What would be the appearance of the Moon if it hadvk(lqo /ky -a 7a*ltc ow)/r7h
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman5sv7qha) u 6 f.xjj6flj :laq/ fleet in the harbor of Syracuse aj lu6qx5v/hfl :sfqj6.j)7a by focusing the rays of the Sun with a huge spherical mirror. Is this reasonable?

Although a plane mirror appears to reverse lef2ya c,nr(qhc +t and right, it doesn’t reverse up a +na ch2rq(,ycnd down. Explain.

If a concave mirror produces a real image, is t:zfj 2 nf*fq:she image necessarily inverted? Explainqnzff:*s2f :j.

An object is placed along the principal axis of a spherical mirror. dib4 *vo.yo8yby*twr 1r2,5wunr , gaThe magnification of the object is -3.0 Is the image real or virtual, inverted or upright? Is the mirror concave orgo*rbw1 a4.,n5yyvr du,82*w ybto ir convex? On which side of the mirror is the image located?

Using the rules for the three rays dil-pb+th : xnr8oac0n7 scussed with reference to (Fig. Below a), draw ray 2 for (Fig. Below brl08ac+:xhn-p 7otnb).
(a)
(b)

What is the focal length of a plane mirror? What is the magnificatioh+wq*g, vw. +pno1l vnn of a plane mql*ovn np++vwg .1wh,irror?

When you look at the Moon’s reflection fr6vsj9n5u e epch1cq0pps;0r4a9m a(v om a ripply sea, it appears elongated . Ex0nc(cee59 qaa0u6 s9; p r4vmhj1 psvpplain.

What is the angle of refraction when anhel; t p89xv) light ray meets the boundary between two materials perpen ;l)x8nt9hpvedicularly?

How might you determ i;a; n i5bv8hfoy8e 7saq 4voo*)9uunbmf7h:ine the speed of light in a solid, rectangular, transparent obj4:y;i7v m*nv )n f8aauboo8e9 ibhof5;q 7husect?

When you look down into a swimming pool or a lake, are you likely to underestimhfhsqn etn:mh,2 o:3*ate or overestimateon, *s:3 hh2mfn:qe th its depth? Explain. How does the apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks bent when part of it x*/v .e139 hngtvmzn bis under water (Fig. Below). /eg .zn3txv9v nb*1mh

Your eye looks into an aquarium and vi.84vnli vq8f8ir ex ;uews a fish inside. One ray of light that emerges from the tank i8;8i vf vr4euqx nl.8is shown in (Fig. Below), as well as the apparent position of the 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 o8ptcw k4; n4ttn a table even though the water is transpart;wt 8c4tn 4pkent and colorless?

When you look up at an object in air from ben.6mg l, orsj2mhz30n hn (4fvjeath the surface in a swimming pool, does the object appear to be the same size as when you see it d hj zj mrm04n2hlovgsnf .3(6,irectly in air? Explain.

How can a spherical mirror havq0t03 j0yzvioe a negative object distance?

Light rays from stars (including our Sun) alwayxywh:7-myvi*/4cucs 3 oi x(js bend toward the vertical direction as they pass imiuy chcxw :x jso/y43 -*v(7through 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 plad0x xe08csqfxhv8 3x t 2fys43ced if a camera lens is to make a sharp image of an object very faxcse 32xtxh83sqff4vd 0y08x r away?

What type of mirror is shown in (Fig. Below)?o2b: / y (b3s7coypdzz Explain.

A photographer moves clos. c3edc5)dsk9d*f,g g6ms -c;ttcu0yai4 dd ser to his subject and then refocuses. Does the camera lens moveei43uma90fds sd;).*d,- tc c sc6gkgty5 dc d farther from or closer to the film? Explain.

Can a diverging lens form a real image under any circumwhhfo+ ;7xaxwjm;3s+k9z2s9rlw nii: 0f( z mstances? Explain.

Use ray diagrams to show that a realq rf m1d7qja 2b 4a2nm.);qacu image formed by a thin lens is always inverted, whereas a virtual image is always u.bu27mq mdaq ;4 )jaq f2c1narpright if the object is real.

Light rays are said to be “reversible.” Is this ocdz*-c tc.-))(vvs.slatj .jjysw / consistent with the thin lens equatiyj*jt vvwazo/-)c sc- d )s.s.l. t(jcon? Explain.

Can real images be projected on a screen? Can virtual imanzqjv *mc+,u2ges? Can either be photograp+2j,* vncz umqhed? Discuss carefully.

A thin converging lens is mc+/kjr6fa+ l loved closer to a nearby object. Does the real image formed chl+6lkf c+/ jarange
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index ( 3o ozz p7cig1tuy81pof refraction n = 1.30 In air, it is a co7o 1gpt8( youz 31icpznverging lens. 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 tusnhxkx pddg*6+; w0 4he air stands facing a converging lens. If the nose and the tail are each focused on a screen in 0p;w* xhdgnd 4kxus+ 6turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands faci6/w) oz hbi)grbi 9ea1ng a converging lens. Under what circumstances (if any) would the image of the nose be virtual and the imag) 1r9)h6eg/iwb baz ioe of the tail be real? Where would the image of the rest of the cat be?

Why, in Example 13, mus:+uj1plb24r,d 6fccemf7q yn,8 4sv sdnfc)mt the converging lens have a shorter focal length than the diverging lens if the latter’s focal lengt6euvf bdm:1qrsn+,jsl ,n2m 4 47dc)fcfcyp8h is to be determined by combining them?

Explain how you could have a virtual objj;k a;)t2+a 4qrzyna1nnwd ero8e.l) ect.

  An unsymmetrical lens (say, planoconvex) forms nq5hhx/ijr4s9mr1it5 ws fy g/: w:y7 an image of a nearby object. Does the image point change i 5grf9h/ssy ht4rqxn w :7yij1wm: i5/f the lens is turned around? ----待选择----yesno 

The thicker a double convex lesf8+9p48rl ;skqtzz u ns is in the center as compared to its edges, the shorter its focal length for a given lens d9s88 tls qr+;z4zfpukiameter. Explain.

Consider two converging lenses sex1yj,caz;)pbzt f*8gf 9 8:zr iuqhq9 parated by some distance. An object 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 image? If so, where? ar:qubf8,9y t*)8 ;q9g cfxz1pzzjhi If not, why not?

  Suppose that you want to take a vum2 2va7l3a+ugt+k uphotograph of yourself as you look at your image in a flat mirror 2.5 m away. For what distance shoua g u7 ktauvu2+lv3m2+ld the camera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mirror, you se0* y:*qnw ojzte the same amount of zwo: j* 0q*tynyour body whether you are close to the mirror or far away. (Try it and see.) Use ray diagrams to show why this should be true.

  Two mirrors meet at a 135 5t: 0pcv8pdk 1unigd;tb49np$^{\circ}\,$ 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 thsu la81*y9- zo1zumyze floor stands 2.20 m in front of a vertical plane mirror whose bottom edge is 43 cm above the floor, (Fig. Below). What is the horizontal distance x to the base of the wall supporting the mirror of the nearest point on tho 1z8-sa9 yu1lmu*yzze floor that can be seen reflected in the mirror?    cm

  Suppose you are 90 cm from a n e+m ,s+5r3wa :eexifplane mirror. What area of the mirror is used to reflect the rays entering one eye fro+emewfan: xs5r 3,+ei m a point on the tip of your nose if your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors05bv)ptb k+4ifiki4 r 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 mirror pointed at the Sun, focuses the Sulg2aq:w m)45 ymp)djv n’s rays 18.0 cm in front of the mirror. What is the radius of the sphe4d5mapl2vjmyg ))w :qrical surface from which the mirror was made?    cm

  How far from a concave mirror (radius,pmj x9ec/u8r-8 ;s6fbghnum 23.0 cm) must an object be placed if its image is to be at infinc- u u/j x,mbpgn;hfr9s68me8 ity?    cm

  If you look at yourself in a shiny Christmas tree ball wit82 aor b+1paz9spf v9uh a diameter 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 invertedaop 29a18uv 9+szf bpr?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shows anfy+, r *4qqe qv mzqlzn; ;,yv;;6e-/ljfejo f upright image of any person who stands 1.4 m in front of it. If the image / ezl;6 j y-;*er zoqv,fmny +v;qlj,efqq;f 4is three times the person’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror that, when 2.20 cm fromu*k b5kkxuo .zi6( n/c 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 4zif 5 um(4 0hudf1tdksmaller than they would be if the mirror were flat. Are the mirrors conf i zmu41u4fk0dhdt(5cave 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 mirror o,85ew)9j v sw8 puj/hv9htpbof radius of curvat)9/8,vh9pwp5uw tobhej8 sj vure 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 ln6x (rl3wub-hem apm0 )u,)-xovx2z convex security mirror in a store. You estimate the height of your image to be half of your actual height. Estimate the radius -oax2- l0)le uvrhm, mxb p( 6xwz3u)nof curvature of the mirror.    m

  (a) Where should an object be placed in front of a concave mirroqhv* qte ct7+7r so that it produces an image +e qt77t vh*qcat 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 ifu8 erskd v(-4n a curved mirror. Thskdf uv84 r-e(e 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 techniq y:uqp;1smtr 9ues,
(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 co 9 (11+i-y:0vut uyen yxmxculq9s jh:nvex 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:t(* l)o hqji5l fzqz tw/b06s that the mirror equation, Eq. 23–2, is valid for a conv*/btzh0tf(j) :l 6iloq5 zsw qex mirror as long as f is considered negative.

  The magnification ofzyix3 qyj*)/78mdsw c a convex 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 b52o7-tai66 sxwq alcw bjof0;p )j *bcm in front of a spherical mirror. It is desired to produce a virtual image that is upright and 7 -wbja2)w56o6i;o 0abxf*jptlqcsb 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 cu o8)ky 13oeba factor of 1.33 when your face is p)1ek c ybou8o3laced 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 lighef q2g.(gad.z9 udnx r,e++vn t in
(a) crown glass,    $ \times10^{8 }\;m/s$
(b) Lucite,    $ \times10^{8 }\;m/s$
(c) ethyl alcohol?    $ \times10^{8 }\;m/s$

  The speed of light inc(xi+6+1o t,iyaq8kqn l x:dd 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 substance is 89% of its valueadkvl 1jo s31reun91+ in water. What is the index of refraction of this su +na1du j3o19lvsr1 ekbstance? n =   

  A flashlight beam strikes th kyot4:1d4wk4r cpl-h e surface of a pane of glass (n = 1.58) at a 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashlight upwa2/zvqwbyd3ez3rh6 (mn yc /6ze(.jmbrd from beneath the water at a 42.5$^{\circ}\,$ angle to the vertical. At what angle does the light leave the water? $\theta_2$ =    $^{\circ}\,$

  A light beam coming from an underwater spotlight exits the water at an an3ka2dnw17pkf gle of 66. a7nkpd21w kf30$^{\circ}\,$ to the vertical. At what angle of incidence does it hit the air–water interface from below the surface? $\theta_1$ =    $^{\circ}\,$

  Rays of the Sun are seen to 6vzaukq- o0k 2make 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 index of rodygb 7e8 su.-efraction is 1.52. A beam of light from outside the aquarium strikes the glass at a 43.5° angle to the perpendicular (Fig 7-uodgyse 8b.. 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 shinespumv4-ocs a7/ry;1 ws a narrow beam of light from his flashlight, 1.3 m above the water level, onto t14s op7ur; ysam/cw- vhe 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 gd(;k nj 1 bq*dc5l gjm50 sd9egn10t un,dj5lflass prism at a 45.0$^{\circ}\,$ angle to one face, (Fig. Below). Calculate the angle at which light emerges from the opposite face. Assume that n = 1.58.    $^{\circ}\,$ from the normal

  A beam of light in air strikes a slab of glass (n = 1.52) andz85f eva*y(ag0i) 7 blf ec52tcm kpf) is partially reflected and partially r tka *b75 v(y5f)8a )ezm2lpfcgiecf0efracted. 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+ttembgucs z59nh,vo) .i 8jv7s h,y9 on a uniform layer of transparent material, as in (Fig. Below), the direction of the emerging beam iho + s9nsjvvg.tz )um,y,t8579ibechs 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 otvw; zil(n (k:f glass with index of refraction n as in (Fig. Below). Show that if the iliwnkt(z v (;:ncident angle $\theta$ is small, the emerging ray is displaced a distance $d=t\theta(n-1)/n$ from the incident ray, where t is the thickness of the glass and $\theta$ is in radians. [Hint: for small $\theta,\sin\theta\approx\tan\theta\approx\theta$ in radians.]

  What is the critical angle for the interface between water )nq (dnni- rta z.7 g6xny)-zoand Lucite? To be totally internally reflected, the light musxd6ain-y r(.n-o t7)gnqzn z )t start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–air surface ihtvh iob 4(w;nve10:g s 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 c7feu* - iq pd/bjf.;6xq4vgmfm. Where must it strike the air–water interface, 7 fgu4d* qj ;ffv/xqb mpe6-i.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.x.*kag71oy4 z8 x*hhpw2t ebo0 cm beneath the surface of a liquid and strikes the surface 7.0 cm from the point directly above 1oa7g*pz2xh. bkt8ey 4wo*xh the source. 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) atgjfae)b;wm t c +l8 au7d06o/f2 qhiv9w7ciz1 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 showr1x5st sd (7 m-fugb7i/u extp8w6m,ln 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 intuplxw m 7t8,(f di7mx bss6-rgteu5/1o the material at point a.

  (a) What is the minimum index of refqe)h r+ m(e w6x g5y)k,,nblbsraction for a glass or plastic prism to be usw qh mr+ xbnks,))5yglee(6 ,bed 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 locato+3f2 /oxxjp6ja6ehel5 ntb -ed 78.0 mm behind a 65.0-mm-focal-length converging lens. Find the object distance hxxb+jpaooj2 e5e6n3f/- tl6
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.5 cm a0 s2ank0czh6behind a lens.
(a) What kind of lens is it?  ----待选择----converging lensdiverging lens 
(b) What is its power in diopters? P =    D

  A certain lens focuses light from an object 2.75 m away as an image he *a 6i j(v(0guptkz,qp w ,:jgx*h2k48.3 cm on the other side of the lens. What type of lens is it and what is its focal length? Is the image real orp2az(ep q,v0h*jkt hk,wj:* x(i6u gg 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-fo, u)qmo t nd92mom/m9wo8d;n acal-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 fg2qqjyw s0 a/, t/8yf9yi ior;ocal length 24 cm to view a stamp 18 ciya; qf/ 02twio g8syj,yr 9q/m in front of the lens.
(a) Where is the image located?    cm behind the lens (virtual)
(b) What is the magnification? m =   

  A -5.5-D lens is helg4ply c ay7b(y d0d26zd 14.0 cm from an object 4.0 mm high. What are the position,(yby7g c0d4a 2z6ydlp type, and height of the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to fpt 8 pzuecytz4h9* f/v(0pw-xocus an image on the film of a camera. The tvz(c-eyzt p 89h/*p 0u xp4fwmaximum distance allowed between the lens and the film plane is 120 mm.
(a) How far ahead of the film should the lens be if the object to be photographed is 10.0 m away?    mm
(b) 3.0 m away?    mm
(c) 1.0 m away?    mm
(d) What is the closest object this lens could photograph sharply?    mm

  It is desired to magnify readiggh9 *ppv/qmbie+ bmb),d 2z+ng material by a factor of 2.5× when a book is placed 8+mmzg +b,)p g9b2 / iqdbv*hep.0 cm behind a lens.
(a) Draw a ray diagram and describe the type of image this would be.  ----待选择----realvirtual 
(b) What type of lens is needed?  ----待选择----converging lensdiverging lens 
(c) What is the power of the lens in diopters? P =    D

  An object is located 1.5 m from an 8.0-D lens. By how much does the iujzrl213 +ejkr jy7ow x:z1f5mage move if the object is moverz:xf3jjz5ry e17j1 + wulok 2d
(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;b )f wfs,dok1 o3zty4y f/r0n with a focal length of 25 cm should an object be placed to produce a real imagez bwf)f 1 3ot;4sdyk nr,of0/y which is the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-l)j3 0wb0mp vhkength lens must an object be placed if its image is to be magnified 2.00× ) bhm0v p03wjkand 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-focaj(ti+ 2nh 2g w4kmx/qrl-length lens must an object be placed if its imaxmgirq/kh 2t n j+24w(ge is to be magnified 2.00× 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 isg5 igtqs5i3m( 1.20 m from a 135-mm-focal-length lens. Where is the image, how high is it, 55( tsiggim 3qand 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 fox4,05n excf ihll2u4grmed by a 75-cm-focal-length converging lens n0xue i45 4lhcxlg,f2 if the image is 2.5× larger than the object and is real?    m

  A bright object and a viewingjnd;pi 6xqn :tzu( p(g u/.vk1 screen are separated by a distance of 66.0 cm. At what location(s) between the object and the screen should a lens of focal length 12.5 cm be ppudnqiu( ;/(jtn1vgk.:zx 6placed 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 lenses are placed 16.5 cm apa ao:qt 81 bkly/+g1ykq/s (fkbrt. An object is placed 36.0 cm in front of one lens. Where will the fin:o la+ykfq /kbb1g k (/1y8qstal image formed by the second lens be located? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens with 4:x;a2yrp z zf zu3vgr ,2y.y/dlao* czp4e9r$f=-31.5\mathrm{~cm}$ is placed 14.0 cm behind a converging lens with $f=20.0\mathrm{~cm.}$ Where will an object at infinity be focused?  ----待选择----realvirtual ,    cm beyond second lens.

  A 31.0-cm-focal-length converging lens is 21.0 cm behind a diverging lens. Paramlb mm:5ht*( op5km:ullel light strikes the diverging lens. After passing through the converging lens, the light is again parallel. Whmmm 5k:(om b:h*t5ul pat is the focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lensea1p.9na ekka)s of Example 23–12 are now placed only 20.0 cm apart. The object is still 60.0 cm in fa)k9ak ap.1 neront 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 d dqehvb6qbn+3 by-9( are 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 + b9ye dq3n-6qhb(vbd15.0-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 lengthjn cq 0o;ach01v qv)p; of is placed 12 cm to the right of a converging lens with a focalaq n occh1v;qpj;)v00 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 length 20.0 cm and one diverging with foc2:cwr*9mwjqgo mm:xx -+ke h 4al length are place rjewxo ch:4 g-m *92wqm:k+xmd 25.0 cm apart. An object is placed 60.0 cm in front of the converging lens. Determine
(a) the position    cm to the right of the diverging lens
(b) the magnification of the final image formed.   
(c) Sketch a ray diagram for this system.

A diverging lens is placed next to a converging le1hi m q8d/j2rcns of focal length $f_C$ as in (Fig. Below). If $f_T$ represents the focal length of the combination, show that the focal length of the diverging lens, $f_D$, is given by
$\frac{1}{f_\mathrm{D}}=\frac{1}{f_\mathrm{T}}-\frac{1}{f_\mathrm{C}}.$

  A double concave lens has surface radii of 34.2 cm and 23.8 cm. What is t447rt8byn. jqsgwwaz 5//u g orx6i9khe focal length if n = 1.52? jo4u4qy7g i 9z/6wbg.8x/ras nrk5tw   cm

  Both surfaces of a double convex lens have radii of 31.0 cm. If .ueuc,fsybi6 6/h19 y:ajr.l kt)zwjthe focal length is 28.9 cm, what is the index of refraction of the lens material?rh9j .fk1 w6cz,: 6ulei/jayus)yb.t    cm

  A planoconcave lens (n=1.50) has a -e)aj()5jed4ace ffk focal length of -23.4cm. What is the radius of ef)j 5kj4(eace)afd -the concave surface?    cm

  A Lucite planoconcave lens (s*pz7l vpv7f8 z 03aposee Fig. Below) has one flat surface and the other haz7pp73v0sp*afv zlo 8 s R = -18.4 cm. What is the focal length?    cm

  A symmetric double convex lens with a focal length of 25.0 cm 8tc8nk9tjbghf e ;a:8is to be made from glass with an index of refraction of 1.52.e9 cjt h8; ft:bgkn8a8 What should be the radius of curvature for each surface?    cm

  A prescription for a corrective lens calls for +1.50D. The lensma(ogxg7yfc2-d4 a * wedker grinds the lens from a “blank” with n=1.56 and a preformed convex front surface of radius of curvature of 40.0 cm. What shoy7o *c2x(egag f- d4wduld be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart aaf2 xvs4.:l ejs in (Fig. Below). You stand 1.5 m away from one of these mirrors and look into it. You wilv j24.e:axfsll see multiple images of yourself.
(a) How far away from you are the first three images in the mirror in front of you?
$d_1$ =    m
$d_2$ =    m
$d_3$ =    m
(b) Are these first three images facing toward you or away from you?
the first image is facing  ----待选择----toward youaway from you ;
the second image is facing  ----待选择----toward youaway from you ;
the third image is facing  ----待选择----toward youaway from you .

  We wish to determine the depth of a swimming pool fillewdl jc7cpb8p0 b. :,lmd with water. We measure the width (x=5.50m) and then note lc mppd ,0jbbw:cl. 78that 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 pi s- 8lw;)yrfi u5okk;qece of plastic in air is $\theta_{\mathrm{C}}=37.3^\circ.$ What is the critical angle of the same plastic if it is immersed in water?    $^{\circ}\,$

(a) A plane mirror can be considered a limiting case of r54zs 1ig3uw gfszk 8x;ki1 3ta spherical mirror. Specify whatx33iwg1sz5ur;k zikf 8g4ts1 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 the;h(kt; s7pxrg y form a 90$^{\circ}\,$ angle as in (Fig. Below). When you look into this double mirror, you see yourself as others see you, instead of reversed as in a single mirror. Make a careful ray diagram to show how this occurs.

Show analytically that a diverging lens can 3pklqqi ll,.zfug- 8a* uo6n8never form a real image of a real object. Can you describe a situation in which a diverg68. nq8ukig,olul-zq 3lp a*fing lens can form a real image?

  Each student in a physics lab is assigned to find the location where a mz.2arxojp-1rvf,w2(6q ww bh l 8+ znbright 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 the2.nw8x6hq,+1pz -w mzbr2r(l vao fjw 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 abaq33x vmw)k 7 prism 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 w;kg;ke9xthhzqp*e d6 m k0imx3,8g+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 converg yl3 jj:ul8dpgwwh6k..c 0jv8 ing lens of focal length $f_1=15\mathrm{~cm},$ which in turn is 55 cm in front of another converging lens of focal length $f_1=15\mathrm{~cm},$ (see Fig. Below).
(a) Draw a ray diagram and estimate the location and the relative size of the final image.
(b) Calculate the position and relative size of the final image.

A bright object is placed on one *-njj yoxo7.hside of a converging lens of focal length f, and a white screen for viewinjoon y*7-.hxj g 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 avj9+lwof-jv/ b);we x s the object whose image is project jwbe-ojlw+; )x9 vv/fed on a screen (Fig. Below). If a 105-mm-focal-length lens is to project an image on a screen 8.00 m away, how far from the lens should the slide be? If the slide is 36 mm wide, how wide will the picture be on the screen? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (picture size is actually 24 by 36 6ktwfo)ce0u 6mm) 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 icfu6)6 o0tk ewf the image is to cover the screen?    cm

Show analytically that the image formed 2f7lf3) spvlog)s 1bc* 1,cikyl )xmx by a converging lens is real and inverted if the object is beys )vyc1 l)kx )slp7mi l3b1o,g*ffc2xond 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 catches0b wqasno,bm pq(.44o,-p8isayyko , a reporter shooting pictures of her at home. She claims the reporter was trespassing. To prove her point, she gives as evidence the film sheo iws,nsyq,0ya4(okq4a om8. p-b p, b 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 u*mn 2/etomrtx3g )d a0(qi xl,xi wy:gayw*(2sed 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/3sufiv .fbp) front of a certain lens is imaged 8.20 cm in front of that lens (on the same side as the object). What type of lens is this, and whatbpi/f )sf v3u. is its focal length? Is the image real or virtual?    cm (diverging)  ----待选择----virtualreal 
(b) If the image were located, instead, 41.5 cm in front of the lens, what type of lens would it be and what focal length would it have?    cm (converging)

  When an object is placed 60.0 cm from a certain c*o8;-r fwa(zf/x4bflo nlk jk4y4v8jonverging lens, it forms a real image. When the ob k488jav4 ;fbfo nr *k(oxj4zf/ll wy-ject is moved 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