What would be the appearancp u: j(kpm;,dte of the Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fleet in the haj (iessi2nc 6/fh57x:al 2 hd 8sxjbh,rbor of Syracuse by focusing the rays of the Sun with idxsh572jec n6ha s(, ijsh b8:lf2/xa huge spherical mirror. Is this reasonable?

Although a plane mirror appears to reverse left and4l( +tlav,knz right, it doesn’t reverse up and down. Explain.alnv t+k(z4,l

If a concave mirror produces a real image, is the image necessarily invertedbvu82-8kwn g *9xl uyd? Explain.u8*lg bk 8xu-nw2yvd9

An object is placed along the principal axis of a spherical mirror. The magnifang.c1 qzdmryp(+dd8h) 9) ddication of the object is -3.0 Is the image real or virtual, invehgrz a.q y)n1 m)d+p ddcd(9d8rted or upright? Is the mirror concave or convex? On which side of the mirror is the image located?

Using the rules for the thvquu1 tu0x1 b,ree rays discussed with reference to (Fig. Below a), draw ray u0utxb ,11quv2 for (Fig. Below b).
(a)
(b)

What is the focal length of a plane mirror? 98ztyr z ox4i8What is the magnification of a plane mirror8t8z94oxyi z r?

When you look at the Moon’s rhh:t:b1c fs,i4eu2 m leflection from a ripply sea, it appears elongated . Explain. if:be:ctsh ,h1mlu42

What is the angle of refraction when a light ray meets the boundary bet /vs/ :gq/vj5dly 8kemween two matk ysv:v5g qle///8 jdmerials perpendicularly?

How might you determine the s n+ 4t7-:jytp)tlyfbd; ize1w peed of light in a solid, rectangular, transparent object?ptd;t+:y-j4ntfil z1) 7 b ywe

When you look down into a swimming pool or a lake, are y*8qdz5 , p7liji kc:.;gba2 xhij dbb)ou likely to underestimate or overestimate its depth? Explain. How does the apparent depz.bgk*2i cbaq i, :bh l;pix8j 57dd)jth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show whhm:m:louy o5 :-cz a.jy a stick looks bent when part of it is under water (F- mo::auo:cm5jhyzl. ig. Below).

Your eye looks into an aquarium and v t +oxoj1pc6z;0ec e0 vegu d/u+w3ds3iews a fish inside. One ray of light that emerges from the tank is shown in (Fig. Below), ud;gouxcoves60cept0we+ 3 j1d/ +z 3as 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 wateuo5w r.ov: p*b*esnl ;r on a table even though the water is transpbo5*.s;vw*l: p r noeuarent and colorless?

When you look up at an object in air from beneati;nvkt ; 2+-5nfy2*o +*g xtrixwzxs rh the surface in a swimming pool, does the object appear to be the same size as when youxrvxygw tz + r5ok ;nxsnf-;2*2+ tii* see it directly in air? Explain.

How can a spherical mirror have a negative object d g4-g7h /z,p(o b rpr,rq)hdbyistance?

Light rays from stars (including oumfxgcgv5 xtc;zvohi 3x:20 eh :jh4/*l.,uu f r Sun) always bend toward the vertical direction as they paslhgmfvc0otvh xxi; u /. jucg:3:f4 e,x2h5z *s through the Earth’s atmosphere.
(a) Why does this make sense?
(b) What can you conclude about the apparent positions of stars as viewed from Earth?

Where must the film be placed if a camera lens is to make a sharp imageav7 72qx3 uu+nrxl f :;7tlyqd of an object very far aw3:+utrlnudv7;a xq27yf7 q x lay?

What type of mirror is. ,*)z*g7bs yaca rzsbje)m4s shown in (Fig. Below)? Explain.

A photographer moves closer to his subject and then refwt 3o1/gsca/focuses. Does the camera lens move farther from or closer to 1ft/c3 sgwao/the film? Explain.

Can a diverging lens form a real image under any circumstances? Explaiqe1 a g3y8.kson.

Use ray diagrams to sh0 lk,zvgw7fiv/m*57j2d v3 b fmacuw.ow that a real image formed by a thin lens is always inverf,5g c7ub/7dlwm*v k0imwv. f2jv az3ted, whereas a virtual image is always upright if the object is real.

Light rays are said to be “reversible.” Is this cotb4rvq8.m d+a6qpa.knsistent with the thin lens equation? Explainm .qqbkparvt d .86+a4.

Can real images be projected on a screen? Can virtual i, m+he87j.bq,8p7pw84epfmo muyjsrmages? Can either be photographed? Dis8 ,p8emr.juhbjpo7e my qw+ m,7 fp84scuss carefully.

A thin converging lens 4ylb68b)s d mb4/ *wmhe(e -ie xtcu:nis moved closer to a nearby object. Does the real image formed chul/)yd-w *4 cm b m4e6eh:8 (bexbsnitange
(a) in position,
(b) in size? If yes, describe how.

A lens is made of a 87 por7 +sw) r-nllkfcmaterial with an index of refraction n = 1.30 In air, it is a converging lenw7fr8 +ps kol7-) cnlrs. Will it still be a converging lens if placed in water? Explain, using a ray diagram.

A dog with its tail in t9u5o)ma +e njpkx-300 2p5qlsqkmnofhe air stands facing a converging lens. If the nose and sf5pujq+32kkm 5xnn0p mql o-) eo90athe tail are each focused on a screen in turn, which will have the greater magnification?

A cat with its tail in the air stands facing a converging lens. Under whzawda ,mnf4c*j38 u 8qat circumwama q34ucj,z* 8 nf8dstances (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 9)s32 4k2y7y7iz7f haos yad+e ip tenshorter focal length than the diverging lens if the latter’s focal length is to bt74k7iany97)pseiy ez + fao d3yhs22e determined by combining them?

Explain how you could ha.6 xud hek,q4u:(btgi ve a virtual object.

An unsymmetrical lens (say, planoconvex) for adfp):p 5-wzzms an image of a nearby object. Does the image point change if the lens is turned arou z) pwf5d-:azpnd?

The thicker a double lu5kej) j js5z v+39 ;zfji.rlconvex lens is in the center as compared to its edges, the shorter its focal length for a given lens diameter. Explairj.lj e vz5 fukzl)5ij+3;j9s n.

Consider two converging lenses separated by some distance. An object is placedcf 4jj 0tgu19xlp7k-k so that the image from the first lens lies exactly at the focal point of the second lens. Will this combination produce an image? Iftk7fj9c uk-0xgpj l41 so, where? If not, why not?

  Suppose that you want to take a photograph of yourself as you look at y a3z)db (j-rqkour image in a flat mirror 2.5 m-rkb d)3 za(qj away. For what distance should the camera lens be focused?    m

When you look at yoursel 9dsrwmh,n)dkn9u zdl)2e , w:f in a 60-cm-tall plane mirror, 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 ) sd 9,undk ewd mrzh9n)w2l,:why this should be true.

  Two mirrors meet at a geub 3 c42yq.l:ctbf0135$^{\circ}\,$ 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 abov t9jdmtt8ur7 mecol :+n*6se;ym 6j6ve the floor stands 2.20 m in front of a vertical planemtdemv*:e6 6tumj7 + st nlojr;y968c 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 mirror?    cm

  Suppose you are 90 cm from a plane mirror. What area of the mirror is used t14nx-l9 poiwa*oro g+o reflect the rays entering one eye from a point on the tip of your nose if your pupil dpr+1no lgw-a4oo9x*iiameter is 5.5 mm?   $\times10^{-6}\mathfrak{m}^2$

Show that if two plane mirrors meet at an anij ,t kl3z1qvxo gtx-5v,c6n5gle $\phi$. a single ray reflected successively from both mirrors is deflected through an angle of $2\phi$ independent of the incident angle. Assume $\phi<90^{\circ}$ and that only two reflections, one from each mirror, take place.

  A solar cooker, really a concave mirror pointed at the Sun, focuses the lo9ezglv 98.1lc zw2y Sun’s rays 18.0 cm in front of th9elzc y1z8 wgov9. l2le 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)4i*sqojosk1 6fp q27r must an object be placed if its image is *s2i skqoj6orf1 pq47to be at infinity?    cm

  If you look at yourself in a shiny Christma. -*gw imsdpu0s tree ball with a diameter of 9.0 cm when your face is 30.0 cm away from it, where is your image? Is it real or virtual? Is it upright or inverteid.-w*gps0 u md?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shows an upright image of a tqwkz8:fbd67kp sjf at8.+v/ny person who stands 1.4 m in front of it. If the image is three times the person’s height, what is the radius of curvat8 a7bs:/t fj.fdqz8+vkwp k6ture?    cm

  A dentist wants a small mirror that, when 2.20 cm from a tooth, will proddu c+; bms*rbok*ob;+uce a $\text{4.5×upright}$ image. What kind of mirror must be used and what must its radius of curvature be?
 ----待选择----convexconcave 
r =    m

  Some rearview mirrors produce images of cars behind you that are shiwnoeda/q 7k 7-t 2glti(f6 9maller than they would be if the mirror were flat. Are the mirrors concave or c-/f (nwqoikl96age t i7h2d7tonvex? What is a mirror’s radius of curvature if cars 20.0 m away appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is placed 20.0 cm from a 0 rq6a*7vbvotpx./1a - cm:hehv1 ndhconvex mirror of radius of curvature 20.0hx a 1r7b e.hh:c 0tpvavn6-*vq/dmo1 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. You estimate ljj+od*wy wq8 /eu d52xm/qj2the height of your imag w j/jxou2m *8le/d w5qy+2qjde to be half of your actual height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an objess h0h**v5sbn1: s0yetr:i kwct be placed in front of a concave mirror so that it produck t: ves* bn ssy:0w0ri*5hs1hes an image at the same location as the object?
(b) Is the image real or virtual?  ----待选择----realvirtual 
(c) Is the image inverted or upright?  ----待选择----invertedupright 
(d) What is the magnification of the image?   

  The image of a distant tree is virtual and very small when v9-1xi33v d wc)xpchnmiewed in a curved mirror. The image appears to be 18.0 cm behind the mirrxcwp-1idm c 39v3h)xnor. What kind of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniques,s e+d5ozmh 3:e
(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

Show, using a ray diagraf w90- u5vjbzkm, 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 show tha*(qg: g bnsyp3 hwlj83t the mirror equation, Eq. 23–2, is valid for a convex mirror as lngg q3bpjy83w *hs:(long as f is considered negative.

  The magnification of a convex m7 +og,1:ox/rsqzpx, fbj gyw)irror 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. Itl zgq2ta)rd;cn.41 ce tnz51 g*a4jw d is desired to produce a virtual image that is upright and 3.5 cm ztg dr. c*w)a1njng;5da144l q ezc2ttall.
(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 magniwns .m9x5 s5hbfy your face by a factor of 1.33 when your face is placed 20.0 cm in front .ss5whnm9bx 5 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 i9gakim0 an(c29j t.d j r5rwg,n
(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 is ia *)/ l4vkfeo$2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain substance is 89% of its valuevq7;p z0tft1qk spu1h6qb 6t1 in water. What is the index of refraction of this su1t716h6utpq t f qqs0;zpb1kvbstance? n =   

  A flashlight beam strikes the surface of a pane of glaq t89jwg: :y:nn)qx9gt )prqpss (n = 1.58) at a 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashlight upward from beneath the waterugm.otza03h0mj af.9 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 spotlig* sx4ier/q6ikjzmw yg , 1d5b(ht exits the water at an angle of 6x6 q1 keyzwsdibij4* /(m5g r,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 make a u;0daoksq0)gc*mcm)iqib14v5k1 v v 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 si/a/ yj60vq6g ki1kuse des whose 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 angle of this q1 vyakgj 6ik0/e/u6 slight 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 zb.lxg-n2fr1: k g s(xshines 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 hit the bottom of the pool, measured from the walxggnrs(.k- zlxf1b:2 l beneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equilateral glass prism jq39eld6lw+/ :; ietlshie -yat 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 partiam4(nq-:gvtkh hs65p9 md4++ c0acz,wyb m slxlly reflected and partially refracted. Find the angle of incidence if the angle of reflection is twice the angl, a5nh9gp(hk6s4q ++ bwtlcsdc0 4mmv:-m xyze of refraction.    $^{\circ}\,$

Prove in general that for a light beam incident on a uniform layer of trl55ag,8vw 6 laz65l soh+my amansparent material, as in (Fig. Below), the direction of 6+5w 56a8m v,agzshl y5lmoa lthe 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 refractwpw pcgc42 1nilh4rt5j db8 24ion n as in (Fig. Below). Show that if the incident a r 45w th4wn8 jpl122pbgdicc4ngle $\theta$ 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 foa ,0in16 l2cap:+wicp+c-oltc6 p nq vr the interface between water and Lucite? To be totally internally refllacn0n6, 2i t:vw+pl ppc co61 +iacq-ected, the light must start in which material?
$\theta$ =    $^{\circ}\,$
 ----待选择----waterLucite 

  The critical angle for a certain7gp. ciy(4hxq liquid–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 cm. Where mfjh ba1s cufg/gu1(n55p *n 4bust it strike the air–water interface, relative to the spot directly above it, in order t nhu1/(f4jpg*bua55cgn s bf1hat the light does not exit the water?    cm

  A beam of light is emitted 8.0 c.eh :9ovsr0 syvp7yp9gn mgq*upk: :; m beneath the surface of a liquid and strikes the surface 7.0 cm from the point directly above the source. If total internal reflection occurs, what can qm: g 7pvurs9;nysp9h:g0 e* .voypk:you say about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face sn x.p)1gnx+g)ib5a7m 5epii 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 shown in (Fig. Below). Sho b9myfy wm3lf8+ nqy..w that we can guarantee total internal reflection at the side surface of the material (at point a), if the index of refraction is greater than about 1.42. In other words, regardless of the angle the light beam reflects back into the mater83f my ly+qy..9wn fmbial at point a.

  (a) What is the minimum index of refraction for a glass or plastic prism to be plibvt fj.-z,c(m9 5se zf6-sused in binoculars (Fig. Below) so that total internal reflection occurs at zs.jp5lev-ib f9tc mz,sf(-6 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-length convergiry+lq ;o;eyj-ng lens. Find t jl;-q ;+eyyorhe object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focu5bb1f g *x/b(6 v(fqnv*+fflgu7whvv s at a point 18.5 cm behind a lens.
(a) What kind of lens is it?  ----待选择----converging lensdiverging lens 
(b) What is its power in diopters? P =    D

  A certain lens focuses lig n/p9 9vncd95eb)hg-:a dse0xi pi,dlht from an object 2.75 m away as an image 48.3 cm on t ,n hl09gn-) e9c adbvix9/sd5:ppie dhe other side of the lens. What type of 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 of a 20.5-c2qns ezvg-*u(m-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 le;nbk 8:gi0 kus5i uzu9ns with focal length 24 cm to view a stamp ugi:zb8n9s0k iu;k5u18 cm in front of the lens.
(a) Where is the image located?    cm behind the lens (virtual)
(b) What is the magnification? m =   

  A -5.5-D lens is held 14.0 cm from an object 4.0 mm high. What are the posiw.k*ywh -ux 1h jxrh4f7t- cz,tion, type, and he.ch4-, fzw7j1y*rtwx h -k xuhight of the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens ikq0xha qlo67 .s used to focus an image on the film of a camera. The maximum distance allowed between the lens xq.qkl6 7o 0haand 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× z6wss)sh 4ilincv2e7v3 -e. vwhen a book is placewiel2ehiz nv 647s-s.3vscv) d 8.0 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. Byexem 0emyav.t 3 ( 4r(ciwx(.m how much does the image move if tm(yex4eatcmv(m i w x3(.r0.ehe 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 m7.j /tliao3 zwith a focal length of 25 cm should an object be placed to produce a real imagm3jz/i7a lot.e which is the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-lene vt kwxxmb.: qs1o289gth lens must an object be placed if its imagxtmwqv. 2ok9e:b1x s8e is to be magnified 2.00× and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm

  Repeat Problem 53 for a lens. [Hint: consider objzjk*bs)8w le/o bkg );ects real or virtual (formed by some other piece of opticgoj); w)eks8l bk/b z*s).]
(a)    mm
(b)    mm

  (a) A 2.00-cm-high insec ggbwu0 nn7bi* v)/ uqm.2y*uht is 1.20 m from a 135-mm-focal-length lens. Where is the image, how high is it, and what type is it? *.) m /n7b*qh ivygu0ubgn2uw
$d_i$ =    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 formrmjd7er rrfkiwg-9c225 g:i tee:6g;0ic ,hzed by a 75-cm-focal-length converging lens if the image is 2.5× larger than the objecthw 2rrjr r9gt:g 6ei7:02ce,migikecz 5df;- and is real?    m

  A bright object and a viewing scree .xx7t.4 tmhg a/ q ,(g6k)frzxlhw2 cmbndz4(n are separated by a distance of 66.0 cm. At what location(s) between the objdzl 6h gx .xg(nzwm./m,k(tacbr24fqt)h47xect 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 ld)dr :.a 8ypwxenses are placed 16.5 cm apart. An object is placed 36.0 cm in front of one lens. Where will x):awpy dr.d8 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 withm :hlsa afyz43j2rd- bo2wg +8 $f=-31.5\mathrm{~cm}$ 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 md zp,*9jksu4 diverging lens. Parallel light strikes the diverging lens. After pj dk4m*s u,z9passing through the converging lens, the light is again parallel. What is the focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Ex eg9b sbi.o;az k05(auample 23–12 are now placed only 20.0 cm apart. The kboe a9(s5b.u a0izg;object is still 60.0 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. The -59 eummqdf.u 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 located9 mmudeu -5.qf 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 placed 12 cm to the right of a con 7aq 7.+vlh:j+ gb:zecpd8dvb verging lens with a focal length of 18 cm. An object is +j c8d egq:vpzl.a :bd +7h7bvplaced 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 divz. 9zpwv zg2fhs4o/o;8ut.q terging with focal lep2 .sq.z 4;fz8vu /togwoh9 tzngth 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 a2xh7ck0yf j 5z p(iuye- 4i(lh 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 ob (*ws -kb 2t*o6gahzsurface radii of 34.2 cm and 23.8 cm. What is the focalgbk*6(*ts-ao2hw b oz length if n = 1.52?    cm

  Both surfaces of a double convex lens have radii of 31.0 frmia (nwu74u3o2c 9:m d:2jd:tmher cm. If the focal length is 28.9 cm, what is the index of refraction of whjcu: fi:(odm: ma3 d4re7r9mt2nu2the lens material?    cm

  A planoconcave lens (n=1 5ykc2wgu2mfyzljau8 c :-: f;.50) has a focal length of -23.4cm. What is the radius of thyuf82j:zcgw :af-5;ul2ymc k e concave surface?    cm

  A Lucite planoconcave lens (see Fig. Below) has one 1c dfjr4pf3j xs0iwo-ov4h ; 1flat surface and the other has R = -18.4 cm. What is the focal ls44;irpx3 f0jv-1co ofw 1hd jength?    cm

  A symmetric double convex lens with a focal length of 25.0 cm isfh-v r+93l,pa uv o0xv to be made from glass with an index of vavf93plrxo v+ -u,h0refraction of 1.52. What should be the radius of curvature for each surface?    cm

  A prescription for a corrective 9mp*w olndakv./s1jmlo+43igo:/dmw v *(qm 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 cu l9 oipqmmv mdw3sn 1vk+oogdjmwl :(/.*4/a*rvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fig. Below). You stand qal+8h 1u 3eerc/)qa c1.5 m away from one of these mirrors and look into it. You will see qe reh1c 3a8q/a )lc+umultiple 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 de 3.k3qz; 8ks5l vke6 7glfr :kndhyg8opth of a swimming pool filled with water. We measure the width (x=5.50m) and then note that the bottom edge of the pool is just; d.g q3rzlk g5e 8k7y6vhkk:sf83o nl 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 +xcak/cxq /q98 gxaw.in air is $\theta_{\mathrm{C}}=37.3^\circ.$ What is the critical angle of the same plastic if it is immersed in water?    $^{\circ}\,$

(a) A plane mirror can be considered a limiting case of a lds uodg4u* q4,x94brspherical mirror. Specify what this limit isgldqr u9*o4b,s4xd u4.
(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 theyi/a.ji/l17 pebzj;hc,w kpm qm+/ 1kr form a 90$^{\circ}\,$ angle as in (Fig. Below). When you look into this double mirror, you see yourself as others see you, instead of reversed as in a single mirror. Make a careful ray diagram to show how this occurs.

Show analytically that a diverging lens can never form a real( )lyd6ngfop4cwqo. t((wc.k+dvm ( t image of a real object. Can you describe a situation in which a diverging lens can form a r(cdy)n kpg(t (.oom .lct +vwqf(d6w4eal image?

  Each student in a physics lab is assigned to 6z 2b0 va tg1/a)q;w8doqlsfefind 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, bu q1q b)d0ve6w/lgt a82;safzo t when they compare notes later, they discover that their answers for the object distance are not the same. Explain why they do not necessarily need to repeat the lab, and justify your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of a prii.gywmnyz .p m;,sw.6sm is $\phi=72^\circ$ see (Fig. Below), what is the minimum incident angle for a ray if it is to emerge from the opposite side (i.e., not be totally internally reflected), given $\mathrm{n=1.50~?}$ $\theta_1$$\geq$    $^{\circ}\,$

The end faces of a cylindrical glaaf6 i +*cx*nwbpfdh0/ ss 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 u/ (v +hfop.mln.d5rh ; cnsp5cm 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 l., 4gfdff4w weens of focal length f, and a white screen for viewing the image is on the opposite ge44 fwff,.w dside. The distance $d_T=d_i+d_o$ between the object and the screen is kept fixed, but the lens can be moved.
(a) Show that if $d_{\mathrm{T}}>4f,$ there will be two positions where the lens can be placed and a sharp image will be produced on the screen.$d_T$>4$f$
(b) If $d_{\mathrm{T}}>4f,$ show that there will be no lens position where a sharp image is formed.
(c) Determine a formula for the distance between the two lens positions in part (a), and the ratio of the image sizes.

  In a slide or movie proj -y*7 ggfan vk.z8f)wo u6gvo5ector, the film acts as the object whose image is projected on a screen (Fig. Below). If a 1v.o n -w )k5z8 6gg*ffgao7vuy05-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 to be proje,* zvdqos :jh5cted on a screen 1.80 m by 2.70 m placed 7.50 m from the projector. What focal-length lens should be used if the :sq*oh,v5zd jimage is to cover the screen?    cm

Show analytically that the image formed by a corg7t zb+, retv9x/pi q f.-v 4rv;rrs(nverging lens is real and inverted if the object is beyond the foca,tbt9xsvpfqvrgz/7(r-v +4 .;ir rerl 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 homee fs ;3wxtrh ;*6uwmr(yd6x, s. She claims the reporter was trespassing. To prove her point, she gives as evidence the film she seized. Her 1.75-m height is 8.25 mm high on the fsx6wr(6yx f*rh t d,3 m;eswu;ilm, 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 fifv5.n hg(i 6koh3c5cclm used in a camera with
(a) a 28-mm-focal-length lens,    mm
(b) a 50-mm-focal-length lens,    mm
(c) a 135-mm-focal-length lens?    mm
(d) If the 50-mm lens is considered normal for this camera, what relative magnification does each of the other two lenses provide? The Sun has diameter $1.4\times10^6\mathrm{~km},$ and it is $1.5\times10^8\mathrm{~km}$ away.    for the 28 mm lens    for the 135 mm lens.

  (a) An object 34.5 cm in front okw:k8b exk7j8d)-a,sf( x yjz f a certain lens is imaged 8.20 cm in front of that lens (on the same side as the obje(kzxeb-:j,fj8a kx8 k d 7)wysct). 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 converging lens, it forms a realh :y*6 y2cprxinr/2fn image. When the object is moved to 40.0 cm from the lens, the ipyc2*6n xy2h:r/ i rfnmage moves 10.0 cm farther from the lens. Find the focal length of this lens.    cm