What would be the appearany.kpi1y(s(m91 zk g. g ef, /the1itxkce of the Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have b g2 f.k ./d*/upxnhr i1zjg3mourned the whole Roman fleet in the harbor of Syracuse by focusing the 1 2rnmi/f*jpxzo gud3.h ./kg rays of the Sun with a huge spherical mirror. Is this reasonable?

Although a plane mirror appe *6so4ue6*ud 7zrt9zglf-hoqars to reverse left and right, it doesn’t reverse up and downfu ztou9*d 6g*rolez67h-s4 q. Explain.

If a concave mirror produces a real image, is n9defgrvzhu3 pq* +8+:yhh0xthe image necessarily inverted? Explain fqeh+ nyx8h0d+g uvh p93z*:r.

An object is placed along the principal axis of a spherical mirror. Thxvwes 9 0 o:5fpu51erie magnification of the object is -3.0 Is the image real or virtual, inverted or upright? Is thpos:9rx1 v5 ie 0ef5wue mirror concave or convex? On which side of the mirror is the image located?

Using the rules for the three rays xr4lv,q7qd;bkph j 0) discussed with reference to (Fig. Below a), draw r x dbq4qp,)rkv0 l7j;hay 2 for (Fig. Below b).
(a)
(b)

What is the focal length of a plane mirror? What is the magnification of a p)-e xt4qzx3kzr6kg z9;bdt (clane trg kxzt(qz;ez)ck d x 64-93bmirror?

When you look at the Moon’s reflection from a ripply se93) osibd6 qbea, it appears elongated . Expl6bo9b3q )d iseain.

What is the angle of refraction when a light ray mee5zynhtd m4gh ,u1jo3:ts the boundary between two mateju dt,nh53gm:14 hzoyrials perpendicularly?

How might you determine the speed of light in a solid, rectangular, transparengcl +;4cta:i2lf z(h rt objectlccr(za2gf+ 4 ;l h:it?

When you look down into a swimming pool or a 4(y08yl1 y(9cfp0tp viw toqllake, are you likely to underestimate or overestimate its depth? Explain. How does tt 0qyp l4081c vtp((fo9 ywliyhe apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks bent when fknd(oof +3k8f 5mi)qpart of it is under water qf3(k+if k8 dmon5 of)(Fig. Below).

Your eye looks into an aquarium and views a fish inside. One rayoyim+g2,1x:lxt(q j l of light that emerges from the tank is shown in (Fig. Below), as well as the apparent position of the g+(x:xmiolq1,l2yjt fish. In the drawing, indicate the approximate position of the actual fish. Briefly justify your answer.

How can you “see” a round drop of water on a table even though the waaca m5ixy, x-y1* 1d(mf x(mldter is transparent and colorle5 mxxmf11ydl,d(am*yic ( xa-ss?

When you look up at o)v3urfm3g h4cic-:u pgjz/(h4l q hhsd63: man object in air from beneath the surface in a swimming pool, does 6u:r(3mvq3p-zc )4iu 3/do4 fh :ghjg lshcmh 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 objec,q wz-la2hdhh2*x x;gt distance?

Light rays from stars (including our Sun) always9xqq.n rrio76x7pgx 0 bend toward the vertical direction as they pass through the Earth’s atmosphere7nr7qx9 oqx0prxg .6i.
(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 irx 38mifc br5in* 3g3camera lens is to make a sharp image of an object verg33c5nrx * fi ibi8mr3y far away?

What type of mirror is shown in (Fig. Below)? E,9s rov)gq; fi078hem nx;fa sxplain.

A photographer moves closx9 i+.pbe n+geb9mv7ier to his subject and then refocuses. Does the camera lens move farther fr xeb+97pm. i9ngi+ bveom or closer to the film? Explain.

Can a diverging lens form a real image under any circumstane 8*iqa7uk n;-ue* mkoces? Explain.

Use ray diagrams to show that a real image formed by a g 3d l wd9hd9r6x7gb4jthin lens is always inverted, whereas a virtual image is always upd6j4x 9hl3g7dgr9bwd right if the object is real.

Light rays are said to be “reversible.” Is this r 4xx nbt,/k af(a(-ofconsistent with the thin lens equatio4f,x rkftanob- (/ ax(n? Explain.

Can real images be projected on a screen? Can virtual ij6a,eks4ps c8 mlc k-6p)z.tjmages? Can either be photographepzt.cm68)jk j-p ,e s sacl6k4d? Discuss carefully.

A thin converging lens is moved closer to a nearby object. Does the reaun.fb l-,uvxe6qww-) l image formedl.6, q)u- bxwne-uwfv change
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material w njqyqk a 12up+g00lc0ith an index of refraction n = 1.30 In air, it is a converging len a q0pgnu kl10yqc+20js. Will it still be a converging lens if placed in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stan/3evp 6k1vu8cas1 u:gtap/lrds facing a converging lens. If the nose and the tuea 11av8 r:tskg 6v3u/pl/cp ail are each focused on a screen in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air kfq,(hm1gw3;.e(grtl9gwm y stands facing a converging lens. Under what circumstances (if any) would the image of the nose be virtual and the image of the tail be real? Whereqw rykl;3t g(9g ,1mgh m.wfe( would the image of the rest of the cat be?

Why, in Example 13, must the converging lens have a shor7cbp5)if5se fhs/r j9ter focal length than the diverging lens if the latter’s focal length is to be determined by combin97jp b5 e5s/ frfh)sicing them?

Explain how you could have a virtual object.l i6+5p+sgwks

  An unsymmetrical lens (say, planoconvex) forms an image of a nearby ob)kpzl5sf tw;l139jh b/8kemb ject. Does the image point change if the lens is turned aroun mjlk9 zpbw513f;k8bsl t) /hed? ----待选择----yesno 

The thicker a double convex lens is in 12wke s,ksmn x/a6 i;hfkk)x6 the center as compared to its edges, the shorter its focal length for a given lens diameter. Explwk, a;i eh/fs1nk m 2xxs6k6)kain.

Consider two converging lenses separated by some distance. An objec6zl(uyoio+ r)zo8/yf t is placed so that the image from the first lens lies exao(u i8yo+f)o/6lzrz y ctly 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 jcm czl-x/uo) h6g-mrw08z+v as you look at your image in a urwm6)z0xh cvzo-8g -j /cm l+flat mirror 2.5 m away. For what distance should the camera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mirror, you see the same prk- uw ry4/;y;nj+u cwgy*)wamount of your body whether you are close to the mirror or far away. (Try it and see.) Use ray ywgw;p yk*;uy cju)r r- +nw/4diagrams to show why this should be true.

  Two mirrors meet at aq j ,en fwecgg6,8d.o(-w7 gwd 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 f)7bnnat 1near y3q5;lront 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 thqen7a;)13n5ly n rbat e floor that can be seen reflected in the mirror?    cm

  Suppose you are 90 cm from a plane mirror. What area of the mirror n4-7i4txr.k s qc7pl fis used to reflect the rays entering one eye from a point on th.ipn4 f lxrqt-c s7k47e 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 angle xdo g 20ps+egg yp9ie50g0gd* $\phi$. 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 llgwc 1jjp/h6+18b hzthe Sun, focuses the Sun’s rayl8l jph1/hw 6bj+z1cg s 18.0 cm in front of the mirror. What is the radius of the spherical surface from which the mirror was made?    cm

  How far from a concave mirror (radius 23.0 cm) must an object be placed if i 2h .iw8yyytqp(r3,ic ts image is to be at infyyi wyrc.hti2qp , 38(inity?    cm

  If you look at yourself in a shint- s/3iykjx9aw1dc ,f1dom d5y 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 real or virtual9 c1tdj, d-xws3 aifdy15mko /? Is it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shows an upright image of any person w)smau(mzt p y6r*9;ql ho stands 1.4 m in front of it. If the image is three times the person’s height, what is the radius a9*)q y( pmmult zs6r;of curvature?    cm

  A dentist wants a small mirror that, when 2.2 klxa9uc1+3 oj0 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 behind yyt d6biae) fq9- 28tqyou that are smaller than they would be if the mirror were flat. Are the mirrors concave or conyy8 )-6 q2tfedqi9 atbvex? What is a mirror’s radius of curvature if cars 20.0 m away appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is placed 20.0 cm from a convex mirror4tzoo0+t*l 1dc8cp rt of radius of curvature 20.0 * rdpc41ttzo0oct+ l8 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 meo15qnu(w) : tvwlj05(vgrcw from a convex security mirror in a store. You estimate the height of uj v 05c wnltw )r5oe(:1wgqv(your image to be half of your actual height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object be placed in q-he :rv6j ayyrqe 270+1gtuwfront of a concave mirror so that it produces an image at the same location as the ob6v+7yh2tj-w 1 0rg ae :ueqqryject?
(b) Is the image real or virtual?  ----待选择----realvirtual 
(c) Is the image inverted or upright?  ----待选择----invertedupright 
(d) What is the magnification of the image?   

  The image of a distant tree is virtual and very small when viewed in a curveen*31yvfs9 m 4x+mxbod mirror. Th+4*xn feo93m1 xmybsve image appears to be 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 tech;bg pdzhe25/eniques,
(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 magnif pwk-e qqk)o43q.;i3iltvf3 oication 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 tha9cc q6 *umosm85j 2asr vk/)hkt the mirror equation, Eq. 23–2, is valid for a convex mirror as long as aj vh925) kou8m*q/m6c sks crf is considered negative.

  The magnification of a con wmfhzz *o74ibe/fw 21vex 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 plac,t yt)shvepy wdw8rbsh qh3)o14 +/f2ed 28 cm in front of a spherical mirror. It is desired to produce a virtuv )y32 4s )hwyso8tprhq+,1te fhdw/bal 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 designed to magnify your fhzk 1-1hv6md oace by a factor of 1.33 whe dh16k oz1vh-mn your face 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 light in( (8fcw mitzwchjfvgj h-5 1ox.10v k.
(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 ice3n b(rm07 va7ndwes t; is $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain substance is 89% of its value in water. What is +5iq .ju. 2kyro.y1zdoo4 cs hthe index of refracty.sd521hoo 4.uc jkriqy z +o.ion of this substance? n =   

  A flashlight beam strikes the surface of a pane of glass (ng3m +)wiib bd j9w5;cw = 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 bene1 bk: lwr4k(hexz8jb/ath 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 tn-,x4gif r;gs he water at an angle of 6; fr-g i,sxgn46.0$^{\circ}\,$ 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 8au,y7wpt0 7xfamif .to make a 31.0$^{\circ}\,$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?    $^{\circ}\,$

  An aquarium filled with water has flat glass sides whose ina-sc. 7y/gu xndex of refraction is 1.52. A beam of light from outside the aquarium strikes the glass at a 43.5° angle to the perpendicular (Fig. Below). What is the angle of this l.xu c g7s/ny-aight ray when it enters
(a) the glass, $\theta_2$ =    $^{\circ}\,$
(b) the water? $\theta_3$ =    $^{\circ}\,$
(c) What would be the refracted angle if the ray entered the water directly? $\theta_3'$ =    $^{\circ}\,$

  In searching the bottom of a pool at night, a watchman shines a 9q( 1z5tmewlr1ao ft 1narrow beam of light from his flashlight, 1.3 m above the water level, onto t9 ta5rtlmfq1o ez (w11he 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 45.0:ox31jjb rp:c1 :76vbjo z mmv$^{\circ}\,$ 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 partially refleywq y9,ym b9d-cted and partially refracted. Find the angle of incidence if the angle of reflection is twice the angle of refrwb9yq,-my 9y daction.    $^{\circ}\,$

Prove in general that for a light beam incident of:8mom8vg /yj n a uniform layer of transparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the incident beam, indepen8g:m 8omfy/j vdent 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 refranw *x8h,hbhp9 ction n as in (Fig. Below). Show that if the incbx nh, 9*pwhh8ident 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 nkzh 1br24i6z angle for the interface between water and Lucite? To be totally internally reflected, the light must start in whichn 4z1r z2i6bhk material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certai:6ggsviy1jem-npy mss. 1 .;hn 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 n(7/fx rtho o,a depth of 62.0 cm. Where must it strike the air–wa/ 7o (nthr,xofter interface, 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 beu -0v5qr o6nsp96gm; j:yhtil neath the surface of a liquid and strikes the surface 7.0 cm from the point directly above the source. If total internal reflectio096muh;gs t pjnl: vy65qo- irn occurs, what can you say about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face of the prism in (Fig. Be 2vorc9ngn1- mlow) 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 shox2 jw d ydx:-an i(t,6ea(qrqb/g3fy8wn 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 reflects back into the materiaij-fyadw2xe bq q(/,:a ( 8tyg rn36dxl at point a.

  (a) What is the minimum index of refraction for a*9 q*f(.lgoh+ei w7q:l ykeea glass or plastic prism to be used in binoculello q+7w*9fe ehk :agi y.*q(ars (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 65.0-mm-focal-length converging lensoz,g g 94ua-jvh 9fkjx5m(yu/. Find the object distajfg xzv(hm9,y5u/og-9 u 4jkance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to fojpo1w owu39 x+cus 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 lightj vi4o2-g6js j from an object 2.75 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 focal length? Is the imj-6ovj4j2sig age 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 aek8vdbnkc-hf2/ xv y0tf1y: /ei-l).5-cm-focal-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 converging lens with foip:bprpm:h,y ;, avo/ cal length 24 cm to view a stamp 18 cm in front of the :piahob ;,: p/,yvpmrlens.
(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 mmobga i 2 ew +l-hxxr(m3tuv288 high. What are the position, type, and height of the bxh a-egu22wl83 (i txrv8om +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 came ab4p *q f /u;7killc9rm/a1dera. The maximum distance allowed bet 4l7bl e fa;m1cpku*q /arid/9ween 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 oe c+t- d( hbm jho/*y)78fwcbpo;zuh.f 2.5× when a book is placed 8.0 cm behindf(*-phcoho um. )bw+d zjcy /e8 ht;b7 a lens.
(a) Draw a ray diagram and describe the type of image this would be.  ----待选择----realvirtual 
(b) What type of lens is needed?  ----待选择----converging lensdiverging lens 
(c) What is the power of the lens in diopters? P =    D

  An object is located 1.5 m from an 8.0-D lens. By how much does the 72zwh d0 ;ex1 e(plislimage move if the object is moved 1s; pei2xe7dlh( z0wl
(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 2sdygy 4p+zj9)q:w .ar5 cm should an object be place.a:dy) s p94+yg jwzqrd to produce a real image which is the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens mustx14o7*n7lae0v kk u h i9me2ks an object be placed if its image is to be magnified 2.00× vue 79nl 4k*1x ko7h2m a0kseiand 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 qb+.zv: 4 fl uo5cgxxb8nfq4n+hoj1, placed if its image is to be magnified 4xhv+x+5, qqj.g84: 1fb unobc zfl on2.00× 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 is 1.20 ia+dfgo,n,t eoal j9ka6 h6(aa7u5h( m from a 135-mm-focal-length lens. Where is the image, how o7ea uknhfa+65(ja,gat ail6d ho9(, 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-fufimg5h*b*- ;fm zc s1ocal-length converging lens if the image is ms5 *mb iffhzcg*1u- ;2.5× larger than the object and is real?    m

  A bright object and a viewing screen are separated by)aftmv9od ;a +e1f4ja a distance of 66.0 cm. At what location(s) between the object and thae f49j1 +m)aaotv;df e screen should a lens of focal length 12.5 cm be placed in order to produce a crisp image on the screen? [Hint: first draw a diagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length converging lenn9gdra p;giy )p9a,lqs-v 53k2nt kq5 ses are placed 16.5 cm apart. An object 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 magnificatiiy9q 5;qd ,t n3p5vgs-r 2kpgnaak)9l on?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens withhic 2 rmw7k:7u $f=-31.5\mathrm{~cm}$ 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)n ktb ap0n;1z lens is 21.0 cm behind a diverging lens. Parallel light strikes the diverging lens. After passing through the converging lens, the light is again parallel. What is the focal length of the diverging lens?zn kb)ap;0tn1 [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Example 23–12 ar68egrqrso (xl,ov3d /e now placed only 20.0 cm apart. The object is still 60.0 cm in front of the first lens as inqx/8, ( rr6lodoesg3v (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 p-w mfuy/d +0ozlaced 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 place fuwoz+- y/0mdd 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 original object?    cm

  A diverging lens with a focal lengts-ohod x2f+boe -:7izh of is placed 12 cm to the right of a converging lens with a focal length of 18 cm. An object is placed 33 cm to the l:f b-deoxo7h+ z2s o-ieft 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 diverg* z2zy00 ogda- pckzz7ing with focal length are placed 25.0 cm apart. An k70dzy-*zagpz cz02o object is placed 60.0 cm in front of the converging lens. Determine
(a) the position    cm to the right of the diverging lens
(b) the magnification of the final image formed.   
(c) Sketch a ray diagram for this system.

A diverging lens is placed next to a converging lens of fo. ,ggpkkpj-b -cal 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 is thujdto +oi)*fh-t67rg-twkudy(3 t- t e focalkhoyguf -ttdr)+ditjt7-6u o (w-*3t length if n = 1.52?    cm

  Both surfaces of a double convex lens have radii of 31.0 cm. If the foc5uvc9b sy2*r i7emy0nal length is 28.9 cm, what is the index of refraction of the lensr*5eiuv9ny0 byc 7sm2 material?    cm

  A planoconcave lens (n=1.50) hasn.q3lu2s77 av 3fyimw a focal length of -23.4cm. What is the radius of the conca7i a.l yvnq32s3muf7wve surface?    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat surr 3)g7jaki-twr f* dx:face and the other has R = -18.4*wdia:ktr)xgj3 7f- r cm. What is the focal length?    cm

  A symmetric double convex lens witvb iq j,q44;fprg4 i-jh a focal length of 25.0 cm is to be made from glass with an index of refraction of 1.52. Wha 4q iji44 rjp-qfvb;,gt should be the radius of curvature for each surface?    cm

  A prescription for a corrective lens calls for +1.50D. The lensmaker grinds theg cma-lx3d/+lbv b2c3 lens from a “blank” with n=1.56 and g b32c3a/-cblxm+ vlda preformed convex front surface of radius of curvature of 40.0 cm. What should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fig. Belon1xxo2: )ae how). You stand 1.5 m:nxa 1 2ho)xeo away from one of these mirrors and look into it. You will see multiple images of yourself.
(a) How far away from you are the first three images in the mirror in front of you?
$d_1$ =    m
$d_2$ =    m
$d_3$ =    m
(b) Are these first three images facing toward you or away from you?
the first image is facing  ----待选择----toward youaway from you ;
the second image is facing  ----待选择----toward youaway from you ;
the third image is facing  ----待选择----toward youaway from you .

  We wish to determine the depth of a swimming yf3s x7cv8:(fb rjj 6yr2h(sapool filled with water. We measure the width (x=5.5073j(jhsy c:xrf6b2a8 vy(frs m) and then note that the 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 plastic in air is 2u63wk dae/ ow$\theta_{\mathrm{C}}=37.3^\circ.$ 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)on v5t1gblf( a spherical mirror. Specfolvn )t51 (bgify 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 for b6k0.j tkhm-iviant8up3 l6 0m 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,-y tcl:oen1b real image of a real object. Can you describe a situation in whi:ncb yol-t, 1ech a diverging lens can form a real image?

  Each student in a physics lab is assigned to firevm. nksk (cwh+ ao06- 7:huwnd 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 why they do not necessarily no k aw6hv.rskw-:e0un7m( +c heed to repeat the lab, and justify your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of a prism oxn51n dlde94is $\phi=72^\circ$ 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(2pu fuh* 3uy (vmf /t4t,ddl .ab5ius glass rod $(n=1.54)$ are perpendicular to the sides. Show that a light ray entering an end face at any angle will be totally internally reflected inside the rod when the ray strikes the sides. Assume the rod is in air. What if it were in water?

A lighted candle is placed 33 cm in front of71 i gewx1hpee-qxp74i++ ak y 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 plan kca,)wxcji./ w2h pb ;u1da;ced on one side of a converging lens of focal length f, and a white screen for viewing the cpu, 2a;d/w;.1h)kbw iajcxnimage 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 projesut7cnvcfv :;xteo9+v2m( 3a ctor, the film acts as the object whose image is projected on a screen (Figeca+oc mx9; t vf3tunv:s(72v . 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 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 mpehl:/ai4,1jiv bbd5 -dx .:,c guub actually 24 by 36 mm) is to be projected on a screen 1.80 m by 2.70 m placed 7.50 m from the prj4dieu:bdah/-1b u5civ p ,x. :,blmgojector. What focal-length lens should be used if the image is to cover the screen?    cm

Show analytically that the image formed by a l c7 88r33w0 sly7bcf4mr alkrconverging lens is real and inverted if the object is beyond the 4cr 73wrcysrl b8kl7a f0l38mfocal 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 ouaynz xh: x2s +kc0*c;8j2pd vf her 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 o2x2+adhcnz 8yku jp: cs;*xv0f the camera lens was 210 mm. How far away from the subject was the reporter standing?    m

  How large is the image o6qngbs; ea4qvs 7*e7hf the Sun on film used in a camera with
(a) a 28-mm-focal-length lens,    mm
(b) a 50-mm-focal-length lens,    mm
(c) a 135-mm-focal-length lens?    mm
(d) If the 50-mm lens is considered normal for this camera, what relative magnification does each of the other two lenses provide? The Sun has diameter $1.4\times10^6\mathrm{~km},$ and it is $1.5\times10^8\mathrm{~km}$ away.    for the 28 mm lens    for the 135 mm lens.

  (a) An object 34.5 cm in front of a certain lens is imaged 8.20 cm in fr -c9 )w *p:xkzwcjfid-ont of that lens (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 pcci9)w-x*kfz :-wdj?    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 cons.k fy /ojjr:;verging lens, it forms a real image. When the object is moved/:.ryksf ; joj to 40.0 cm from the lens, the image moves 10.0 cm farther from the lens. Find the focal length of this lens.    cm