What would be the appearance of the Moon if it o(n p gj.ypqr3f);wbbm v+* +thad
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fleet in the harbor of Syracusxz-9 vquc(zn) exuz-9)cvq(z n by focusing the rays of the Sun with a huge spherical mirror. Is this reasonable?

Although a plane mirror appears to reverse left and right, it doesn’t reve:u2o/( knapke rse up and down. n( p:uo2/keka Explain.

If a concave mirror produces a real image, is the imgx0bjv/ptb;+/ b2 w lbage necessarily inverted? Explvb+j20t / blgx;pwb/b ain.

An object is placed along the principal axis of a sp/z n*rrvo4db1 herical mirror. The magnification of the object ir1zd*n o/rvb4s -3.0 Is the image real or virtual, 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 reference to (Fig. Below wstwr)2nyv(.a), draw ray 2 for (Fig. ytrwvsn( 2) w.Below b).
(a)
(b)

What is the focal lendey5jd/kzscgo0 v -;6gth of a plane mirror? What is the magnification of a plane mi0vdc5g j6/ozyskd; - error?

When you look at the Moon’s reflection from vc.xc4glzl1a208idtg l8lr:a ripply sea, it appears elongated . Expl8z.t1ai8l4 ll2xvg c :rdgl0 cain.

What is the angle of refraction when a light ray meets the boundary between twot )r.3bz7o ifs bor .) sfzti73materials perpendicularly?

How might you determine the speed of light in a solid, rectangular, tranv6c*dqeoox (moj4q; 6sparent obje4e *6codoq;xjvoqm 6 (ct?

When you look down into a swimming pool or a lake, are you likely to underest ye kf+**tf hxc7 07wnrj(;zrs;9oiwwimate or overestimate its depth? Explain. How does the apparent depj* or* irff9z kw7cws7w;ne(0h+x ;tyth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks bent whesng 1 rtq5strw95i2vq o9h .d3n part of it is under water (Fig. Below)t sro293gq5.5h1qt w nvd9r is.

Your eye looks into an aquarium and views a fish inside. One ray of light; ; o-xbza6.cqbkayg; 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 fish; 6z akbaqc-.b;;g yox. Briefly justify your answer.

How can you “see” a round drop of water on a table even t v.r4*osmu+xr hough the water is transparent and colorlesov *+.4r mxrsus?

When you look up at an object in air from beneath the surfady,pl+ +ljdij5dk- d5ce in a swimming pool, does the object appear to be the same size as when you see it dl-+li5k jdpjd,+ 5dyd irectly in air? Explain.

How can a spherical mirror have a negative object( 6txhuycj3o*o3of g p.pe0 )r distance?

Light rays from stars (including our Sun) always bend towp+lvq(g m*ubk ;h/o, s voai0/ard the vertical direction as they pass through thgq*o;u/pa sh(k/bvm, l v0+oie 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 placedbj6 qao*3p.gpq,pjo - if a camera lens is to make a sharp image of an object o pqj bpg36*q.o,p ja-very far away?

What type of mirror is shown in (Fig.)xphn, ma:evq r;s-a( ju0oz, Below)? Explain.

A photographer moves closer to his subject and then refocuses.+oh*yrty2,z r Does the camera lens move farther from or closho,2y+z* ry rter to the film? Explain.

Can a diverging lens form a )4v(vqmp -hjv2 q*aroreal image under any circumstances? Explain.

Use ray diagrams to show that 7 *)vg( p 5upcqlc.ngnpcc w/)a real image formed by a thin lens is always inverted, whereas a virtual image is always upright if the objec gp*5wc7vngp)c /ncp)uql.c (t is real.

Light rays are said to be “reversible.” Is this consist*4)dvfb)9azm z on:xwent with the thin lens equation? Explaiz woa:)dx9f bz*) nvm4n.

Can real images be projected on a screen? Can virsxjzp2 bsi-shfvy 5hw*0l6lh0 k2*;y tual images? Can either be photographed? Discs p;vszh*s-jh0xl*f65b lkiy20h y 2wuss carefully.

A thin converging lens is moved closer to a nearby obj.gnctau3t07 82b5dvaclgmtw 5r 17 lf ect. Does the real image formed chan l cggm5dlu.c 52f7vw8bnatrt t1a0 73ge
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index opac0)c,c,qdvlm- swm o+y9 f3 f refraction n = 1.30 In air, it is a converging lens. Will it still be a conv yqfc3calvc9 ,0 dp+wo-m)m,s erging lens if placed in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands facing a converging lens. If the nosetm6ip f /wa7.m and thw t.m/ifa 7m6pe tail are each focused on a screen in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facing a converging l se.,s.zb:/vm/g1i r-w mw j ..xkcxjzens. Under what circumstances (if any) would the image of te:ir.1z.v,w cxjm/s/-w.b.sg jzk mxhe nose be virtual and the image of the tail be real? Where would the image of the rest of the cat be?

Why, in Example 13, must the converging lens have a shorter focal length h4 cdrj)zq::b than the divergirq ::j4 zhc)dbng lens if the latter’s focal length is to be determined by combining them?

Explain how you could have a v 0kjowlmol7, cav3v; qq,(qq/ irtual object.

  An unsymmetrical lens (say, planocoo8.l s8 yq)93egg4j;esvsuiy nvex) forms an image of a nearby object. Does the image point change if the lens is t;gv4)qs jsg8euy.eoy89 i s 3lurned around? ----待选择----yesno 

The thicker a double convex lens is in the centeqiw .oyn/fv 20r as compared to its edges, the shorter its focal length for a given lens dia/w 2n.0foqi yvmeter. Explain.

Consider two converging lenses separated by some distance. An ol i h(nvt5wxde2cey.pudd)/*e r4* g+bject is placed so that the image from the first lens lies exactly at the focal point of the second lens. Will this combination produce an i tl/nr4p2whd* y xu*.c(ieg d+ed5e)vmage? If so, where? If not, why not?

  Suppose that you want to take a photograph of yourse,r( : clcb/xqelf as you look at your image in a lcx(qeb/ ,r:cflat 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 p1u,e 5gc,x eq- uknk+nlane mirror, you see the same amount of your body whether you are close to the mirror or,xunuq e-e,5kc1 g+nk far away. (Try it and see.) Use ray diagrams to show why this should be true.

  Two mirrors meet at a 135 og+1p e7 -e98dzipyem.catrk-a4w5n $^{\circ}\,$ 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 h 3l9* ;tafq m+om;fssm in front of a vertical plane mirror whose bottom edge is 43 cm above the floor, (Fig. Below). What is the horizontal distance x t mm 9*t3+alsfsh;q ;ofo 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. What area of the mirror qag4-6 5nvmw +) yvfc dw8t )u1,aewkxis used to reflect the rays entering one eye from a point on the tip of your nose)f5v6qnwk,wcey 8dv4m)x t ga-wu+a 1 if your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mw):-agupc*,k+ f yq1 x sqj)bpirrors meet at an angle $\phi$. a single ray reflected successively from both mirrors is deflected through an angle of $2\phi$ independent of the incident angle. Assume $\phi<90^{\circ}$ and that only two reflections, one from each mirror, take place.

  A solar cooker, really a concave;+gzwuy z07nwar ,c1 b 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 frwrz 0nub ,wc1y+7zg a;om which the mirror was made?    cm

  How far from a concave mirror (radius 23.0 cm) must an object be placed if i4k;u4h sx sh1dts image is to bed44 ;susxhhk1 at infinity?    cm

  If you look at yourself in a shiny Christmas fz ;448lvpfgv x4 jwx3tree ball with a diameter of 9.0 cm when your face is 30.0 cm away from it, where is yvzffw8444pxgx vlj;3 our image? Is it real or virtual? Is it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shows an upright image may1xv 7wlqx 312:9)umvu otu of any person who stands 1.4 m in front of it xu79qv1oux3:mlwv ut1m2 y)a. If 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.hr(pyf a, r dr4j9o;1fg;,k hj20 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 you that are smaller th ( p e7ujax4p)yggbjvj5 q9ya;9ep2))4dmkn kan they would be if)q) 4(y9 p )veekunjbk 7jga54djya92p gpm; x 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?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is placed 20.0 cm from a convex mz o /05bif ath,fj+zg(irror of radius oh/0z a(iozj5bt gf f+,f curvature 20.0 cm.
(a) Show by ray tracing that the image is virtual, and estimate the image distance.    cm
(b) Show that the (negative) image distance can be computed from Eq. 23–2 using a focal length of -10.0cm
(c) Compute the image size, using Eq. 23–3.    mm

  You are standing 3.0 m from a convex security mirror in aj s7k c-a ;)q 0scw9i2zm8amgx store. You estimate the height of your image to be half of your a w7-smajc8 c9s mq2gixzk )0;actual height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object be placed in front of a concave mirror so th jno r-6(e(gfiat it produces an imnge -(i(rof 6jage at the same location as the object?
(b) Is the image real or virtual?  ----待选择----realvirtual 
(c) Is the image inverted or upright?  ----待选择----invertedupright 
(d) What is the magnification of the image?   

  The image of a distant tree is virtual and very small when viewed in a cusx **;z*pv-1k:ei bg4epxqo brved mirror. The image appears to be 18.0 cm behind the mirror. What kind b * x1:;4eo -ke*vbsp zqp*gxiof mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniques, i,t+l3hrwxhz ,e,:ut
(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 mirror 6 vrb bc:7stic1wf oxa ml+/)5is $m=-d_\mathrm{i}/d_\mathrm{o},$ 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. 2gs2(-lycf zfi3x)x t .3–2, is valid for a convex mirror as long as f is considered negaty.lzg-(xs i3fx c t)f2ive.

  The magnification of a conveyop l 2xn2m/yhc /at-1x 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 /d 8p5an/u thwwuj7q;cv* 2(ozg-fjbgc-wg* front of a spherical mirror. It is desired to produce a virtual image that is uprighb --* 7za vjghdg;/wgt52*q cn(/cp8jowuuf wt 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 designepy/ s,/tl,de 9e+ zbvcd to magnify your face by a factor of 1.33 when your face is placed 20.0 cm in de c/,b z+vyle /tsp9,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 in1z qar er: e-;ymk9*jp v/pj+;m4oqxt
(a) crown glass,    $ \times10^{8 }\;m/s$
(b) Lucite,    $ \times10^{8 }\;m/s$
(c) ethyl alcohol?    $ \times10^{8 }\;m/s$

  The speed of light i)2elbgh zk,r,a.i5 h qn ice is $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain substanc2(2o a/gozkbzg8 ti 3te is 89% of its value in water. What is the index ofkgt3oz 8b (ta /zi2g2o refraction of this substance? n =   

  A flashlight beam strikes the surface of a pane of glass (n = 1.58) ate7a*ucsv so95e(vo)hvac(r ( 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 a 42.cka2r ylk 3/w-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 y ex( r6v1g-k75sjmfvs1i;pqat an angle of 6;j1gy i(sk5v1-e rx mqs67pv f6.0$^{\circ}\,$ 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 ss isa(0y;5e dguv8uz55a 8(jr+f pmf keen 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 si/mk ,h wbmv/+zv7fy8i3 m-uw zdes 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 wf ,mk 3u 8w+m-i zvm/hyz/vb7perpendicular (Fig. Below). What is the angle of this light ray when it enters
(a) the glass, $\theta_2$ =    $^{\circ}\,$
(b) the water? $\theta_3$ =    $^{\circ}\,$
(c) What would be the refracted angle if the ray entered the water directly? $\theta_3'$ =    $^{\circ}\,$

  In searching the bottom of a pool at night, a watchman shines a narro0hfrt7 d44 c* d+*b1hump)kx hlj 2doiw beam of light from his flashlight, 1.3 m above the water level, onto the surface of the water at a point 2.7 m from the edge of the pool (Fig. Below). Where does the stjflx*4o4m pd7cib2 d+0h1*d kh hr)upot 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 ciyj(; mp62t+i20xqp +xv kyla 45.0$^{\circ}\,$ angle to one face, (Fig. Below). Calculate the angle at which light emerges from the opposite face. Assume that n = 1.58.    $^{\circ}\,$ from the normal

  A beam of light in air strikes a slab of glass (n = 1.52) and is 0pev4 g*n zr8u1bht9tthm9l8 partially reflected and pa184htltu99p0thm z n gve*rb8rtially refracted. Find the 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 4 3dkudw r( tkk l6;he+ucp7f8a uniform layer of transparent ma7ecwd8h3(+ ufk lk6tdr k4pu;terial, as in (Fig. Below), the 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 o 8 lr6u/ejjdl-f glass with index of refraction n as in (Fig. Below). Show that if the incrl euj6j/8- ldident 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 b3gf s: lb-ixm;etween water and Lucite? To be tota3iblxsfgm ;-: lly internally reflected, the light must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain llx(-)ycfcb ro(p b; c8iquid–air surface is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in 6jkgpza:p .2idwx, 6) 5k)y ow/gjofaa pool of water from a depth of 62.0 cm. Where must it strike the air–water interface, relative to the spot directly above it, in order that the light doeyp dw. :6iwo,6/zgg)xj2a ) kofapkj5s not exit the water?    cm

  A beam of light is emitted 8.0 cm beneath the surface of a liquid and 18aqfj q j 36x8xr(tlcstrikes the surface 7.0 cm from the point directly above the sourq 6a8j1xrcj(t3lfq x 8ce. If total internal reflection 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. Below) at 45.9(sew7cle n 4+7nfkvo0$^{\circ}\,$ 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 e,hqtby) z78suo ,z3pel c/d/the end of an optic fiber as shown in (Fig. Below). Show that we can guarantee total internal refe s /,u o7btped83z /qhc)lyz,lection at the side surface of the material (at point a), if the index of refraction is greater than about 1.42. In other words, regardless of the angle the light beam reflects back into the material at point a.

  (a) What is the minimum index of refracm4:obbq yz p:i). secgp(0 ctw6us26n tion for a glass or plastic prism to be used in binoculars (Fig. mebc g:2s) :wy szcq4np6pi0t.6uo (bBelow) 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 (gq tdj: ok00ibehind a 65.0-mm-focal-length converging lens. Find the object distancet :gdqok0(j0i
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a poin-e4ns5a.ujstu+ffti9 r hv//t 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 9e.+ ;j hvhhsfobject 2.75 m away as an image 48.3 cm on the other side of the lens. What type of s9 hhhf+ j.v;elens is it and what is its focal length? Is the image real or virtual?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the powe2 gi4knr+.lrz r of a 20.5-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 focal length 24 cm pf;7ooekv ;tzst9r0 qb(e 4d6to view a stamp 18 cm in froe6; se qdvop94 kfz(0 trtb;o7nt 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 hh ;ps21 vo ygg. a0m.-2gdiot6h.(vf q d2abiobject 4.0 mm high. What are the position, type,yq ipm g.16o gai2;.s2thg2h0 f-abd(dvv.oh 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 ae2xg7s:p evkv9e 2mz4 camera. The maximum distance allowed between the lenm :k47gp v9z 2evesex2s 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 af v-bu/*0( 6:njao q ,3uw zvj)nkeumg factor of 2.5× when a book is placed 8.0 cm beh ka:v/w jne60-bu(zmv j*qo,fuu 3ng)ind 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 ho7o. sozv v*4tkc u)(ghm2r 6czw much does the image move if the object is moved c .42zrmvhutvck z7o*o)s6(g
(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 converging98jkv1e- o)(sg 6kencypmwgh(toy +0 lens with a focal length of 25 cm should an object be placed to produc(p-o0gvcyg+kwm9h )nj6syeo81et (k e a real image which is the same size as the object?    cm

  (a) How far from a 50.0-mm-f0k9 (pcctxx2nl*tdwp2l7k9m ocal-length lens must an object be placed if its image is toxn9l 2(kcl mwkpx02ctpd t9 *7 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-focal-length lens musj sm,dbln, 7)*st:(urf y3.sqbll7wot an object be placed if its image is to be magnified 2.0qmuw7olnj7 bf d ls*s: bsr., 3)lt,(y0× 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 m fdj)po(0 k9lqqlh y4h0rom a 135-mm-focal-length lens. Where is the image, how high is it, and what type4jdq )h0l(y 0ph9 kolq 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 4/b3e c 5xla,rwbivr+ formed by a 75-cm-focal-length converging lens if the image is 2.5× larger than the obje53 ar xbi wr4/bv+cel,ct and is real?    m

  A bright object and a viewing screen are separated b3)g5/zy sghb ey a distance of 66.0 cm. At what location(s) between the object and the screen should a l3gyhb)g sz5 e/ens 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(p xe)itixe l)qqoz 4o9ms5w) xq:-9h converging lenses 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 magnification:m49z)x isqxp o)q- x(we q9) 5otilhe?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens wit*6av b.s nocm1-ez/dah $f=-31.5\mathrm{~cm}$ is placed 14.0 cm behind a converging lens with $f=20.0\mathrm{~cm.}$ Where will an object at infinity be focused?  ----待选择----realvirtual ,    cm beyond second lens.

  A 31.0-cm-focal-length converging lens is 21.0 cm behind a divuhl0zzia n a5je)pyr *+* m:p )y3ovcz6u;ex0erging lens. Parallel light strikes the diverging lens. After pazovjch0l5iz 03+:6y)m up z ) p*anxueeary*;ssing 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 only9f,l 1gc+aa9cii v o2o 20.0 cm apart. The object is still 60.0 cm in front of the first lens as in (faviiooa9 l ,9cc1 g+2Fig. 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 areundwo2f*-mjxr r e5/ : placed 30.0 cm apart. The focal length of the lens on the right is 20.0 cm, and the focal length of the lens on the left is 15.0 cm. An object is placed to the left of the 15.0-cm-focal-length lens. A final image from both lenses is inverted and located halfway between t/ur5d f*wm oe2:j-xn rhe two lenses. How far to the left of the 15.0-cm-focal-length lens is the original object?    cm

  A diverging lens with a focal length of is placed 12 cm to the righd7+kv c 7iepx*t of a converging lens with a focal leng kvx+e*c7pd 7ith 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 (kv0pqw.ts)k with focal length 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 convergingpt. v)kq0 w(sk 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 ti5lon4c:j zg /o 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 ram1n3s jq/ nt.mf8 xj+ovr ou:*dii of 34.2 cm and 23.8 cm. What is the focal length if n = 1.+ /fqroj1o3 ujm8tv nmx .:s*n52?    cm

  Both surfaces of a double conv+kup i k+/mk. ak/rl2qex lens have radii of 31.0 cm. If the focal length is 28.9 cm, what is the index of refraction of the lens materiapk k.++ /2ak irlmu/qkl?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm. What is the vd n62srtu.32hor kx :radius of 3v2sd.rh: ktxru6n o2 the concave surface?    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat suxpv6 ;o2x3h4rkz/7mmkx sq.l0;rlt irface and the other hastpvk4 k73lsxr0 xm.r ;/x;2mqo6hzli R = -18.4 cm. What is the focal length?    cm

  A symmetric double convex lens with a fdw,v4da w )zgdee/t(/ocal length of 25.0 cm is to be made from glass with an index of refraction of 1.52. What shoul/(/ae4 tdwdw )zvedg,d be the radius of curvature for each surface?    cm

  A prescription for a corrective lens calls for +1.50D. The lensmaker g ; c a6-fpj:ci7dsxi)zrinds the lens from a “blank” with i 7s) cdj;-icx: 6fazpn=1.56 and a preformed convex front surface of radius of curvature of 40.0 cm. What should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.iwde9pvj4(r yy bz( *-0 m apart as in (Fig. Below). You stand 1.5 m away from one of (9 -vyb4di rw* pzjye(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 sv9uuv ,vv)*c+hj r+kbwimming pool filled with water. We measure the width (x=5.50m) and then note that the bottom edge of the pool is justvj 9v+ vbrc*v uu,+)kh 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 ioyy, kz2xz 0o,8ahi 2rs $\theta_{\mathrm{C}}=37.3^\circ.$ 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 cal1 + 8:rok8imsb kp3lrse of a spherical mirror. Specify what ts: 1m klbk3p88lr+ior his limit is.
(b) Determine an equation that relates the image and object distances in this limit of a plane mirror.
(c) Determine the magnification of a plane mirror in this same limit.
(d) Are your results in parts (b) and (c) consistent with the discussion of Section 23–2 on plane mirrors?

Stand up two plane mirrors so they form ,mp,8n:qmjoijb ) e+ca 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 auu r2mkvk6re* u( 7kl: real image of a real object. Can you describe a situation in which a div rm6*luk 7v( kuer:2ukerging lens can form a real image?

  Each student in a physics labp eobl3 )9l4ct 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 object. Two students complete tc3tb )l94l poehe 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 pr kq jnkg+(xr5ccq*va. g:ng 3a-rq1u*ism 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 cylindnb 1jcfzl5cki:mij.(eb 9).u rical glass rod $(n=1.54)$ are perpendicular to the sides. Show that a light ray entering an end face at any angle will be totally internally reflected inside the rod when the ray strikes the sides. Assume the rod is in air. What if it were in water?

A lighted candle is placed 33 cm in front of a converging lens orgnfb 1cz2 wj)u 6,t4af 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 lens of focal lengthz-l v29g*s9f:al bkwt f, and a white screen for viewing the imagek-2sg9lzb9avl*w:f t 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 projes(: 6le2mxa 4; z9 ow/7qtj8qzkmqntrctor, the film acts as the object whose image is projected on a screen (Fig. Below). If a 105-mm-focal-length lens is to project an image on a screen 8.00 m away, how far from the lens shou:(el ; /m9kmrj 2sxaqq7wqz4nt 6tzo8ld 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 j98 s 3ovy)gq*soa/g ssize is 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 projector. What focal-length lens should be used if the image is to cover the scjg/s)89ov aq o3s*ygsreen?    cm

Show analytically that the image formed by a converging lens is real +imd.m.fa,a ;b9yk dhand inverted if the object is beyond the focal pad;9+ y.mf .bidah, kmoint $(d_0>f),$ 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 pvj z 1-c(ejk+victures of her at home. She claims the reporter was trespassing. To prove her point, she gives as evidence the film she s-vz1cejv(+ kj eized. 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 came q/mao9 z lnkj9mbh(7,fni4, yra 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 b, :r ql0fst 1mhab;)uis imaged 8.20 cm in front of that lens (on the sa 1bf :rla0su)t; m,hbqme 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)