What would be the appearance of the Moon i n7+h4mku e9q 0w.qrovf it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the 13w:sbj k0ck iwhole Roman fleet in the harbor of Syracuse by focusing the rays of the Sun with a huge0 s3kkbcj1iw: spherical mirror. Is this reasonable?

Although a plane mirror appears to reverse left and right, nxmfi 3xl2 :+xq 5isn9it doesn’t reverse up and down. Explaxfs9l xn x2n+iqm:53i in.

If a concave mirror produces a real image, is t y2h j1ocxta:7he image necessarily inverted? Explain. axty ocj:h127

An object is placed along trs27vdw/fx5 ) ukkr y;he principal axis of a spherical mirror. The magnification of7;s f k)vwrk/ xdy52ru the object is -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 a), kg5m1w gx fq p;u0eo/xf0q2m.0j/ oaidraw 5x0qgwfo e; p . m/mgkxf u2i/qjao010ray 2 for (Fig. Below b).
(a)
(b)

What is the focal length of a plane mircx*(/eih 5wod ror? What is the magnification of a plane mirror?eh di/(ow*x5c

When you look at the Moon’jafzm/.an4x(/ 9vj nts reflection from a ripply sea, it appears elongated . Explain..a4mn/(jzn9 t /fjxva

What is the angle of refraction when a light ray meets the boundary betweefk4/a 8ux-z iyn two materials -uf4ky xi/za8 perpendicularly?

How might you determine the speed of light in a solid, rectangulm tc lt7xo:81q(ca imam;u bv4-54 orhar, transparent a ubr(o7m4c-xavm1til;m :o8tq4 c 5hobject?

When you look down into a swii5eah-pm;8 dz mming pool or a lake, are you likely to underestimate or overestimate its depth? Explain. How does the apparent depth vary with the viewing angle? (Use ray dp 5hm8d;zie- aiagrams.)

Draw a ray diagram to show why a stxfm,r*i i9xtu(j lzel0l c652 ick looks bent when part of it is under water (Fig. Below)2e mr l9xi0i*(u ,l56ljtcxfz.

Your eye looks into an aquarium and vi*kkibrfc1,yze6 8 ( vyews a fish inside. One ray of light that emerges from the tank is shown in (Fig. Below), as well as the apparent position of the fish. In the drawing, indicate the approximate position of the actual fkzickr ,*1v e(8byyf 6ish. Briefly justify your answer.

How can you “see” a round drop of water on a table even thoxd-+5v4nsm1 rr +ef cuugh the water is trans+cv4+usrx rm1ed nf- 5parent and colorless?

When you look up at an object in air from beneath the surface in a+ k8cbbia5bxkka 7+j/ swimming pool, does the object appear to be the same size as when you see it directik kax /bjbbck+ 8a+57ly in air? Explain.

How can a spherical mirror h7mh8y- cxt)r vai1n 2fave a negative object distance?

Light rays from stars (including our Sun) always bend toward the vertical x+b-j vbrl3h :8r: wabdirection as they pass through the Earth’s atmosphererb xvb+r:-aw:jbh8l3 .
(a) Why does this make sense?
(b) What can you conclude about the apparent positions of stars as viewed from Earth?

Where must the film be placed if a camera lensnx3 -tho ys+r* is to make a sharp image of an object very tsny3oxr- * +hfar away?

What type of mirror is shown in (Fig. Below)? Expla, wv2p/k5ukb din.

A photographer moves closer to his subject and then refocu x4u.uo3v xc+wses. Does the camera lens move farther from or closer to the film? Explu voxw.u34 xc+ain.

Can a diverging lens form a real image under any circumstances? Explainp4 r8xovp5mb pmlx+2 9.

Use ray diagrams to show that p7hx5aungl, k8 4p2o ba real image formed by a thin lens is always inverted, whereas a virtual image is al,kb54lp axuo 287ngh pways upright if the object is real.

Light rays are said to be “reversible.” Is this consistent with the thin lens :fhsw3y7 bf8fequatiyhw3ff: 8sb f7on? Explain.

Can real images be projected on a screen? Can virtual images? jd-4p5 gl;u g xz0rl rcr:0s)yCan either be photographed? Discu ;ysj ldg5c-l :x4rrpgr) zu00ss carefully.

A thin converging lens is m, efb-4vihk wd9p,;v boved closer to a nearby object. Does the real image f-v9wp ,;hd bkfeib ,v4ormed change
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of refractior4 yw2b6f-g fun n = 1.30 In air, it is a co r2-b4fu6 wygfnverging 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 the air stands facing a convqcbud d2j8tt 3 6xn;,5ke-uv(jggas 6erging lens. If the nose and the tail are each focused on a screen in turn, which wgetd;acvugu k ,5sjb2 (6 tnd38 jqx-6ill have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facing a converging lens. Under what (ukv.3(c;v5n b( lyh1f g8efok b q:uycircumstances (if any) would the image of the nose be virtual and the imageuock q(efylngbvvhk;fu 85b:( 1y3(. 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 than th fgq,pb+7k 8txyh 4q1xe diverging lens if the latter’s focal le+7 4fbhpxxq81 qkgty, ngth is to be determined by combining them?

Explain how you could haveqqqkqywo ,q(nu69zsi j +.t1;ys ,c1a a virtual object.

  An unsymmetrical lens (say, plan6 w)agpa:4tqhoconvex) forms an image of a nearby object. Does the image 4:agpqt 6ahw)point change if the lens is turned around? ----待选择----yesno 

The thicker a double convex lens is in the center as com29olpg4 j4ny +cg*xdlpared to its edges, the shorter its focal length for a g94 l*gon4+c yj2lpdxg iven lens diameter. Explain.

Consider two converging lenses separated by some distance. An object tk7c i/r*8 i5chy1et vwhzdp479a ik7 e ;imi:is placed so that the image from the first lens lies exactly at the f/4iw h 78ev751c hpkd9*i;iak iezyc:7 tmir tocal point of the second lens. Will this combination produce an image? If so, where? If not, why not?

  Suppose that you want teu9 p6 6fme2r5pe b1fbo take a photograph of yourself as you look at your image in a flat mirror 2.5 m away. For what distance should the camb9 fep u261ber6epf5mera lens be focused?    m

When you look at yourself in a 60-cm-talxsmie m+ 6;; i2eh3tell plane mirror, you see the same amount of your body whether you are close to the mirrorm 3xs;eee ;+lh26itmi or far away. (Try it and see.) Use ray diagrams to show why this should be true.

  Two mirrors meet at a k l1em wi2 7tggs)qs4l2kw2a4r 7eu0hm q5:ff135$^{\circ}\,$ 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 a)0yu im wydh/5re 1.68 m above the floor stands 2.20 m in front of a vertical plane my/i)5 uhmy wd0irror 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 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 is used to 5ru38c chqw-l0- hoj6x jq; kqreflect the rays entering one eye from a point;30kho 6jqhrx cql--j8 wquc5 on the tip of your nose if your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mira*6h m4qfx/4 rt3a acbrors 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 po7d) xt6 +hknu8wo9uueinted at the Sun, focuses the Sun’s rays 18.0 cm in front of the mxh u8w6ednu)k u9 to+7irror. What is the radius of the spherical surface from which the mirror was made?    cm

  How far from a concavefbx; j 0*i/hhh mirror (radius 23.0 cm) must an object be placed if its image is to be at infin/h0;xfh jbhi* ity?    cm

  If you look at yourself in a shiny Christmas tree balwx lebhf8 oizm.*m* 5x:wjb1,l with a diameter of 9.0 cm when your face is 30.0 cm away from it, where is youmjw el ,x:mobh.8* ix*f 5bz1wr 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 uprigm5jjbj8vu d1 7ht image of any person who stands 1.4 m in front of it. If the imag j1d7j8jubvm5 e is three times the person’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror that, when 2rg 3;;rsf2su u.20 cm from a tooth, will produce a $\text{4.5×upright}$ image. What kind of mirror must be used and what must its radius of curvature be?
 ----待选择----convexconcave 
r =    m

  Some rearview mirrors produce images of cars behind you that are-;0g gh- r cj2mk5kkah smaller than they would be if the mirror were flat. Are the mirrors concave or convjmagchkhk0- ; 2 -rkg5ex? 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 uci549a+a odpconvex mirror of radius oidua59c+o pa 4f 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 3.0ncv vfy,gqf8fy; 4v3* m from a convex security mirror in a store. You estimate the height of your image to be half of your actual height. Estimate the qvfcf,g3;y8nfv4v* y radius of curvature of the mirror.    m

  (a) Where should an object be placed in front of a concave mx sl+e6- vsh4ass4gz;*zi0joirror so that it produces anhss 04 igsaxz ;s e-ol+jv*6z4 image 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 vitt0z 1mxed *7gidzyo1 ;ye0o9ewed in a curved mirror;t7o*m9oe yzx10dt0 idyzg1e. The 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 tec(mh, +go jb-azh*hjn4hniques,
(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 i( fftypg 70 jmpw(7i)5vo8qik.oa*p the magnification 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 that the mirror equation, Eq4p4 bpe)c hil). 23–2, is valid for a convex mirror as long aip ep4)cl)4hb s f is considered negative.

  The magnification of a convex +o2 :j+5i weynwsff0 cmirror is $+0.65\times$ for objects 2.2 m from the mirror. What is the focal length of this mirror? $\theta_2$ =    $^{\circ}\,$

  A 4.5-cm-tall object is placed 28 cm in front of a spherical mirror. It is desi1d5b,4td yfok f3p sw;poxyc q(hg*2( red to produce a virtual image that i 2 (qf*oc(d5dyp s,fokp1x; tg3ybh4ws 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 f :ce9wblw5x6y ace by a factor of 1.33 when your face is placed 20.0 cm 5wl:y bwxec6 9in 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 ivl4ab x ((y.hkn
(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 ika t c9s99:ba egpa,,ece 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 wat2rv76sa 4i.i+vquo hf er. What is the index of refraction of this s4i.a 6voqfvr+2 hius 7ubstance? n =   

  A flashlight beam strikes the surfapa owaw )j;bb6z8+w+ece 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 flashlightyw.ks7p+ qz8p n:og c4)-vcuj upward 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 spotlightmab 2z8up s6g-zy * qkgb-ju*- exits the water at an angle of 66azg-kb u*zsqy6 -u2pm*g- 8jb.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 s1(yw,lqjbqa wgn0; 6h,*s cfu een 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 wat h4xn8c*i r+ewer has flat glass sides whose index of refraction is 1.e+4x * ncrhiw852. 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 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 narz3)h+n.fmbz 7q.zm cn7: batf row beam of light from his flashlight, 1.3 m above the water level, onto the surface of the water n 73c7. zhn za .q+bfmzmfb)t: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 /lto iw(,dvm;.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) andx j vx;2zp z7q5hz,v/n is partially reflectez5/n ,zvpq 2jx7vh z;xd and partially 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 a uniform layer of i8dvmnuhm l) ld fec5)/9f 5+ktransparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the incident beam, independent of the incm) e5nh fu5c)8/+d lkvfi 9dlmident angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on a flat piece of glas t2.7,wup yknas with index of refraction n as in (Fig. Below). Show that if the ,n2k pu.7yatw incident angle $\theta$ is small, the emerging ray is displaced a distance $d=t\theta(n-1)/n$ from the incident ray, where t is the thickness of the glass and $\theta$ is in radians. [Hint: for small $\theta,\sin\theta\approx\tan\theta\approx\theta$ in radians.]

  What is the critical angle for th ;4+v6cu 5ybfl2ssv*8a gobpke interface between water and Lucite? To be totally internally reflected, the l8*2s;4u+v a b5scb6kvpgyof light must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–airf, nb7wfgj6 h1 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 oiu+ucxl lf a )v+d*4m1f 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 does not dl 1ci4 a+l x)u*fuv+mexit the water?    cm

  A beam of light is emitted 8.0 cm beneath the surface of am2t0 g zlph:w7 liquid and strikes the surface 7.0 cm from the point directly above the source. If total internal reflection owtm hgl z:270pccurs, 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 e ic3ocxznpkz 7v4y +jg2wjwkh;y* zp0:y17+ in (Fig. Below) at 45.0$^{\circ}\,$ as shown, but is totally internally reflected at the opposite side. If the prism apex angle (at the top) is $\phi=75.0^\circ,$ what can you say about the index of refraction of the prism? $n \geq$    (retain three decimal places)

A beam of light enters the end of an optic fiber as shown in (Fig. Belo bvqno*go7v*o* m4/ nyw). 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 1nobogm yq* **o/vn7v4.42. In other words, regardless of the angle the light beam reflects back into the material at point a.

  (a) What is the minim 2quz5;q;dn0cb tj b*uum index of refraction for a glass or plastic prism to be used in binoculars (Fig. Below) so that to*c2;;udz0 uqqtjb5 bntal 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-m3o.(eme (yombm-focal-length converging lens. Find the object y(.eb(3moo m edistance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to fo j*dpsyh6,ljjop* 7) zzn ,wnmf7f:6 zcus at a point 18.5 cm behind a lens.
(a) What kind of lens is it?  ----待选择----converging lensdiverging lens 
(b) What is its power in diopters? P =    D

  A certain lens focuses light from an object 2.75 m away as xr:*sx0+uf 0*rlnq5trif*j l 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 image real or virtuaitxsj*rl:*f0n0l ur*fq x5 r+l?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the power of a 20.5-cm-focal-oeq2zt1 c 3iiy5o+ l.ulength 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 converginfq ial/dmcd (71 2yisg :d81fng lens with focal length 24 cm to view a stamp 18 cm in front of the l1y 2q/:fd dmsgc7i(1n8fi dalens.
(a) Where is the image located?    cm behind the lens (virtual)
(b) What is the magnification? m =   

  A -5.5-D lens is held 14.0 cm from an object 4.0 mm high. Whvdaz )(7u rqu-s(1elv ha hu+,at are the position, type, and lu z7 a +uqva (dhve)1ruhs(,-height of the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lensy; s)w0t 5azoca+w xx: is used to focus an image on the film of a camera. The maximum distance allowed betweexzoc+ w 5wxaat0;s:)y n the lens and the film plane is 120 mm.
(a) How far ahead of the film should the lens be if the object to be photographed is 10.0 m away?    mm
(b) 3.0 m away?    mm
(c) 1.0 m away?    mm
(d) What is the closest object this lens could photograph sharply?    mm

  It is desired to magnify reading material by a factor of 2.5× wz z:co14g1p8wf o-:qypu aa: ahen a book is placed 8.0 cm befzc-a paa8u: :yz1gq1ow o p:4hind 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 froj.pz5gf7wh9h e8uhj( m an 8.0-D lens. By how much does the image move if the object h zwh .pjh(jeu597f8gis moved
(a) 1.0 m closer to the lens,    cm away from the lens
(b) 1.0 m farther from the lens?    cm cm toward the lens

  How far from a converging lens with a 8b1up 2ymwm*n focal length of 25 cm should an object be placed to produce a real image which is the same size as theub n* 2mm1wp8y object?    cm

  (a) How far from a 50.0-mm-focal-length lens must 7hr0+avu uyvhgkc0 (.-d fpd.an object be placed if its image is to be magnified 2.00× ckahr.07. f0-uvg d+h(u dypv and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm

  (a) How far from a 50.0-mm-focal-length lens must an object be placed ifx :0y5x6oln2oz lltaz)w t 3zjg6yh6- its image is to be magnified 2.00× alll zzytxw526ht)n3z-ao 6o60 j gxy:nd be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm (formed by some other piece of optics).]

  (a) A 2.00-cm-high insect is 1.20 m from a 135-mm-focal-length lensjteockl159 95 incpi 3. Where is the image, how high ic5 koinpci3lte9j1 59s 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 ob rq) q7i*241xh)1 dmxki pjjkcject and an image formed by a 75-cm-focal-length converging lens if the image)k)7 4 1kj2qmhxq1r*x ji pcdi is 2.5× larger than the object and is real?    m

  A bright object and a viewing screen are separated by a distance of 66.0 cm.nucj h684i8doo h b9o:ggxa;/ At what location(s) between the object and the sj8 o:o9oiaxh68 g/4 gh;ducbncreen 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-lengqpq4:. ke 5w4rszbj4 mth 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 mag4swkj .e :qb54zprm4q nification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens witi90/; y ibu0+1 gq ua-csehak ye6(qtxh $f=-31.5\mathrm{~cm}$ 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 cw;5tgti5 gs g(m behind a diverging lens. Parallel light strikes the divergsg;w5gt 5( itging lens. After passing through the converging lens, the light is again parallel. What is the focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Example 23–12 are now placed nboou)u39;v xtbg v( )only 20.0 cm apart. The object is still 60.0 cm in front of the first lens as in (Fig. Below). In this cnu;oxb3)o 9tb)vgvu( ase, 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 a bns77 1/tlux zvkrs/5re 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 locateds 7vksnl/ur 1 /zb7x5t 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 length of f8om4uubv - n( 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 left oomvn(u8 -4bfuf 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 focwyq094.84 ,mlma9s wzmjcyr cal length 20.0 cm and one diverging with focal length are placed 25.0 cm apart. An object is placed 60.0 cm 9m9.rl40wsm ,c8q j zwmcayy4in 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 oa:l k14rfl ws4vv8;t5 s yej1uf 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 85hc9yt2e sh i7vf rp:c8ur a/)uxae/*d 6 pfvcm and 23.8 cm. What is the focal length if n = 1.yt u/h75p e ucf 9xha 6r8f ve28*a/dips):rcv52?    cm

  Both surfaces of a double conv0+6f0 nsyp :,bezdbx kex lens have radii of 31.0 cm. If the focal length is 28.9 cm, what is the index of refraction of the lens material? +p dns0x6b0e,: bfyz k    cm

  A planoconcave lens l0756 dz7l)z : g2gqchq(w tlneq+ko v(n=1.50) has a focal length of -23.4cm. What is the radius of the concave surface? q+zo ):wcd6elz 7l (0 lg7hkgqn tvq52    cm

  A Lucite planoconcave lens (see Fig.uvyk2u3x 1 +zy Below) has one flat surface and the other has R = -18.4 cm. What is the focal length? +uxzkuv2 y3y1    cm

  A symmetric double convex lens with a focal le0hon cj r1yss- ynm-/ x;t( dvm*-vw)gngth of 25.0 cm is to be made from glass with an index of refraction of 1.52. What should be the radius ofm(-rs1 )gxtmvhy-jv c/ sd* own-0; yn curvature for each surface?    cm

  A prescription for a corrective lens calls for +1.50z uu:c;lj i)n9 h 4afb-c+bym.D. The lensmaker 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 should b hc+umzcf.:4aby ;)lui 9-j nbe the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fig. Below). You stand 1.ai73/p 5cf1++k dpfj9jcerqr6ip zo, 5 m away fr r 6kz/ejc9oi5j+ip p+,cfda1 7fqp3rom 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 th+9 dej ma8z*;v:u7a /aa5vmzheca7i ye depth of a swimming pool filled with water. We measure the width (x=5.5:a ic5/jzem9 had7ae *y v;8uam7+vza0m) 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 n q2yh3q( dyt 93pdh9ja certain piece 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 cac/x8,hd4ti34wub bzvngy9 /ves c )5je: lf -sn be considered a limiting case of a spherical mirror. Specify ,c/tnb /4dhu95x eswg8zv:-c lie b4j3 fv)yswhat 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 tr r0b/n t0dg;d*- j ,,iomdfwshey form a 90$^{\circ}\,$ angle as in (Fig. Below). When you look into this double mirror, you see yourself as others see you, instead of reversed as in a single mirror. Make a careful ray diagram to show how this occurs.

Show analytically that a diverging lens can never form a rea*wsmhd53ty +j v w8zn.l image of a real object. Can you describe a situation in which a diverging l3 mnsjwh*8vy. tdz 5w+ens can form a real image?

  Each student in a physics lab is assigned to find the location where a bri yi8bmo9vjy0 lyjs76 3ght object may be placed in order that a concave mirror with radius of 97vm i j80b3yoj 6yylscurvature 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 need to repeat the lab, and justify your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of a prism is x0ns) 1w( ubh f3zy3t-qtoo2 k$\phi=72^\circ$ 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 lq6x;i v 4z/(y6 80prjmouhniglass 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 33pg62nc l0kf6j w*oc;p cm in front of 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 placed on oneph;injzw2(6i/4 wgj f side of a converging lens of focal length f, and a white screen for viewing the image /wjhw(f 2pn4;6gj ii zis on the opposite side. The distance $d_T=d_i+d_o$ between the object and the screen is kept fixed, but the lens can be moved.
(a) Show that if $d_{\mathrm{T}}>4f,$ there will be two positions where the lens can be placed and a sharp image will be produced on the screen.$d_T$>4$f$
(b) If $d_{\mathrm{T}}>4f,$ show that there will be no lens position where a sharp image is formed.
(c) Determine a formula for the distance between the two lens positions in part (a), and the ratio of the image sizes.

  In a slide or movie projector, the film acts as the object whose image/ )e)wgz upt4q0pws8 w 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 should the s pwe)s /up)w0wt8gz4qlide 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 actualqoqj nc/i59lwqb w)1 /ly 24 by 36 mm) is to be projected on a screen 1.80 m by 2.70 m placed 7.50 m fromwo 9 j)/bqicn5qwq /l1 the projector. What focal-length lens should be used if the image is to cover the screen?    cm

Show analytically that the image formed by a converging lens is r*gae4s ce0ig )eal and inverted if th0 g) csi4gae*ee object is beyond the focal point $(d_0>f),$ and is virtual and upright if the object is within the focal point $(d_0>f),$ Describe the image if the object is itself an image, formed by another lens, so its position is beyond the lens, for which $-d_0>f$, and for which $0$<$-d_0$<$f$.

  A movie star catches a reporr oh00:m ztsaq:1ewb 2ter shooting pictures of 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 of the camera lens waswzh::0rm1qbet0a s 2o 210 mm. How far away from the subject was the reporter standing?    m

  How large is the image of,znh)5q 2 jbwk 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 nf qb/83ke1k4.zc9jn ze k3gr8.20 cm in front 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 ./en8jn f3qz1cb4r9egz kkk 3or 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.khvv ,: ih)vw:0 cm from a certain converging lens, it forms a real image. When the object 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 len): h ivkhv:v,ws.    cm