- krcqa 520 mm high is placed 20.0 cm from a convex mirror of radius of curvature 20.0+ 3x u x6kc2azk1r-rnh q4qcu5/ cgp2n 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. Yo74v5.e 5g ri 9qzfp-rsda:.gonzs+/2w ajo h qu estimate the height of your image to be half of your actual height. Estimate the radius o754.wqr.a p s+gfgoe5/a s:zhjv-nqo2z i9r df curvature of the mirror.    m

  (a) Where should an object be placed 0c*;dy+.bj xjjp pg3d in front of a concave mirror so that it produces an image at the same location a+j y*dxgcjpjb ;dp. 03s the object?
(b) Is the image real or virtual?  ----待选择----realvirtual 
(c) Is the image inverted or upright?  ----待选择----invertedupright 
(d) What is the magnification of the image?   

  The image of a distant tree is virtual and very small whq2vy6xzot dff o+0y ::en viewed in a curved mirror. The image appears to ::oy6 tvqo 0fz+xy2 fdbe 18.0 cm behind the mirror. What kind of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniques+tvuehex ;k76b561 -nrqdt vs,
(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 conv whf gl,74femh,(q;) 5yzzblnex 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. 23–2, is valid for a 8: ,sw) aida)/kcz5 ji ec3wpaconvex mirror as long as f is consi):5 a /eca,)8wk wdzas pcij3idered negative.

  The magnification of a convex mirrob)n k)qfb (iy(r 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 (a txmf2:m0ex spherical mirror. It is desired to produce a virtual image that is upright0me2:(tfxxam and 3.5 cm tall.
(a) What type of mirror should be used?  ----待选择----convex mirrorconcave mirror 
(b) Where is the image located?    cm behind the surface
(c) What is the focal length of the mirror? $f$ =    cm
(d) What is the radius of curvature of the mirror? r =    cm

  A shaving/makeup mirror is designed to magnify your face by a factor of 1.33 whecd uoc/:x /7gfn your face is placed 20.0 cm dfg/x/: ou 7ccin front of it.
(a) What type of mirror is it?  ----待选择----convex mirrorconcave mirror 
(b) Describe the type of image that it makes of your face.
(c) Calculate the required radius of curvature for the mirror. r =    cm

  What is the speed of light in m h;ibide.7z,
(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 iuxm- qqz(o; 8ice 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 i )jb;weky :blci3 1dttlo o5-,n water. What is th llj; :tdobb)51 ewyc i,-tk3oe index of refraction of this substance? n =   

  A flashlight beam strikes the surface of a pl7c7 (al ,7jx1 inhwd;nxi( nvane 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 water at auzfrl s *.k /e8+dbb)9kljh /m 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 skyb8n1b 5 mzru 24e8oppotlight exits the water at an angle of 8zeyom kub1b24p r85n 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 t ftlmp(xaok zd o;3hb4:7v:s* o make a 31.0$^{\circ}\,$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?    $^{\circ}\,$

  An aquarium filled with water has flat glass sides whos 4ht:mk-lo). j6c v1 gnjar0hne index of refraction is 1.52. A beam of light from outside the aquarium strikes the glass at a 46l4 -). gc:nh1nmjk0raoh jt v3.5° 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 ni0y w89c r:dpesbflns2;1q yi1 ght, a watchman shines a narrow beam of light from his flashlight, 1.3 m above the water level,yiycepw8 df sq1r20l1b;:9 ns 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 equi0n7 jnx5oxfi )lateral 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:shbd 5 bei6ka.d 2t*i slab of glass (n = 1.52) and is partially reflected and partially refracted. Find the angle of incidence if the angle of reflection is twice the ang.6ah5d2 b:is *kt dieble of refraction.    $^{\circ}\,$

Prove in general that for a light beam incident on a uniform layer of transpal:vv; tt- 1t,5 pci1mom)fnuprent material, as in (Fig. Below), the direction of the emerging beam is parallel tv1,tmut;fc t1mil-npp ov ): 5o 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 refractdlj/vmd d7 ,ag1x;rx(ion n as in (Fig. Below). Show that if the incident anxd,gam d7dr;/x1j( vlgle $\theta$ 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 2 ti9tcsq(q )iapfd4 u w*(nyjz5hy* 5and Lucite? To be totaydqis q5t zh 54j)n* f((cuwat92*piylly internally reflected, the light must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–air surfac60pkm5/ z5vkdnruh:ukz gtr,ul0lx l7 3a 78b e is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in a pool of water from a depth of 62.0 cm. Where m+cb xu5qcsw59 ust it strike the air–water interface, relative to the spot directlycbcq9 uxw+s55 above it, in order that the light does not exit the water?    cm

  A beam of light is emittla(arry8* f9 1tbf 6eded 8.0 cm beneath 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 can you say about the index of refract yb*6d8ftre9faa( l r1ion of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face of the prism in (Fig. dui 2wxgd y0rvlu3(;zoo)4a. 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 shee y-tq ok1(9hown in (Fig. Below). Show that we can guarantee total internal reflection at the side surface of the material (at point a), if the indekqy-91h et( oex of refraction is greater than about 1.42. In other words, regardless of the angle the light beam reflects back into the material at point a.

  (a) What is the minimum index of refraction for a glass or plaswk cxh:i lpxw,pltsk(8s:5+5 tic prism to be used:ts:p xpk+5ixc,sl5wk 8 (lwh in binoculars (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 wsdoc,m2 du.y352uno .0 mm behind a 65.0-mm-focal-length converging lens. Find the o2yw5d d3 .numc,o2sou bject distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.5 -lwj y)yn ns31cm 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 imagepzz1: m m,w:/, rmzrgf 48.3 cm on the other side of the lens. What type of lens is it and what is its focal lengthw/z1m zzgfmr , p::,mr? Is the image real or virtual?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the power of a 20.5-cm-focal-length lens?z78 hl6uev22n1q wjf:v jsv )c P =    D  ----待选择----converging diverging 
(b) What is the focal length of a lens? $f$ =    cm  ----待选择----converging diverging 
(c) Are these lenses converging or diverging?

  A stamp collector uses a converging lens with focal length 24 cm to view a6it0e: o6.kh/vo mm)0lfz rh avsk(1m stamp 18 cm in frontt mk 10iv zvmarook0)hlf.m/: e6sh 6( 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 :l68g-oc.m 8c cqy n(yqvmh9w position, type, and height of the image? :qly m6 mcwvqc- 988 .coygnh(
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to focus an image on the3tklh58g;n *ttshj h j//ucg)n/ j zx8 film of a camera. The maximum distance allowed b)*hjl h5u /jjh/knntt8 cz8 3/;sgg xtetween 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× when a book is ;d.niaygb/k rb(r/mz *a5 ,ntplaced 8.0 cm kn;ytd mbzabi*,(/n rr./g a5 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 8.0 t. skigpfc8uiruu9h65:h7 h5-D lens. By how much does the image move if the objhsgt8u purk6:i7 5 u5hi.f9chect is moved
(a) 1.0 m closer to the lens,    cm away from the lens
(b) 1.0 m farther from the lens?    cm cm toward the lens

  How far from a converging lens with a focal length of 25 cm should an objd,as2qze 1 6pfect be placed to produce a real ise,a61dqzf2 p mage which is the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an object be placed if its imaoh0v4,6p f0lc lk+qao zmwj+n;p/a 8dge is towaz8pnmh ;apc+o d,kv 6o+f0j0q/ ll4 be magnified 2.00× and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm

  (a) How far from a 50.0-mm-fo 6aln bcs7ca,1 .;lu u,l1upircal-length lens must an object be placed if its image is to be magnified 2.00× al1b1 cllpi.;ruua7u,c6,n asnd 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 lz+0t bb f.,yirens. Where is the image, how high is it,iz+ tb0 f.yrb, and what type is it?
$d_i$ =    mm (real,behind the lens) $h_1$ =    cm (inverted)
(b) What if $f=-135\mathrm{~mm}$?
$d_i$ =    mm (virtual,in front of the lens)
$h_1$ =    cm (upright)

  How far apart are an object and an image formed by a 75-cm-focal-;u8y4mo w8(kkjgz zy( +r;orxlength convergiyr+orkm;j ux kz ( (g84yz;wo8ng lens if the image is 2.5× larger than the object and is real?    m

  A bright object and a viewing screen are separated by a distance of 66.0 mq; 2u r.26uu (zbyf nxb/+mg7 ncfhphi/j*b9cm. At what location(s) between the object and the screen should a lens of focal length 12.5 cm be p/if y ;hb u+ruf9mhmbcb2.u (2*gqjp x 6n7zn/laced 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 r+jk a rds4j-26j3pwclenses are placed 16.5 cm apart. An object is placed 36.0 cm in front of one lens. Where will the final ijakw 2d rcj-+r4spj63mage 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 with p 69- lxqor :eox2k3se$f=-31.5\mathrm{~cm}$ 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 c/za.,-a::vduk3t skyvl zty)n cun/r n lj -11m behind a diverging lens. Parallel light strikes the diverging lens. After passing through the converging lens, the light is aa 1-k y.ynu):s3vl zn/1ul-vnzcr,kt :t/ ajdgain parallel. What is the focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Example a ; b*ao uabx/,)eyj*a23–12 are now placed only 20.0 cm apart. The object is still 60. y)aeaa*/ a*o;j ubb,x0 cm in front of the first lens as in (Fig. Below). In this case, determine
(a) the position of the final image,    cm
(b) the overall magnification.    cm
(c) Sketch the ray diagram for this system.

  Two converging lenses are placed 30.0 cm apart. The focal length owq0 pco * wwdi,2/*apvf 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 iwq,**wc0vad ip wp/2o s the original object?    cm

  A diverging lens with a focal length of is placed 12 cm to the rixu 4c goxh4z:*ght of a converging lez *hcoug x44x:ns with a focal length of 18 cm. An object is placed 33 cm to the left of the converging lens.
(a) Where will the final image be located?    cm to the left of the converging lens
(b) Where will the image be if the diverging lens is 38 cm from the converging lens?    cm to the right of the diverging lens

  Two lenses, one converging with focal lengtpqg0(ydirp +5 h 20.0 cm and one diverging with focal length are placed 25.0 cm apart. An object is placed 60.0 cm in front of the convergyprdq p (g5i0+ing 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 convergine n08 vivxu,6sg 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 ran()a67cntnd(q,* yfts )a swydii of 34.2 cm and 23.8 cm. What is the focal length if n = 1.52n qcf) 6d ynwy(nsta*(, 7ts)a?    cm

  Both surfaces of a double convka4l26sgflv o ;(qca1qb)b grzy+ dh1 n6.ft2 ex lens have radii of 31.0 cm. If the focal length is 28.9 cm, what is the index of refraction of the vrn4.gz;q)h+1t 6yl12ob cfqa d6g2fsa ( lkblens material?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm. What is thch. 6frg+j9g se radius of the concave s.jf9h gc s6rg+urface?    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat surface and the other 06e3aq otb8:fbx4 etf has R 08etbq:4fbo3ef6a xt = -18.4 cm. What is the focal length?    cm

  A symmetric double convex lens with a focal length of 25.0 cm ish/f08xslfym fw(/q a)5 clbm . to be made from glass with an index of)hflw5x0m c /s(lf .qfam/ 8by refraction of 1.52. What should be the radius of curvature for each surface?    cm

  A prescription for a correctiva+j4omvshfim: -d u8 gwr,o1ab+;pc 8e lens calls for +1.50D. The lensmaker grinds the lens from a “blank” with n=1.56 and a preformed convex front surface of radiu,c:m+ g4+vhrb8aj;a - 8fimodu w1opss of curvature of 40.0 cm. What should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors fac),t eovli3(eq kcu+r acb4-q919 exmce each other 2.0 m apart as in (Fig. Below). You stand 1.5 m away from one of these mirv-etee 39)qq( i9o1bxa cul,k 4mc +crrors and look into it. You will see multiple images of yourself.
(a) How far away from you are the first three images in the mirror in front of you?
$d_1$ =    m
$d_2$ =    m
$d_3$ =    m
(b) Are these first three images facing toward you or away from you?
the first image is facing  ----待选择----toward youaway from you ;
the second image is facing  ----待选择----toward youaway from you ;
the third image is facing  ----待选择----toward youaway from you .

  We wish to determine the depth+ 1z(kwbw xzt,g:y k1m of a swimming pool filled with water. We measure the width (x=5.50m) and then note that they(kz1kx w+1mwg z:bt , bottom edge of the pool 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 ,h8 4eg azwncja4pt*;f ) 5iagplastic 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 consi2pabu* (cxj2idered a limiting case of a spherical mirror. Specic* xuj2bip 2a(fy 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 formx6g+/m b1z7v0qawhsx 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 k6t1p 0u+3rxwve o ao6never form a real image of a real object. Can you describe a situation in which a diverging lens can f1a p3 0 vr6kexo+utw6oorm a real image?

  Each student in a physibu4z8pq 4 uh6ucs lab is assigned to find the location where a bright object may be placed in order that a concave mirror with radius of curvature r = 40 cm will produce an image three times the size of the ob u 64pbuhuqz48ject. 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 pri7hn,k+pf+g y nsm is $\phi=72^\circ$ see (Fig. Below), what is the minimum incident angle for a ray if it is to emerge from the opposite side (i.e., not be totally internally reflected), given $\mathrm{n=1.50~?}$ $\theta_1$$\geq$    $^{\circ}\,$

The end faces of a cylindrical glass rod /.f+gbng2q0 bn pzkt5$(n=1.54)$ 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 fo:e0f-euz*fw9ur w5tki1vyo 1cal 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 onf)ag tczb;d 8dc3ed +ae+9 iw.e side of a converging lens of focal length f, and a wh8ecizda+ d3)dbe9.; w fc ga+tite screen for viewing the image is on the opposite side. The distance $d_T=d_i+d_o$ between the object and the screen is kept fixed, but the lens can be moved.
(a) Show that if $d_{\mathrm{T}}>4f,$ there will be two positions where the lens can be placed and a sharp image will be produced on the screen.$d_T$>4$f$
(b) If $d_{\mathrm{T}}>4f,$ show that there will be no lens position where a sharp image is formed.
(c) Determine a formula for the distance between the two lens positions in part (a), and the ratio of the image sizes.

  In a slide or movie projector, the film acts as the object whose image is pr-0tzdr*; dc6n:bjybvojected on a screen (Fig. Below). If a 105-mm-focal-length lens is to project an imagb- bdvrd;n0:y ctj6*ze 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/ b 1rduu+ 2enuzz pw :fi04686reonnm is actually 24 by 36 mm) is to be projected on a screen 1.80 m bnbfrnezem uoz p8/64:d1i +w260r u uny 2.70 m placed 7.50 m from the projector. What focal-length lens should be used if the image is to cover the screen?    cm

Show analytically thau;k+p)k.l,0ts ;x tduu w d3paplja +0t the image formed by a converging lens is real and inverted if the owt0l .da);p akuuup+,jkx0 sl p+; t3dbject is beyond the focal point $(d_0>f),$ and is virtual and upright if the object is within the focal point $(d_0>f),$ Describe the image if the object is itself an image, formed by another lens, so its position is beyond the lens, for which $-d_0>f$, and for which $0$<$-d_0$<$f$.

  A movie star catches a reporter shooting pictures of her.awl s 5/tyty3 at home. She claims the reporter was trespassing. To prove her p ls/ at3.5tywyoint, 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 of the Sun on film used in a camivr/4by- ;od aera 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 froh)m e 648xgbg 25gnoi)p-ikl5ng1uc ont of a certain lens is imaged 8.20 cm in front of that lbggelx8o5g6o h5)ikmg-i)nc24 1n pu ens (on the 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)