What would be the appe:cz8 w3 /h. 5fmcpojdsarance of the Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman r )wk1 lxgc0u5fleet in the harbor of Syracuse by focusing the rays of the Sun with a huge spherical mirror. Is this re5wlkx 1g)0cru asonable?

Although a plane mirror appears to reverse left and right, it doesn’ql9ko,u-lz9d p9l f;(u3/bf msd,blm t reverse up and down. Exmldfk 3fl; ,ubsl(m pqz9- uld99,b/oplain.

If a concave mirror produces a real image, iovn) suyizm 8/vm6. v hs8ss7,s the image necessarily inverted? Explv zuyvm sis78v,h/)6 s nm.os8ain.

An object is placed along the principal axis of a spherical mirror. The matr hz u(:z3ljy, k+2d)mmlr,wgnification of the object is -3.0 Is the image real or virtual, inverted or upright? Isu2)z(jtmr ,wmy 3 ,zrdkl:l+h 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.4w ,jxy av(-tb Below a), draw ray 2 for (Fig. Below b). 4xvtj y( awb,-
(a)
(b)

What is the focal length of a plane mirror? What is the magnific 9z4te zgjh*8/obmy sn8a. cqp h3 (abo;6dy;cation of a plane mimq8hbaz8ysz9 /.;;3a6oc dbojy p c4*e(hg tn rror?

When you look at the Moon’s reflection from a ripply sea, it appears elonga ly:y, u.q nkshkj87sr3r c+r6ted . 6l,jy yn8usc7 rr+k.rh kq3s:Explain.

What is the angle of refraction when a light ray+g8n v) m gryq:vnu+u/ meets the boundary between two mater ggrmnyu/+un :8q)vv+ ials perpendicularly?

How might you determine the speed of light in a solidpr(5h7;juzt s, rectangular, transparent obju7 jp t;h(rz5sect?

When you look down into a swimming pool or a lake, wp7vj) /nl 8stare you likely to underestimate or overestimate its depth? Explain. How does the apparent depth8v/nwtjl )7sp vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick lo zbele- -fb r(a3p7/cpoks bent when part of it is under water (Fig. Below -leera (p-cz/ 3bf7pb).

Your eye looks into an aquariumus7w-cw+ wtbgj 5k m )+ vvp+4ufvhm(0 and views a fish inside. One ray of light that emerges from the tantm bmjf+05gpw 7 4vwu-vh+wvks(+cu )k is shown in (Fig. Below), as well as the apparent position of the fish. In the drawing, indicate the approximate position of the actual fish. Briefly justify your answer.

How can you “see” a round drop of watevxpfmg3 qptl67 jap( t)v57c*r on a table even though the water is transpartv*5a (p l)7g7jx 3cm6fqtp vpent and colorless?

When you look up at an object in air from beneath the 72e fzf/f pu5 ba:5xy64ya deasurface in a swimming pool, does the object appear to be the same size as when you see it directly 45 ypza5a6a7eye: f/fx ufbd2in air? Explain.

How can a spherical mirror have a n /xgfmih6i /j*egative object distance?

Light rays from stars (including our v3nniw 0 +iy05r90tp vch/yy zSun) always bend toward the vertical direction as they pass through the Ez yh30rt yc+n/yw 0niv0 piv59arth’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 e;rth *0 .44jmnfy t nq-iwfzn2xv )7dbe placed if a camera lens is to make a sharp image of an obj z)f4nv qwe42f rdy*n jt- in0x7tmh.;ect very far away?

What type of mirror ;chc ciawd ch3vavy69es /jef8++; x 5is shown in (Fig. Below)? Explain.

A photographer moves c dshxl5cv415itrh -u mauh+(4 loser to his subject and then refocuses. Does the camera lens move4u-h5(m5t1v4 xr+s ulc dihh a farther from or closer to the film? Explain.

Can a diverging lens form a-uyv4dsk 878cwii3s50r x q pa real image under any circumstances? Explain.

Use ray diagrams to show that a real im+3tlq)g2i wu(lu5:) o8lyh 2snhbdvfage formed by a thin lens is always inverted, whereas a virtual imagw3+bno)l52fhs (y:d2hl uv8l uqg)tie is always upright if the object is real.

Light rays are said to be “reversible.” Is this consistent with the thin l* z,fabau 95ybens equation? Explain.9 5auba *zby,f

Can real images be projected on a screen?tdy zcv40.cpyo i1j48 Can virtual images? Can either be photographed? Disc dy01yocvt4 zci8p4j. uss carefully.

A thin converging lens i);lcpdfc 02xd03 j; wtj*zchbs moved closer to a nearby object. Does the real image formed change; bx cwph fd;d3*0c0zjt)lc2 j
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material4n.,voekvo ws gl3,c ; ;-yeaz with an index of refraction n = 1.30 In air, it is a conver e yvo e;kz,lo43cv a;-n,swg.ging 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 converging lens. If tewq6-2 nmhm29wu e1be he nose and the tail are each focused m un6eh2-2ebm 9wqw 1eon 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 cong-:jb2 noiz -5uvn:dsverging lens. Under what circumstances (if any) would the image i:nb:jzn-2ugd5o -vs of the nose be virtual and the image of the tail be real? Where would the image of the rest of the cat be?

Why, in Example 13, must the converging lens have a shorter focal lengtqk-:;ytdpc(j*, t niqh than the diverging lens if the latter’s -*qj:d yq(c,pn ;tiktfocal length is to be determined by combining them?

Explain how you could have a vcigwbbr 7ii z:9uiq8*qs6hdo5:u9 a 5irtual object.

  An unsymmetrical lens (say, planocon)tmmv-. /c6a )ndrjnd0u8h ktvex) forms an image of a nearby object. Does tn)- j) .hdk/0uc8d6tvnam rmthe image point change if the lens is turned around? ----待选择----yesno 

The thicker a double convex lens is in th,0uf:j 8zvg kse center as compared to its edges, the shorte,u :svgk08fjz r its focal length for a given lens diameter. Explain.

Consider two converging lenses separated by some distance. An obvj 93uabk +)*3qfk pkwject is placed so that the image from the first lens lies exactly at the focal point of the second lens)a j+ukf pw kk3v93qb*. Will this combination produce an image? If so, where? If not, why not?

  Suppose that you want to take a photograph of yourself as you look doa6 +)kxnb p(md q 5w;xxs.d3at your image in a flat mirr.d kdwqabd( 5 o6px)n;sxx+ m3or 2.5 m away. For what distance should the camera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mirror, you se/j lpim52t9pni8 db am 2af/y3uv*h n*e the same amount of your body whether you are close to the mirror or far away. (Try it and see.) Use ray diagrams dl/m/b ti*ui8pnjvf*225 3aap 9hynm to show why this should be true.

  Two mirrors meet at a qxs m867oit*c 135$^{\circ}\,$ angle, (Fig. Below). If light rays strike one mirror at 40$^{\circ}\,$ as shown, at what angle $\phi$ do they leave the second mirror?    $^{\circ}\,$

  A person whose eyes are 1.68 m above the floor stands 2.20 m in q wm/ np6;qe3ufront 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 m6 q/pnq;3ewupoint on the floor that can be seen reflected in the mirror?    cm

  Suppose you are 90 cm from a plane .wbw-ya8e41wc l7si ( xn5vcmmirror. What area of the mirror is used to reflect the rays entering one eye from a point on the tip of your nose if your pupil diameter is 5.5 mmmce 5wv w 7l c-(1bx8aysi.nw4?   $\times10^{-6}\,m^2$

Show that if two plane mirro++di4;qck7b q5(exw ei*.g r2 nepywi rs 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 mirro1od zfl.le)b1:n tk2m5) 3pon lkkjo0r pointed at the Sun, focuses the Sun’s rays 18.0 cm in front of the mirror. What is the radius of the spherical surface from which:mjzkk25)keof nold 0nl1b 1.)3o pt l the mirror was made?    cm

  How far from a concave mirror (radius 23.0 hr1mlze27 btw57jw :5gqpfalju58 g ) cm) must an object be placed if its iug2pme:t gzrbjwl1jh 77)l5q5a85fw mage is to be at infinity?    cm

  If you look at yourself in a shiny Christmas tree ball witgx1t x33zwm ps5q0 gu.h a diameter of 9.0 cm when your face is 30.0 cm away from it, where is your imagxg3mp x0u15zgqwst .3 e? 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 pa t/.dmv:pvw am*y ).yerson who stands 1.4 m in front of it. If the image is three times the person’s height, what is the radiusm.m*ay/v.ytdwva p:) of curvature?    cm

  A dentist wants a small mirror that, when 2.20 cm ;ja n7 -iqjccurzy9v1 a/5;ybfrom 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 agz9n zwdk+kln,.k 4/ere smaller than they would be if the mirror were flat. Are the mirrors concave wl4n kn /,kg.zek +9dzor 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 sy-;*eio w +zqhigh is placed 20.0 cm from a convex mirror of radius of curvature 20.0ze; ws+qoi *y- cm.
(a) Show by ray tracing that the image is virtual, and estimate the image distance.    cm
(b) Show that the (negative) image distance can be computed from Eq. 23–2 using a focal length of -10.0cm
(c) Compute the image size, using Eq. 23–3.    mm

  You are standing 3.0 m from a convex security m eak-sa5klu8nt4nnyloxy 07w*n3 ./i irror in a store. You estimate the height of your image to be half of your actual height. Estimate the radius of curvature of the mirro./0nweu xyi-ns 43lnt* lknka85ya7or.    m

  (a) Where should an object be placed in front of a concave mir22q*ud eo1jp: j3ko buror so that it produces an image at tp:*eqdubooj21uj 32 k he 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 nxv;i */zecs(*y*h hi when viewed in a curved mirror. /i* ve h*czhnsxi*;y(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 teop-olbv j8y6rapb 52 )chniques,
(a) a ray diagram,
(b) the mirror equation, to show that the magnitude of the magnification of a concave mirror is less than 1 if the object is beyond the center of curvature $C\left(d_0>r\right),$ and is greater than 1 if the object is within $ C (d_0 < r) $.

Show, using a ray diagram, that the magnification m of a convex mirrora5/*n vw 0ggt f*3benz 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, Eq. 23–2, is valid f (,qaw 3/ixv+ubwl)tpor a convex mirror as llwqb,vwp(i a3tx)u /+ong as f is considered negative.

  The magnification of a2(. vdtizmi:nc;zqamxa2+/r h x8 zh + 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 cm in front of a spherical mirror. 1 lf d(od c3;ozykaj:*-px 0zaIt is desired to produce a virtual image that i-31fdokzla(:p y oajxd0z*c; s 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 face by a facpj:vbro n(hbza ,l0o)+ jo.g)tor of 1.33 when your face is plp ). +ozljo:,gh)ov(br bn aj0aced 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 ligu*vnqwsd(.d3l za93i6 nyz* b ht 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 ice ot5cik xq1b 1/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 sm1ekze,mznyys re8.g0lfc h13 *.0t water. What is *t0elz gfrycm, syn8 m. 1h03kz1se.e the index of refraction of this substance? n =   

  A flashlight beam strikes the surface of a pane of glass (n = idph. 8;qa m3m1.58) at a 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashlight upward froze;f0ylhsjj wc.r 79 e,8o /jvm 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 watem+, ok fxouy5)r at an angle of 6m),uof +kyo5x 6.0$^{\circ}\,$ to the vertical. At what angle of incidence does it hit the air–water interface from below the surface? $\theta_1$ =    $^{\circ}\,$

  Rays of the Sun are seen to mak (1yopusjb d+w*p6wo4ewh5o *e 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 wh7;rj ayz-g*(hc d hw7jeql71 bose index of refraction is 1.52. A beam of light from outside the aquarium strikes the glass at a 43.5° angle to the perpendicular (Fig. Below). What is the angld -*g b;7z(7alyh 7r qj1cehwje 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 bottox au/c 50rpya: cl6j8am 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 from the edge of the pool (Fig. Below). Where does the spot of light hitj:pluayxc85raa 0/6 c 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 glasslnqt*;ya j 3x2fj/m o8kl p7r1 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) and is partially rqvmbe) s *y+6feflected and partially refracted. Fbq6v* yfm+ e)sind the angle of incidence if the angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that fovo92wwk( * yd)jwesc1r a light beam incident on a uniform layer of transparent material, as in (Fig. B vww2)1k*j yod(w9es celow), 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 fo;y1 whbsr1:plat piece of glass with index of refraction n as in (Fig. Below). So;1hp1sw:rb y how that if the 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 aw5/ r 6n,phfjfngle for the interface between water and Lucite? To be totally internally reflected, the lr6f n ,hwpf/5jight must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–airqr+xzwku/hn(c q.sq n)- y55t 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 wnu sov/nnjtx;hzz 6+jd)b 12wq/ o 55aater from a depth of 62.0 cm. Where must it strike the air–water interface, relative to the spot directly abovzo1t)6b 5qnzhnjdv+w/ 2j 5;naox/sue it, in order that the light does not exit the water?    cm

  A beam of light is emitted 8.0 cm beneath the suj;6exhlrr/d u4e 4hk oe.2a:0i sf b,brface of a liquid and strikes the surface 7.0 cm from the point directly above the source. If total internal reflection occurs, what can you say about tb f2lix 4o ;,0hrd:46j.ahsrukeeeb/ he index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face of a/c9jp(t .ea r( mkl.v/7vnam 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 shown in (Fig. Below). Show ay ibtup37(1j that we can guarantee total internal reflection at the side surface of the material (at point a), if the index of refraction is greatpujyit17b 3a( er than about 1.42. In other words, regardless of the angle the light beam reflects back into the material at point a.

  (a) What is the minimum index of refraction for a glass or plastic prism; wol /rrg7r8m to be used in binoculars (Fig. Below) so that total interng m/7orr8l w;ral reflection occurs at 45$^{\circ}\,$? $n_1$ $\geq$   
(b) Will binoculars work if its prisms (assume n=1.50) are immersed in water?  ----待选择----totally reflectingtotally transmitting 
(c) What minimum n is needed if the prisms are immersed in water? $n_1$ $\geq$   

  A sharp image is located 78.0 mm behind a 65.0-mm-focal-lenb wqf44iy:)n4;xe bg ugth converging lens. Find the object distanqf)4 g;wb:yxiub4 n4 ece
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at .s7ll3qz n u(sa 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 focuseursw5b sn);a*s light from an object 2.75 m away as an image 48.3 cm on the other side of the lens. What type of l;n5) awur s*bsens 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 of a 20.5-cm-focal-length lq3hatk.; rux4 ens? 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 conghbra 3)k.1z+np,z-e*afoe lverging lens with focal length 24 cm to view a stamp 18 cm in front of the le hkrze*a-1gzp,n+fb l) aeo.3ns.
(a) Where is the image located?    cm behind the lens (virtual)
(b) What is the magnification? m =   

  A -5.5-D lens is held 15. +qv g7o1dge3(sn-wtfj eul4.0 cm from an object 4.0 mm high. What are the position, type, and height of the im 1f(nd s-+7.ogu5 w3etvle qgjage?
   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.z 7m6mz4tj2pe Thepemt 7z j2z64m maximum 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 reading mati5df3as c me p(;u,gp.erial by a factor of 2.5× when a book is placed 8.05ic(u.fsampg3p e,d ; 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 len+uh/uql 8ornlyeo ,v8yi0,y 9y5,h g qs. By how much does the image move if ,,hly0 gl8q5 /q uioyr,8+neu yo9yhvthe object is 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 conve, rso 04mw:bn otvod/ctru6 (6rging lens with a focal length of 25 cm should an object be placed to produce a real imagerom 4bt6u(o :rtw,sv0ndc/o 6 which is the same size as the object?    cm

  (a) How far from a 50.0 ntfb/n gsg*v-*t)vi *-mm-focal-length lens must an object be placed if its image is to be magnified 2.00× inbntg f-* /vv*)s*gtand 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-lengtem/5ght gtkl fw dds8*5-2t; nh lens must an object be placed if its image is to be magnified 2.00× hm* -s;tkf2t5e gl5dgw tn8/dand 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-h5/cxfke1ppg 7 uio 45z (:atjfocal-length lens. Where is the i45iapx khojcet:1 5gf zu/7p(mage, how high is it, and what type is it?
$d_i$ =    mm (real,behind the lens) $h_1$ =    cm (inverted)
(b) What if $f=-135\mathrm{~mm}$?
$d_i$ =    mm (virtual,in front of the lens)
$h_1$ =    cm (upright)

  How far apart are an object and an im4pvaa-d 7fag.k2rie 5 age formed by a 75-cm-focal-length converging lens if the image is7irkpeaaa.vg- d 245f 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. At dmj+pk;qi4d h x-ji3-what location(s) between the ; -i-h+dm4jqxd3ki pjobject and the screen should a lens of focal length 12.5 cm be placed in order to produce a crisp image on the screen? [Hint: first draw a diagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length converging lensenm in5.mt 8se+(m8 hfxs are placed 16.5 cm apart. An object is placed nex m +nf hm5.st8m8i(36.0 cm in front of one lens. Where will the final image formed by the second lens be located? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens witr an26unj,xraj k)m- 6h $f=-31.5\mathrm{~cm}$ 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 behiv-mn3/g 9mjbk *cvt d-nd a diverging lens. Parallel light strikes the diverging lens. After passing through the converging lens, the light is again parallel. What is thc vv- -jmm/3tngd*9kb e focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Example 23–12 are now placed only 20.0 cm apar1s mg+uqsit *yy 98k9tt. The object is still 60.0 cm in front of the first lens as in (Fig. Below). In this tt+8 s*skgm iu99 yqy1case, 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 apartjyjx,8bk(7t6 s; wtq/,ts5i o ztvsp :. The focal length of the lens on the right is 20.0 cm, and the focal lent;6stzq5 xw t 8p,b(sy jk7i,j/ovst :gth of the lens on the left is 15.0 cm. An object is placed to the left of the 15.0-cm-focal-length lens. A final image from both lenses is inverted and located halfway between 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 kest y/)h l/-hx)odc/of is placed 12 cm to the right of a converging lens with a focal lec/o/dehl - hyt)/ks x)ngth 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 divie69e,y c,/f :)xzv)v cgbvxj erging with focal length are placed 25.0 cm apart. An object is placed 60.0 cg9)6ij ye )v:xe,/c,fbvvcz xm 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 ji hpirv1: 68aplaced next to a converging lens of focal length $f_C$ as in (Fig. Below). If $f_T$ represents the focal length of the combination, show that the focal length of the diverging lens, $f_D$, is given by
$\frac{1}{f_\mathrm{D}}=\frac{1}{f_\mathrm{T}}-\frac{1}{f_\mathrm{C}}.$

  A double concave lens has sur frh(2r53r pkuface radii of 34.2 cm and 23.8 cm. What is the focal length if n = 1.52? u(r23krf5hr p   cm

  Both surfaces of a doublenn;4xtsu5; z a convex lens have radii of 31.0 cm. If the focal length is 2u4t;x 5 ;asnnz8.9 cm, what is the index of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal length orf +;7npq st7pf -23.4cm. What is the radius of the concave st qp7ns7f pr+;urface?    cm

  A Lucite planoconcave lens (tc a 1.e .ypeafn8c(i2.-ewj csee Fig. Below) has one flat surface and the other has R = -11yc2j( - naf.twipc.c.eea e8 8.4 cm. What is the focal length?    cm

  A symmetric double convev(9i*)a qfrm2h 5fj1er txr0nx lens with a focal length of 25.0 cm is to be made from glass with an index of refraction of 1.52. What should be the radius e (fq05* t9rax)i2hrfj 1mnv rof curvature for each surface?    cm

  A prescription for a co)2h iuc)6x3yj0ni cdarrective lens calls for +1.50D. 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 be the radius of curvature of th aun6 c )hi0x3)id2jcye other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fig. Below). You stan1 pxc3gy 48d-rapcva;d 1.5 m away from one of 3yxa vgc 4p8- p1ca;rdthese mirrors and look into it. You will see multiple images of yourself.
(a) How far away from you are the first three images in the mirror in front of you?
$d_1$ =    m
$d_2$ =    m
$d_3$ =    m
(b) Are these first three images facing toward you or away from you?
the first image is facing  ----待选择----toward youaway from you ;
the second image is facing  ----待选择----toward youaway from you ;
the third image is facing  ----待选择----toward youaway from you .

  We wish to determine the depth of a swimming pool filled witdlpff/tf b3r-6bg lh k48y+s ;h water. We measure the width (x=5.50m) and then note that the bottom edge of the pool is just visible at an ;fglk8b-fdy f6 43/slb + trhpangle of 14.0$^{\circ}\,$ above the horizontal as shown in (Fig. Below). Calculate the depth of the pool.    m

  The critical angle of a certaixwdy4.be9uf80f pzh6 n 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 can be cong5mzck6a 5lyj nu9.)a sidered a limiting case of a spherical mirror. Specify wk9 am. )jzlyu65ng a5chat this limit is.
(b) Determine an equation that relates the image and object distances in this limit of a plane mirror.
(c) Determine the magnification of a plane mirror in this same limit.
(d) Are your results in parts (b) and (c) consistent with the discussion of Section 23–2 on plane mirrors?

Stand up two plane mirrors so they fp08v-led5/9y.y;l+ ecrwrn +m eikh lorm 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 real image o(2y asb k(r4yvf a real object. Can you describe a situation in which a diverging lens ckr(s4bya (v y2an form a real image?

  Each student in a physics lab is assigned to .;kgt e /kymw7 qzyl5 f2qxln 8.lds92find the location where a bright object may be placed in order that a concave mirror with radius of curvature r = 40 cm will produce an image three times the size of the object. Two students complete the assignment at different times using identical equipment, but when they compare notes later, they discover that their answers for the object distance are not the same.58ll wgdek..lqns2kzm2x yf9 /7 qty; 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;(ob0 odawl k(kz.mb0 a 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 cs k ij9s- u9nl )zsc ,:thp;:lamy-zf+ylindrical glass rod $(n=1.54)$ are perpendicular to the sides. Show that a light ray entering an end face at any angle will be totally internally reflected inside the rod when the ray strikes the sides. Assume the rod is in air. What if it were in water?

A lighted candle is placed 33 cm in front of a converging lens of focal leng ogq.d j0d5b3eth $f_1=15\mathrm{~cm},$ which in turn is 55 cm in front of another converging lens of focal length $f_1=15\mathrm{~cm},$ (see Fig. Below).
(a) Draw a ray diagram and estimate the location and the relative size of the final image.
(b) Calculate the position and relative size of the final image.

A bright object is placed on one side of a cc/: dsqwll zwxid202(; hg-qqonverging lens of focal length f, and a white screen for viewing the image is on the opposite side. The disx2zi0(s wwg;lcl dd/q :q h-q2tance $d_T=d_i+d_o$ 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 objectm,ov s 4/e;bvk whose image is projected on a scvm ;/vok,4s ebreen (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 mm) is toqk*(oif),o j x be projected on a screen 1.80 m by 2.70 m placed 7.50 m from the projector. What focal-length l) ( jq,*kioofxens should be used if the image is to cover the screen?    cm

Show analytically that the image formed by a converging lens is revyd el du nhw3x7*e5-.l:e1qeal and inverted if the oe y- wqvnlddeh3e 57le*1x:. ubject 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 pictpna8n.( (uakvax oo 7)ures 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 he7 x a.o8n)aun( okavp(ight 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 sn.csk1d4v16tn m u+:v qaoz9camera 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 ink0yg/pd.t n hc xu8.0w 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 what is its focauwx/n c.8d0gt.pkh0y l 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 converging (kc: 8w,9hz 45b vbnv0rmig mzlens, it forms a real image. When the object is moved to 40.0 cm from the lens, the image moves 10.0 cm k(5 8z bh0vw nmgi mbvz4r9c,:farther from the lens. Find the focal length of this lens.    cm