What would be the appear g./ f/taky5rjfnq. a7ance of the Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned t-;r css.s:l lche whole Roman fleet in the harbor of Syracuse by focusing the rays of the Sun with a huge spherical mirror.r:ss;l cs.l-c Is this reasonable?

Although a plane mirror appe y+wa6i:qwon3 ars to reverse left and right, it doesn’t reverse up and down. Expl oa36qyn+ :iwwain.

If a concave mirror produy..4 a/1pv;x c ahsv9vsg+vgkces a real image, is the image necessarily inverted? Explain.ha9+s1 v xg akc.v vv.s;pg4/y

An object is placed along the principal axis of a spherical mirror. Theisrq8fg y,k;i2 od89c magnificas2i8dior9;g 8, kyfqction of 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 f01m yq.um5v+to fra-with reference to (Fig. Below a), draw ray 2mff1. vqr0 tm-5+ay ou for (Fig. Below b).
(a)
(b)

What is the focal length of a plane mirror? What is i *,haiee.1w; 7ml u ze/;kxunthe magnification of a plane mirrore n*kmw/1;hue l;iex 7aiu z.,?

When you look at the Moon’s reflection from a ripply sea, it appears ellhknl.:z o2i)ongated . Exphk.lli z2)o n:lain.

What is the angle of refraction when a light ray meets the bodae) lsl.pgz(:8u ;t oundary between two materials perpendicetull. as: ; z8gop()dularly?

How might you determine the speed of light in a solid, rectangular, transpar6 xy9az(u nj8rent object?rzyn au869x(j

When you look down into a swimming pool or a lake, ar.ps6e1 ozrmv j5qyzv)bfp/ 9hg64p 2we you likely to underestimate or overestimate its depth? Explain. How does the apparent depth vary with the viewing angle? (Use rap vgs1of 66)e/wz94y25 bzphqr vmp .jy diagrams.)

Draw a ray diagram to show why a stick looks bent when part of(nnv.x7 f pw3e it is under water (Fig. xfw(e .7v3nnpBelow).

Your eye looks into an aquarium and views a fish inside. One ray of light thatc(m6u kw+pa 7q emerges from the tank is shown in (Fig. Below), as well as th6wacp kum(q +7e 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 on a table even thgdca q8c4v hmk: )h-r(g* fkf7;t5abaough the water is transparent and colorlet8 )ghv f7cba*radg5qm h;ak-kf( : 4css?

When you look up at an object in .ko.c s*t: p1i3fpwzz wr2h0 aair from beneath the surface in a swimming pool, does the object appear to be the skp r0zo1: zw2if3* hw.c.tap same size as when you see it directly in air? Explain.

How can a spherical (v1g/ -a;a gx88b x2sxhpyn bemirror have a negative object distance?

Light rays from stars (including our Sptr zh8/*6jb eevwa am24, f3cun) always bend toward the vertical direction as they pass through the Earth’s atmosphere.mapwj6br v8 * zhee/ta2c3,4 f
(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 uyx vj0//7 3f: 6s(wdo;cgf ajd rp-sibe placed if a camera lens is to make a sharp image of an object v/3 a(fx6sfjjd 0or7dcip :-;w/ u vgysery far away?

What type of mirror is sho0b:5qsvx, cusz 6 y,brwn in (Fig. Below)? Explain.

A photographer moves closer to his subject and then refocuses. Does the camera 9ldz xz;dd8j bff69 vs77iun;lens move farther f7z8f v79z ;dddf;xlsbu9jin 6rom or closer to the film? Explain.

Can a diverging lens form a real image under any circumstances?.xz: 5z3lwj)k/ cn5 udhh rezo6mw7, m Explain.

Use ray diagrams to show that a real image formed by a thin l6qudt 8wpnh0w1 6 lkx m6j (,1qe0onorens is always inverth uo r0(,1xt ewlmjwd6p0o68n1q6kn qed, whereas a virtual image is always upright if the object is real.

Light rays are said to be “reversible.” Is this ct,p* fz7(gun.xr v(p consistent with the thin lens equation? gpfxr,u.cz 7*( np (vtExplain.

Can real images be projected on a scrlg t6 )7u.jfva kx: 7zo8h kfgzhz9i99een? Can virtual images? Can either be photographed? Discuss carefull)axl: hjfz87zk9.g9 ok 6h7tui fz 9gvy.

A thin converging lens is moved closer to a nearby object. Does the real vll5edojex., uub(z.,wo4 9 mimage formed cxz. uuj vwe o5om.9d, ebl(4l,hange
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of refractioamed8v 0y )e5ln n = 1.30 In air, it is a converging lens. Will it still be aev5d)0e amyl 8 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 converging lens. If thsyz/1v6(a+ean+b b4b p(sn66ejmw u v e nose and thesb nj v+ (uvn6ze1ba+4(ywm/bse66pa 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 6dukqoz t.1xg9/ wr, 1 :wuuxcconverging lens. Under what circumstances (if any) would the image of the nose be virtual o6dt1k1wu 9qc w:x .uug,/zrxand the image of the tail be real? Where would the image of the rest of the cat be?

Why, in Example 13, must the cjemja4r en 0s-4ns9u*ip1xgwi -8l9 aonverging lens have a shorter focal length than the diverging lens if the latter’s focal length is to be determined by combining 9rpix0 es*l9a8eg1nm jsuw4 n 4-jai-them?

Explain how you could have9y sz))bi ovdmmj .**b a virtual object.

  An unsymmetrical lensxn9a+ 7emfq 4d jgll34 (say, planoconvex) forms an image of a nearby object. Does the image poi+dx7le 3fj4g4m 9ql annt change if the lens is turned around? ----待选择----yesno 

The thicker a double convex l*y1b .gyj68 kmlbcj/fens is in the center as compared to its edges, the shbb6 m*jgkl j .fc/y8y1orter its focal length for a given lens diameter. Explain.

Consider two converging lenses separatklnv.. : ,;k ojv/m:5bfwozm ted by some distance. An object is placed so that the image from the first lens lies exactly at the focal point of mj.5vooz, b w.:fnktl/k m v:;the second lens. Will this combination produce an image? If so, where? If not, why not?

  Suppose that you want j 1.adtoi:nji3rv6a4 to take a photograph of yourself as you look at your image in a flat mirror 2.5 m away. For what distance should the camera:jv.3a in4jatd61iro lens be focused?    m

When you look at yourself in a 60-cm-tall plane miphab;+ ;qpob0 rror, you see the same amount of your 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.; p+opahbb;q 0

  Two mirrors meet at a 13b*)7 qjpl*2ie :zxd7hxs rf1w5$^{\circ}\,$ 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 floorxzq/d9 ()6iaz7 rc07y ,papwpil.xtv)(pbnq 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 0 w,l/bp ()97aytn6xaqpqdpr(c7)iizx v z.pon the floor that can be seen reflected in the mirror?    cm

  Suppose you are 90 cm from a plane mirror. e5dx iv9haz 8:c vn;b9What area of the mirror is used to reflect the rab :i; d 8vc59ehnxvaz9ys entering one eye from 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 mirrors megcb:hl ek5 7q ts93k5u2lajm(et 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 p5qq5 elr pak/knx j(e)g/y9: a concave mirror pointed at the Sun, focuses the Sun’s rays 18.0 cm in kxrq/nk/p:)5eg e l a(qjpy59front of the mirror. What is the radius of the spherical surface from which the mirror was made?    cm

  How far from a concave mirror (radius 23.0 cm) must akw- 7 59.yw0d 3-vb:dl99hephxjqx c zccp,xhn object be placed if its image is to be,z9 ewx9yx hlpjcq:w5b7.3ph-9- dhk d vcc0 x at infinity?    cm

  If you look at yourself in a shiny Christmas tree bax pmq,9ixjby6x,p) ( lll with a diameter of 9.0 cm when your face is 30.0 cm away from it, where is ybxlpxqmi,6,9yjp) (x 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 of any person who stands 1.l*n.8z* .sn,psgcbiuh,z, y g4 m in front of it. If the image i z un,,py8ng. s*chsbg*li ,.zs three times the person’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror t8nkpf o;rys9) m) xomj2xd9; uhat, when 2.20 cm from a tooth, will produce a $\text{4.5×upright}$ image. What kind of mirror must be used and what must its radius of curvature be?
 ----待选择----convexconcave 
r =    m

  Some rearview mirrors produce images of cars behind you thaef5.v6*;jyxvaj,j us3ep ( d lt are smaller than they would be if the mirror were flat. Are the mirrors concave or convex? What is a mirror’s radius of curvature if cars 20.0 m awjvv5u,aexj f6.;y jpl(eds* 3ay appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is placjz1:jtks:s z;ed 20.0 cm from a convex mirror of radius of curvature 20.0 cm. :1:;st zjsjkz
(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 : g 1p8dci4g(lon;nqlin a store. You estimate the height of your il;o1i d:pg8 (nc g4qlnmage to be half of your actual height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object be p4x9hlna0p, tt laced in front of a concave mirror so that it produces an image at thehatp4,l0 9 txn 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 treed7i- *w th1j 7kos0o-jn;egau is virtual and very small when viewed in a curved mirror. The image appears to be 18.0 cm behind the mirror. What kind of mirror is it, and what is its jt *-su1 0oa-;7e7wn kod hgjiradius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different teches(l* .ea9/it w) shddniques,
(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 div*37j,sd lx1if. eqilu-+ zck agram, that 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 showe8jb7u82 akia3mw60db: i, atnqthc+pl*9 pj that the mirror equation, Eq. 23–2, is valid for a convex mirror as long as f is considered nek ci039nphaelmi6 a8td8bbqt2+p ,:u*j7wj a gative.

  The magnification of a co+, h:xd1ht apbmy9y/r nvex 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 front of qswkn6 5 3o 1lkzu6d064a; jcevg jtt-a spherical mirror. It is desired to produce a virtual image that is upright and 3.5 cm tall. dtgs zut 1l3va66jck- w 54 0k6joqen;
(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 mirrorm 1,,7: o(d5d,acdmzn dfu j: ojqrmb)dn0c6x is designed to magnify your face by a factor of 1.33 when mzcno j,om1d dd d x5 b0cd(f6mj)n::u,ar, 7qyour face is placed 20.0 cm in front of it.
(a) What type of mirror is it?  ----待选择----convex mirrorconcave mirror 
(b) Describe the type of image that it makes of your face.
(c) Calculate the required radius of curvature for the mirror. r =    cm

  What is the speed of light r.c3 1 cz1rh55gnrilu 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 in ic mw i;zihv4xwbb5c 0c:v9fj88n)pdb 7 noc*4fe is $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain subsn0q+0a4 q 7bkn5aq4ut db deo22y n:vztance is 89% of its value in water. What is the index of refraction of this substanb 4 2qq a5ndvez nno2t740budq+ 0yka:ce? n =   

  A flashlight beam strikes the surface of a pane of glass (n = 1.58) at*gb8q6n;*ztnt *-bw lu/y gnegf9h.w a 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashlight upward from beneaq9 m xk(mrn52ath 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 underw m-t orpod5l 9:yli *6ioisz4cm d5g-3ater spotlight exits the water at an angle of 66.0l*dl-oydcp9 s 5 -rio6o5 4mgiz:mit3$^{\circ}\,$ 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 seenxhh8c )*x;xyv to make a 31.0$^{\circ}\,$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?    $^{\circ}\,$

  An aquarium filled with water has flat glass sides whose index of refractions/j8pcds2u t 5ll h:g6(n w0wz is 1.52. A beam of light from outsuw2d/ cwl86hzs(0 s tl pnjg5:ide 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 y 6gtgreso8+;5ffkg9o 0e j(adr-9p y of a pool at night, a watchman shines a narrow 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 fromr gjega+yft9r6-; so 85( y0e9fogkd p 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 whcbjz d:(m8v0se45 7 r4dzdlv(zka + 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 aft09 d nsr sa6s3rcdxi+4cm -7 slab of glass (n = 1.52) and is partially reflected and partially refracted. Find the angle of incidence if the angle of refldtix+3adrssscm7n40rf 6c9- ection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam inm2vm+ fqccwk;-e1ix4cident on a uniform layer of transparent material, as in (Fig. Belowcxfck 4 1vq- imm+2;we), 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 of glass with index of refractionl ,a/* 8zwjo3w(dbe hz n as in (Fig. Below). Show that if the incident angle /wd(*, zab wlh3oj e8z$\theta$ 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 betwemj02 g 7e-5+b 7zkcw scvivf1uen water and Lucite? To be totally internally reflected, the light mus7jzkwe m7cc15v+isb2g0v -uf t start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liq,5tqd.l6o miuuid–air surface is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in a pool of water from a depth of 62.0 pyne8d6u6 ) elb5px3reaa9 1 zcm. Where must it strike the air–water interface, relative to the spot directly above it, in order that the light does not exi3 a8pel xyb9) d5erun6p1eaz6t the water?    cm

  A beam of light is emitted 8.0 cm beneath the surface of a li1 ulik6u(x:ul 5thbpvq731m r quid and strikes the surface 7.0 cm from the point directly above the source. If total internal reflection occurs, what can you uluqi15 (vxrl b 3 6pkt1:hu7msay about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left fkik u0*pce6a/tv+ zf. ace of the prism 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 shownve /7hfd3g7t - z )iss2d9aaybg3h8ha in (Fig. Below). Show that we dgsav)d38szia /y3t bh- 77ef h2hga9 can guarantee total internal reflection at the side surface of the material (at point a), if the index of refraction is greater than about 1.42. In other words, regardless of the angle the light beam reflects back into the material at point a.

  (a) What is the minimum index onx+;b k q+ azsww2g8v0f refraction for a glass or plastic prism to be used in binoculars (Fig. Below) so that total internal reflection occurs at 4n v0waq 2kb8+zx;sg+ w5$^{\circ}\,$? $n_1$ $\geq$   
(b) Will binoculars work if its prisms (assume n=1.50) are immersed in water?  ----待选择----totally reflectingtotally transmitting 
(c) What minimum n is needed if the prisms are immersed in water? $n_1$ $\geq$   

  A sharp image is located 78.0 mm behind a 65.0-mm-focal-length )w3 km-gurh h/mv,u ( 95fgcj,dyi(/aa uu f:tconverging lens. Find the vid:tu5fgcj( ,g/hy - a ar,)uwfhm9m3uk (u/ object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18qd/az)u fn8r 8.5 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 an image 48.3 cm ox/a/n4miq 3a4aw jgui- ug.+un the other side of the lens. What type of uw j-4au/.qu/ag3ni axg4im+ lens 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 power x r0 ,.x::x) y8ojbapds v6lnrof 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 g xh;(qw4mu 3s24 cm to view a stamp 18 cm i4 huxwmq3sg ;(n 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 held e;9 (pe fmww ll.+,onab0r(gg14.0 cm from an object 4.0 mm high. What are the position, ty opg(0ln+gel(we9f , .mwbr a;pe, 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 a camera v+c 14 fcl(r*gnej*iy. The maximum * v1* c(il fg+c4erjyndistance 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 reading material by a factor of 2.5× when a l)v/zqg nz,*p book is placed znl,g/ *vz)q p8.0 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 d 4cew0,ezf bp p5:mf) )ubim)bq+0q ehow much does the image move if the object is movepz500 ed4e)+mu,be)m bip wb: c)qfqfd
(a) 1.0 m closer to the lens,    cm away from the lens
(b) 1.0 m farther from the lens?    cm cm toward the lens

  How far from a converging lens with a focal pn7fig/lyor9; ;l,xl length of 25 cm should an object be / gnllf r9i;,7 p;olyxplaced to produce a real image which is the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an object be plah3zar0f b7 +va7i3au g4pf1mbced if its image is to be magnified 2.00× a40p3bu7i7+ hvf3 fbzr1gaam 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 if its im+ edz47 ziew)-ba 975viipbd t 7eh)qgage is to be magnified 2.00× a zeqdi vi)4btbhe7g7aez97pdi)-+ w 5nd 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 in+yl2uqa;j z k9sect is 1.20 m from a 135-mm-focal-length lens. Where is the image, how high is it, and what type ;kl9jzya2 qu +is it?
$d_i$ =    mm (real,behind the lens) $h_1$ =    cm (inverted)
(b) What if $f=-135\mathrm{~mm}$?
$d_i$ =    mm (virtual,in front of the lens)
$h_1$ =    cm (upright)

  How far apart are an object and an image formed by a 75-cm-focax/ .qhkd z7-qaso5mj8l-length converging lens if the image is 2.mjqzak7d5 sh/x-oq .85× larger than the object and is real?    m

  A bright object and a viewing screen are separated by a distancere)u -fu5 6lk6 b6gpzmd.eg, v of 66.0 cm. At what location(s) between the object and the screen should a lens of focal length 12.5 cm be placed in order to produce a g)u6 v -5k e6dg6 p.urmfe,lzbcrisp 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 166 lqaq u( a4bg270tevs.5 cm apart. An object is placed 36.0 cm in front of oneq42 u ls6atag07bvqe( lens. Where will the final 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 uw4dz.bk xs8/+ 91cjp sm;kjl lx/s;h $f=-31.5\mathrm{~cm}$ 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 1 * s rd 4njrrduv)qz5axm92v8lens. Parallel light strikes the diverging lens. After passing through the converging lens, the light is again paralu*r 2s 84v)rd5j z qmarnvx9d1lel. 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 place*th 0a1wa 9lceqm, 6.je2 t 0d23kcqnlcdl +hjd only 20.0 cm apart. The object is still 60.0 cm in front of the first lens as in (Fig. Below). In this c j e6 cw3,allhdteqqchtalk0c*90j m +n2.d21ase, determine
(a) the position of the final image,    cm
(b) the overall magnification.    cm
(c) Sketch the ray diagram for this system.

  Two converging lenses are placed 30.0 cm apart. The focal length of the lens on73:d s gsmosv e(kz/h8-pb)w l the right is 20.0 cm, and the focal length of the lv/omsz sl h 8 b(kwpgse73:d-)ens on the left is 15.0 cm. An object is placed to the left of the 15.0-cm-focal-length lens. A final image from both lenses is inverted and located halfway between the two lenses. How far to the left of the 15.0-cm-focal-length lens is the original object?    cm

  A diverging lens with a focal length of is pla7pklfv5v :lshvnjye/ 2 9 h:vr 4t25a6nd 7utgced 12 cm to the right of a converging lens with a focal length of 18 cm. An object is 2jr l uhk5v72 ygtvhvn 9el:tap/fs5vn4:6d7placed 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 anhbc)dj4nc6bct)6m 6u d one diverging with focal length are placed 25.0 cm apart. An object is placed 60.0 cm in front of the converging lens. Determ 6dbuh6t4c6 )cbjn)mcine
(a) the position    cm to the right of the diverging lens
(b) the magnification of the final image formed.   
(c) Sketch a ray diagram for this system.

A diverging lens is placed next to a converging lens of focal length9;vc b/m4 fwcu $f_C$ 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. m jb;v9qlr r+hl6-5xqWhat is the focal length if nllmxb rv9h6+j5q;-rq = 1.52?    cm

  Both surfaces of a double convex lens hav;af,m /r/zscve radii of 31.0 cm. If the focal length is 28.9 cm, what is the ind/,asvm/cf; rz ex of refraction of the lens material?    cm

  A planoconcave lens (nm :du 68qqa3hk)5jl bg=1.50) has a focal length of -23.4cm. What is the radius of the concave surface?ugl 6ka8 3mdqq h:5b)j    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat surface and the other rhghn5z 6-9xhyn8mu (:w pyt- has R = -18.4 cnx- y6 8mru pg(wzyhh:5 9n-htm. What is the focal length?    cm

  A symmetric double convex lens with a focal length of 25.0 cm is to be mho19 ha xevj 0bm,o:3sade from glass with an index of refraction of 1.52. What should be the radius of curvature foav:o 3jh0 o9bhs ,1xemr each surface?    cm

  A prescription for a corrective lens calls for +1.50D.*ivz37loh*5)xw su a l3cv2a b3i)aww6mnn:z The lensmaker grinds the lens from a “blank” with n=1.56 and a preformed convex front surface of radiunm)i7bin)a *z 6l*3 5swwv2uc xaawvl:o 3z3h s of curvature of 40.0 cm. What should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fig. Below)0t fi1(m7g bsm. You stand 1.5 m away from one of these mirrors and look into it. You will see multiple images of your mgbtfs710im( self.
(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 dep0e .a ex0;huhtth of a swimming pool filled with water. We measure the width (x=5.50m) and the0euhe.x0ht a ;n note that the bottom edge of the pool is just visible at an angle of 14.0$^{\circ}\,$ above the horizontal as shown in (Fig. Below). Calculate the depth of the pool.    m

  The critical angle of a certain piece of plasti n+13lac us5cuacb9 ,9b3 o, wj9supdfc 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 limitin9 4/cctletbu7 gnm l30g case of a spherical mirror. Specify what this u /7clt03m9ge4b tlnc 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 a 9* mabyel. 9(bq0$^{\circ}\,$ 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 real.fb rkc9woa 9mo,8du/ image of a real object. Cak c. /frbaw o8m9,odu9n you describe a situation in which a diverging lens can form a real image?

  Each student in a physics lab is assigned to find the location where a bk0gpc ng5rc) j,e3,fb 92fbvg right object may be placed in order that a concave mirror with radius of curvature r = 40 cm will produce an image three times the size of the object. Two students complete the assignment at different times using identical equipment, but when they compare notes later, they discover that their answers for the object distance are not the same. Explain why they do not necessarily need to repeat the lab, and justify y,gce29nj5fc0b v, b f3g gpr)kour response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of a prism iuz)n -9339 bozpfvyw ds $\phi=72^\circ$ 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 5st18vd7c 0bpb6m kjzglass 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 ,/x n4e aob*h3wfmg5l1(shcda 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 one hp2yn j:7ifk7kzk3n7i b3zc3mw l 8,qside of a converging lens of focal length f, and a white screen for viewing the image is on the opposite side. The distance k 8jkcwiz,73 m3yhl 7pqin:k3n7b2fz$d_T=d_i+d_o$ 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 q hsydpar+r2: 91.m/vmu 3zswis projected on a screen (Fig. Below). If a 105-mm-focal-length lens is to project an3zm2 ardw.ruv+ ps:m9qh/s 1 y 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 acb4+0v garc(pu tually 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-lengt(gv0arc b+ pu4h lens should be used if the image is to cover the screen?    cm

Show analytically that the image formed by a converging b(4dy o dcx7jh:b/yv5a vv6n9lens is real and inverted if 7byn a4b6hd(y vvx:v5c jdo9/ the 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 reporter shooting pictures of her at home. She )2j4rv .ouxkjva (7pa)g0dzcclaims the reporter was trespassing. To pro j7(oxr2d a))j0 c zkvvpa.ug4ve 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 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 camera with4on n.ws duw2 *pq92bk
(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 frobadqkmwl2u) v03e)n0 nt of a certain lens is imaged 8.20 cm in front of that lens (on the same side as the object) k w02ea)nv)ld0b3uqm. 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)

  When an object is placed 60.0 cm from a certain convergin yc )x8cqqg)r:.q*ewng 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 q)yxncq )c: q*w.gr8e lens. Find the focal length of this lens.    cm