What would be the appearance of the Mo(dwz1oo+ j3jrw: i2r6 w nfzb8on if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fle4o32vlj/utjevf+( wq lu;:r qet in the harbor of Syracuse by focusing the rays of the Sun with a huge spherical mirror. Is t 4 l tj;v/uj(qfuq2lw3+veo r:his reasonable?

Although a plane mirror appears to reverse 3hw kxok:l-bsje1:7hleft and right, it doesn’t reverse up and down. Explejwho3-sbh :l:1 k k7xain.

If a concave mirror produces a real image, 3+pi aj1p auk.plp hi10*qj+cis the image necessarily inverted? Explai*jluj1 i3h .p+kapp pq ci+a01n.

An object is placed along the princi*69sll ps1 9zj, 1pvgxgguz2j *lp npi90 tt7bpal axis of a spherical mirror. The magnification of the object is -3.0 Is the iutv *jgl t1lsspg0pgzi19 6*9zbn9 ,p 7jpxl2mage 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 t95jram e q2 dlk,th6e5nn (,quo (Fig. Below a), draw ray 2 for (Fig. Beloq 5a j,mrheqnlu,dn2k9( et65w b).
(a)
(b)

What is the focal length of a plane mirror? What is the magnifl.p-sjy zfh 8i6e tle1s 3t8z7ication of a plane mirrp88s 1li - 3zyteezjf6 t.lhs7or?

When you look at the Moon’s refle0-bonhi sh5uf. 4kx2u ction from a ripply sea, it appears elongated . n -hi2x5fuh04u o.ksbExplain.

What is the angle of refraction when a light ray meets the1h4ylv tfsm z6rj6q(. boundary between two maters1fqrlzv6 hjyt (6.4mials perpendicularly?

How might you determine the speed of light in a solmal/ be zrqc1 34-jbc1 -jd le/4prpd-id, rectangular, transparent obj3qre jrl-/b4pabdlzpc m/-j1c de-14ect?

When you look down into a swimmi ch-,vnsu/m8k ys9ca1ng pool or a lake, are you likely to underestimate or overestimate its depth? Explain. How does the apparent depth vary with the viewing angle? (Umv yksncs81ch, -/ a9use ray diagrams.)

Draw a ray diagram to show why a stick looksh 1-twy+gud8l bent when part of it is under water (8d1l-ut +why gFig. Below).

Your eye looks into an aquarium and views a fish insi/bi 2 p-k*rqkpde. 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 fish. Briefly ju-p/ipk kr2qb* stify your answer.

How can you “see” a round drop of water on a table even k ncaxwr9*ug:;v 5c m8though the water is transparent and colorless5wkua8 vm xrc:* cgn;9?

When you look up at an object in air from beneath the surface in a swimming poo.c qdq0twe- 3vl, does the obj0w evqct-d .3qect appear to be the same size as when you see it directly in air? Explain.

How can a spherical mirror have a negative zi6y+g*qr asv. qb 1j9hj+ghj-r(yy,n)i;y tobject distance?

Light rays from stars (including our Sun) always bend toward the ct,m1/ .mbg dq;ms7djvertical direction as they pass through tbc ,gmds1; ./qmdj7mthe Earth’s atmosphere.
(a) Why does this make sense?
(b) What can you conclude about the apparent positions of stars as viewed from Earth?

Where must the film be placed if a camera lens is toksn0hfyavb7 -b3:v q5 make a sharp image of an objbhs35:ny7 a kvb0-f vqect very far away?

What type of mirror is shown in (F -h8n0efx2q5 iv +*k adwnr.hwu+q1 asig. Below)? Explain.

A photographer moves closer to his subject and then refocuses. Dc.6xn-7ry xl918gp:7 r 3xk oefgew shoes the camera lens moveofgn3ghpx9cr8ywsk -7e: xe7.r1l6x farther from or closer to the film? Explain.

Can a diverging lens form+,sc j tgm2hs7tv9o 5d.vw o94j-n rfx a real image under any circumstances? Explain.

Use ray diagrams to show trrggqt( * k )e0gou.-n :wd/3kikta* ehat a real image formed by a thin lens is always inverted, whereas *r)ta /okkwkdg n0ieq3*- ( r.egug:t a virtual image is always upright if the object is real.

Light rays are said to be “reversif1u o+c kx)d;ible.” Is this consistent with the thin lens equation? Explain.of ;x)k1 +dcui

Can real images be projected on a screen? Can virtual im5acm y,kh4.b4 wsqx /iages? Can either be phot4s4ma cw h5yi,q/. xkbographed? Discuss carefully.

A thin converging lens is moved closer to a nearby object. Dowbkqt5 i;4npn5ppa h st. )(:: ze8/gluo i0fjes the real image formed changgt q 0a5nt ei(iw5 8)nl 4jb.:huppk;po:/fsze
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of refraction n = 1.30 In air,i4z.pa qnyne w8o 4c/84ey0w g it is a converging lens. Will it still be a converging lens if placed in 4/y48c .iqngp yeaw0 we48znowater? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands facing a converging tzz4bga nyb;u(g.3hnb /9yi+ lens. If the nose and the tail are each focubg y;/t b+(zgy n.nbaizu94h3sed on a screen in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facing a converging qll .1fq0taz2 lens. Under what circumstanq .af0l2q zt1lces (if any) would the image 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 len (,ejq ry4,8qrw+rs paw.w ,bkgth than the diverging ley ersj.+qpr ,wrkaq(ww48b, , ns if the latter’s focal length is to be determined by combining them?

Explain how you could have a vir/n puiu ak)8-bq-svr2tual object.

  An unsymmetrical lens (say:d j;8-fvc/a quj7uxub dal.(, planoconvex) forms an image of a nearby object. Does the image point change if thxbdf u:q/aj;jvd. cul-7 (a8ue lens is turned around? ----待选择----yesno 

The thicker a double convex lens is in the center as 6f/xyt; 3gl8o *- xzswzca5eakg ;1 rlcompared to its edges, the shorter its focal length c rwtla go-;* zegkf z8 as5613l/xyx;for a given lens diameter. Explain.

Consider two converging lenses separated by some distance. An object is placed ni8jv4xg ico*psr/8 , i*cn5pso that the image from the first lens lies exactly at the focal point of the second lens. Will this combination produce an imag,4i/xcpcpgojnii*8* 8v 5 srn e? If so, where? If not, why not?

  Suppose that you want to take a photograph 1 c1fxm*fs nzihbp*)1 of yourself as you look at your image in a flat mirsf)*1 iz*1fp bmnx1 chror 2.5 m away. For what distance should the camera lens be focused?    m

When you look at yourjikxd8hj,t 3um k72b 7self in a 60-cm-tall plane mirror, you see the same amount of your body whether you are close to the mirroh3jj7k ibt2,8d mx7ku r or far away. (Try it and see.) Use ray diagrams to show why this should be true.

  Two mirrors meet at a 135s h uauwjs7+:yq. ((4r acfb-s$^{\circ}\,$ 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 19o 8yv icg.ut0.68 m above the floor stands 2.20 m in front of a vertical plane mirror whose bottom edge is 43 cm above the floor, (Fig. Below). What is the horizontal distance x to the base of the wall supporting the mirror of the nearest point on the floor that can be seen reflected in the.v octug980 yi mirror?    cm

  Suppose you are 90 cm from a plax h6m(0dt ygeel7eh d( .w-5uwne mirror. 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 56xu5(emw gl 0ed.-h thdew(y7.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors meet at an anglr dc)9fu.6y+ jrmhia/a7ezc 6 e $\phi$. a single ray reflected successively from both mirrors is deflected through an angle of $2\phi$ independent of the incident angle. Assume $\phi<90^{\circ}$ and that only two reflections, one from each mirror, take place.

  A solar cooker, really a concave mirror pointed a5d,qcvqm: v yn vmn*rxcp4x-e).q) 3it 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 the mirror was mad m,q5qd-4n c cvxp)niy.mx) vre* :vq3e?    cm

  How far from a concave mirror (radius 23.0 cm) must an object be p8occ) bf: s)oglaced if its image is to be at infgco 8o)fc )sb:inity?    cm

  If you look at yourself in a shiny Christmas tree ball with a diameter o7 r5xmtg fzti d779s ekn3n(;tf 9.0 cm when your fms 7ezn5nd;ft gtrt97( 3x7ki ace is 30.0 cm away from it, where is your 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 standb8r;nh;ti,qdf9t l,i.) rw his 1.4 m in front of it. If the image is three times the p),li,tr f 9;hi.dqiwr h;bt8nerson’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror that, when 2.20 cm from a tooth, will produaxh e )x04hsah:kyxw;,x8m/s ce 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 ca0 -,*yym1yc f870 tabvg likgnrs behind you that are smaller than they would be if the mirror were fl1fi7y0tga -lb,gvc8 nyym*0 kat. Are the mirrors concave or convex? What is a mirror’s radius of curvature if cars 20.0 m away appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mmhe/g7 v 4la:8dspy y mgzf)n(4 high is placed 20.0 cm from a convex mirror of radius of 47mgns)4zhpyvf (: a ly/d8ge curvature 20.0 cm.
(a) Show by ray tracing that the image is virtual, and estimate the image distance.    cm
(b) Show that the (negative) image distance can be computed from Eq. 23–2 using a focal length of -10.0cm
(c) Compute the image size, using Eq. 23–3.    mm

  You are standing 3.0 m from a convex security mirror in a store. Yoam or5d1dz(+xu estimate the height of your image to be half of your actual height. Estimate the radius of curvd5z+ o1x(amrd ature of the mirror.    m

  (a) Where should an object be placed in front of a concave mirror so tb f4sl hith )3f)qp4+ghat it produces an image at the same locatio hh4si bqf) )4+gl3fptn 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 virtuale0 lwfd7fvk zd,;kvk- l 2z(i2 and very small when viewed in a curved mirror. The image appears to be 18.0 cm behind the mirrflv2v2 (kdwl kz,i7e0z ;dkf -or. What kind of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techni*-k mzm 91cdhuques,
(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, * tw1kuv9wr6h: j d(vgesk-p 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 shoff4zva 1. :(h*x/vmy d 4mrlwgw that the mirror equation, Eq. 23–2, is valid for a convex mirror as z/ frf1vmya(m4g d.x:w4* vlhlong as f is considered negative.

  The magnification of a convex mirror is f h++z7ode0zf2cxmfop7r( 9q $+0.65\times$ 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 ma5*ntt* nj33n zsug z*irror. It is desired to produce a virtual image that is upright and 3.5 cm ta* a5jtt *zg3nunns *z3ll.
(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 mo,nvk2n2q.s fqv j 5i h72(moyagnify your face by a factor of 1.33 when your face isvo7q.fvm h2n2yo5 q(,ijsn2 k 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 9z8 u-lxymgj(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 h /2ierkd 7zpt+hd+7g q25er dis $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain substance is 89% of in(bjkvso9(v, wa9(t3jb.* *s efyn yits value in water. What is the index of refractioy( 9(e ys .vbo,an(*jivwjtf kn *s93bn of this substance? n =   

  A flashlight beam strikes the surface of a pane o , 0ebn cp.e1*-dbiwzhf 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 flash,shg g2/ad ce1light 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 a)ut1xg x-7b2wkq bvjq)i.l (in underwater spotlight exits the water at an angle of 66(- qiklbvx)7gtb i1q2.xj ) wu.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 make vmzfb xk; l5 qw8c s(b-jw/g73a 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 refractyv1vsbfr.brwli w *5o ,cr/7 3ion is 1.52. A beam of light from outside the aq*rw5fw3b bc r., vr so1y/v7liuarium 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 n nykmbt sv1i*f.*,3vw arrow 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 spowismn 3 **kvbvft.1y ,t 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 h3p2kfz0v7 lq 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 s.g 04w o*.c,zjb-nlxs5vuwtslab of glass (n = 1.52) and is partially reflected and partw ub4l gczx.vos5,w *ntj.- 0sially 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 incideavg6.kukv)7 chjc n;)fsf/2 d nt on a uniform layer of transparent material, as in (Fig. Below), the direction og djn. uv)ffck2 )s6k7 cha/v;f 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 f:8muf668av .k 0bptue8o nuai+nm (jhlat piece of glass with index of refraction n as in (Fig. Below). Show that if thk8n+vi0of 8 . u( aht:bmmuae8up66jne 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 the interfac7;2se jzp e+e.op(klae between water and Lucite? To be totally internally reflected, the light must start in which kjp;+lzp e7(.o2saeematerial?
$\theta$ =    $^{\circ}\,$
 ----待选择----waterLucite 

  The critical angle for a certain liquid–air surface is 476z:/e4d xjq( x3k 9ilxvtoa+c.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 -0vevc (gi8rc9od6skof 62.0 cm. Where must it strike the air–water interface, relative to the spoeg (rs i8vcvk0 c96od-t directly above it, in order that the light does not exit the water?    cm

  A beam of light is emitted 8.0 cm beneath the surface of a liquid and strikes nh/b-qm ublw 7e5 i4q b.d,xx-op4g1f the surface 7.0 cm from the point directly above the heq-d,7-l/wb1p4gmbiu f o .b4 x5xnq source. If total internal reflection occurs, what can you say about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left fwagvcwef*j2 1xi uta*l(j 8j/us0 z;-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 7a;19 hk+ hfwciye. epof an optic fiber as shown in (Fig. Below). Show that we can guarantee total internal reflection at the side surface of the material (at point a), if the index of refraction is greater than about 1.42. In other words, regardless + e9phe1k;h af w.c7iyof 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 plaspx6xw dxuzz o2w2m 84;zxo1d7tic prism to be used in binoculars (Fig. Below) so xx 4u1doxox;d 6w mz8zwp2 27zthat total internal reflection occurs at 45$^{\circ}\,$? $n_1$ $\geq$   
(b) Will binoculars work if its prisms (assume n=1.50) are immersed in water?  ----待选择----totally reflectingtotally transmitting 
(c) What minimum n is needed if the prisms are immersed in water? $n_1$ $\geq$   

  A sharp image is located 78.0 mm behind a 65.pc15mlru 392y4cx 9ros :cn ax0-mm-focal-length converging lens. Find the object distance 4r u o :1s xcy3ncmarc52lpx99
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus ai8 xsc pob/m12t 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 an image 48.3 cm on ) wcrv2lp6ckqi1qw:v9(s kt6iz ku 08the other side of the lens. What type of lens is it and what is its focal length? Is the image pw16z ctkisu):vivcqk6(k 0 wr9lq 82real or virtual?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the power o5ua.,bsd3lp,vt lb.of a 20.5-cm-focal-length lens? P =    D  ----待选择----converging diverging 
(b) What is the focal length of a lens? $f$ =    cm  ----待选择----converging diverging 
(c) Are these lenses converging or diverging?

  A stamp collector us d7 h 1gwg;w17*ht zghm7xnoa+es a converging lens with focal length 24 cm to view a stamp 18 cm in front of t+gg1 *zhdg; 7h n7wat1 x7ohwmhe lens.
(a) Where is the image located?    cm behind the lens (virtual)
(b) What is the magnification? m =   

  A -5.5-D lens is held 14.0 cm fromvsa.8j)jjrr; ) xklkmhhk /) ; an object 4.0 mm high. What are the position, type, and height o).s;j jx r/k8;rmkh )lv)a hjkf 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 the8ywh :mip tkzn7 zo7h(xs(*s; film of a camera. The maximum distance allowed betwee(t*wkm oh7ih:z;( xp7szs n8yn 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 real:,) kx vg4;x7swzydgxk s9v *8ai,kwding material by a factor of 2.5× when a book is placed 8.xgx zky)s8agdi,7vvs4x*kw 9;k,w l: 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 bdlh4 k/y) fxf*zjt70. By how much does the image move i4jzf0/d*)7kbxft hlyf the 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 converging lens with a focal length of 25 cm should an objec*)b bm ozwxv-p*u( oz:t be placed to produce a rwbozu*:p)x*(mvb - zo eal 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 pl2do 3mul; kn4r7try c4aced if its image is to be magnified 2.00× aol d72m kny4c;ur3rt4 nd 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 play(cua(m zwd j3 n3bnh-ghz5( :ced if its image is to be magnified 2.00× and be j:h-h wndg3( um na5( bzczy(3real?    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-foamq .xklhi,ie,)9f t*cal-length lens. Where is the image, how high is it, and what ty.ie)* lamh, qk,f9x itpe 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 obje q j2- buo4ni04w*er0)yz; 7efi lxlblct and an image formed by a 75-cm-focal-length converging lens if the image is 2.5× larger than the object and islnqwbl4u2 re04*xlfijez7y)b-i 0 o; real?    m

  A bright object and a viewing screen are separated by a distance kufy6v )vz /.kof 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 crisp image on the screen? [Hint: first draw a diagram.] lens shouldk) /6uv vk.zfy be placed    cm or    cm from the object

  Two 28.0-cm-focal-length converging lenses are placed 16x( ,*e-m *viw mxd,m7 uidgbj:.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? Whaiu,xwb m:m-e i*jmv gd,(7 *xdt is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens with q/( pgw*q(+z1iq:ivr/v d+svt g,nhd $f=-31.5\mathrm{~cm}$ 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 bktc+div 05gqhkws 2uvj(;d0(/ 8mpi 21.0 cm behind a diverging lens. Parallel light strikes the diverging lens. After passing through the converging lens, the light is again parallel. What is the focal length of the diverging lenbjth0 pd/k wim(8dgs(qu5vv0c+ k;i 2s? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Example 23 5anz u)c6vu:skr i,m9–12 are now placed only 20.0 cm apart. The object is still 65nu :zaku s6,c9irm)v 0.0 cm in front of the first lens as in (Fig. Below). In this case, determine
(a) the position of the final image,    cm
(b) the overall magnification.    cm
(c) Sketch the ray diagram for this system.

  Two converging lenses are placed 30.0 cm apart. T nbhrye*zp a+ic.9;/2/ vcocghe focal length of the lens on the right is 20.0 cm, and the focal length of the lens on the left is 15.0 cm. An object is placed to the left of the 15.0-cm-focal-length lens. A final image from both lenses is inverted and located halfway between the two lenses.9 ny. /iocr+*2pcce;vz g/hab 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 og.hy;qd9 v(poj1s1f is placed 12 cm to the right of a converging lens with a focal length of 18 cm. An object is placed 33qdjy(gpof9 o h;. 11sv 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 on6h(yndghiip ; asr5 /3e diverging with focal lengt35indg/; (ih 6ryp hsah are placed 25.0 cm apart. An object is placed 60.0 cm in front of the converging lens. Determine
(a) the position    cm to the right of the diverging lens
(b) the magnification of the final image formed.   
(c) Sketch a ray diagram for this system.

A diverging lens is placed next to a converging lens of fh:ojx3ij 8 mb) u;tor)ye/soj*q 7ub. ocal 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 rtey c*rvdfgrz* cqb,0t 1-*2kadii of 34.2 cm and 23.8 cm. What is the focal b ge 0fcc12yqr,-kr* *vtz* dtlength if n = 1.52?    cm

  Both surfaces of a double convex lens havecupp v qs.7.dm zcz+(k-1,u)fp ejc2 g radii of 31.0 cm. If the focal length is 28.9 cm, what is the index of refraction ofck z21pu+dcu)q cjs,pgze-mv (7p.f. the lens material?    cm

  A planoconcave lens (n=1.50) has a focal ler:0wrwddg 0b7z rqa,4uqce: )ngth of -23.4cm. What is the radius of0q,qw: d0r 7zwr bacedgu:)r4 the concave surface?    cm

  A Lucite planoconcave t 07ozh(jmf2pa)2kgtq3 pn z(lens (see Fig. Below) has one flat surface and the other has R = -18.4 cm. Whatg tqpfat o2n )mphz ((3zk027j is the focal length?    cm

  A symmetric double convex lens wit)u**i zjpem u9j4, ,kxi+zx0o hnp2woh 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 of curvatjpk 2n*u0+epzmxih uwoox, ,*)iz9j4 ure for each surface?    cm

  A prescription for a corrective lens calls for +1.50D. The lensmakeypgx0 jkk;5,npzd p ;6r 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 curvzx,; p0;pk5 6 yjkndpgature of the other surface?    m (convex)

  Two plane mirrors face eachyw +8ptbf:q4 1b3hk ** otxclh other 2.0 m apart as in (Fig. Below). You stand 1.5 m away from one ofkh oxby h+tltq84wbc*f p* 1:3 these mirrors and look into it. You will see multiple images of yourself.
(a) How far away from you are the first three images in the mirror in front of you?
$d_1$ =    m
$d_2$ =    m
$d_3$ =    m
(b) Are these first three images facing toward you or away from you?
the first image is facing  ----待选择----toward youaway from you ;
the second image is facing  ----待选择----toward youaway from you ;
the third image is facing  ----待选择----toward youaway from you .

  We wish to determine the depth of a swimming pool filled kjrzqufm : :r;td3fm ./lz:1owith water. We measure the width (x=5.50m) and then note that the bottom edge o.ot1 /zlkdm:z 3u ffjq;mr r::f 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 plastic in air + pvl c1aaw-n/is $\theta_{\mathrm{C}}=37.3^\circ.$ What is the critical angle of the same plastic if it is immersed in water?    $^{\circ}\,$

(a) A plane mirror can be considered a limiting case -a*lq loclr 2p0w*+yn 2 /khnwof a spherical mirror. Specify what thn*ak+ c2h/lql p2 *yo wlrn0w-is 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 formsou; 9m -4scgl 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 of ,zf4dqryq+wsg :q5*o a real object. Can you describe a situatiof y sw45 oqzqgq*,:r+dn in which a diverging lens can form a real image?

  Each student in a physics lab is assigned to fmc, vr;8 6oo/i04dzfad t3pb lsl35f2a(rx mhind 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. Explaif2b/8,4arl3z5is o( oa0 dlmhxp6 ctmvr3;d fn 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.ablr ( gho5)yj.icvdx/ k5* u 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 cylindric ;vk7k65esn af p1v1hbal 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 placei9jq*j osmn(q+ vn,z(4 wl wo:d 33 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 one side of a converging lens of focal5og ili( ovd/y i.f8nq42x uy0 length f, and a white screen for viewing the image is on the opposite side. The distan(yn y xiog.iqo8/ulv5if 24d0ce $d_T=d_i+d_o$ 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 is projec beom ke +mev5+24sd4cted 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 fa4ksv +e2m4oc m5eedb+r 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 actuatyf, ztji;hv;hgyyua/ 4:h0. lly 24 by 36 mm) is to be projected on a screen 1.80 m by 2.70 m placed t; ;t./y ah,g:i0yzhvfy j4hu7.50 m from 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 real1 lv-u )ts3 8hcfeu f qv8f886uqb0eui and inverted 8ueuf3q-vc u s lb8qh8ft8 ui160fve)if 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 f;zi9e b*55 l bd*pssl34anz28kehh h a reporter shooting pictures of her at home. She claims the reporter was trespassing. To prove he bazdi hk ;p5 b*lflh8nh9se z*5se234r 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 oi.6f dxtx0c ;bl.4j mcn 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 c- i9q3gfp rn3mm in 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 focar33npg i -qmf9l 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 c.:t fw))av v)jhr t(1sqq;kkfertain converging lens, it forms a real image. When the object is moved to 40.0 cm from the lens, the image moves 10.01qw)th. (s;jvafrq))tfv: kk cm farther from the lens. Find the focal length of this lens.    cm