What would be the appearance of5onzf6jho /4z 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 harbh 2 e9g/0f() 0oda4j icdst-m+kxttnp*fah t. or of Syracuse by focusing the rays of the Sun with a huge spherical mirror. Is this reasokt)0xd. *a j0g thdfehc+2 tns(/ipfa m94-tonable?

Although a plane mirror appears to reverse left and right, it doesn’t reverse uns97 mzd- 0 rzsd,wzh,p ahz,09 szsz7wd -r,dnmnd down. Explain.

If a concave mirror produces a real image, is the image necessarily inverte l nb-szx/gk9 g4o1sn)d? Explainx/ )9-zg4sl1og s knbn.

An object is placed along the principal axis of a spherical mirror.qk7 tckc5x5dt8 km :l(ln*o(h The magnification of the object is -3.0 Is the image real or virtual, inverted or upright? Is the mirror concave or convex? On which side of the *c(tkh 8tklq(7l:5 oxc knm 5dmirror is the image located?

Using the rules for the three rays discussed with reference to (uzdl -k.*53mdj5dr mbFig. Below a), draw r5ddm-uzr*m j bk35.d lay 2 for (Fig. Below b).
(a)
(b)

What is the focal length of a plane mirror? What is t -d0dv:a: dltqhe magnification of a plane mirdt-q l0v:d: daror?

When you look at the Moon’s reflection from a ripply sea, it appears elongwt:e muu q6d27ated .e mdq 62w:ut7u Explain.

What is the angle of refraction when a light ray meets the bo/ 8 wqy)ogi+ipundary between two materials perpendi8+o)y i qipwg/cularly?

How might you determine the speed of light in a solid, b/ov uvm wu-:0l -akt(rectangular, transparent object? /u:b-tvma ol-uv(k0w

When you look down into a swimming pool or a hd)+kgtcyw2/h )kzat jw w03: lake, are you likely to underestimate or overestimate its depth? Explain. How does the apparent depth vary with the viewikkt+)w)3 hh2wg:wydca/t 0zjng angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks b l5/d oq+bk9pgyy7)zy ent when part of it is under water (Fig. Belog kdyly)5+y b9 p7/zqow).

Your eye looks into an aquarium and views a fish inside. One ray of light that nj 8uy..l.k rxemerges 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 actuay8kx..lr jn u.l fish. Briefly justify your answer.

How can you “see” a round dropy :9gyl y9i6igyul :g4 of water on a table even though the water is transparent anyy 6liygl:9gg:i uy94d colorless?

When you look up at an objec,j(;b t 6zusae2p3left in air from beneath the surface in a swimming pool, does the object appear to be thee l j, tfa;(beus6z2p3 same size as when you see it directly in air? Explain.

How can a spherical mirror havermy:z , umqw56u(prn8t1x.s q a negative object distance?

Light rays from stars (including our Sun n 4 fl-.najdd)os s+b6b+hw7m) always bend toward the vertical direction as they pass through the Earth’s a 4 loans)s7 +wn+j mbh6dfbd-.tmosphere.
(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 plk zh2 *ptz.z. k3/xiilaced if a camera lens is to make a sharp image of an object very fxhkpkzii*tz l/2z3.. ar away?

What type of mirror is shown in y v-7esg9c5u)v iy.sr(Fig. Below)? Explain.

A photographer moves closer to his subject and then refb u2vb;f3:7h-hdwq gfocuses. Does the camera lens move farther from or closer to the film? Expf ; h7gh:vd2 3qbwfu-blain.

Can a diverging lens form a real image undermc,wve.p(h kauf md (rb2*;4g any circumstances? Explain.

Use ray diagrams to showw9 16+yk y2tgtrqz8fn that a real image formed by a thin lens is always inverted, whereas a virtual image is always upright if the object isn16gk9r2 8tyy fqw+zt real.

Light rays are said to be “reversible.” Is tk1/bx7yw 29rtekpc v27dwu*mhis consistent with the thin lens equabdu27xt m w9p 2ew7v yr1*ckk/tion? Explain.

Can real images be projected on a screenhxw4n s x5x/cis)d(0 q? Can virtual images? Can either be photographed? Discuss cahq( )ixxdwss405 cn/xrefully.

A thin converging lens is moved closer to a nearby object. Does the real e6uz*x jfb77v image formed change 7fvz uebj7x6*
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of refracti.8vm9zt5 g dj2x ctr,e/aip r9on n = 1.30 In air, it is a converging lens. Will it still be a c9r8/9zjxt,2 .t5dvgirpmae converging lens if placed in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail inr-ws+,r mt2d h the air stands facing a converging lens. If the nose and the tail are each focused on a screen in turn, whic,swr h2mrt+d- h will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stand81va4 l:4.l r)uutgzt w(du v9izlqz8s facing a converging lens. Under what circumstances (if any) would the image of the nose be virtual and the rlut z4 948d.aqu zlviulvt1w(g ):8zimage of the tail be real? Where would the image of the rest of the cat be?

Why, in Example 13, must xzcxx +gh) l-30ko9iyc3+kzq the converging lens have a shorter focal length than the diverging lens if the latter’s focal length is to be determined by cokx3l)0iq9h +k+cg-z yxzcox 3mbining them?

Explain how you could haw +tttc1y2z y;43sg fkve a virtual object.

  An unsymmetrical lens (say, planoconvex) forms an image of a nearby object. Doz xu,in4 5-r gvkm,f)ies the image point change if the lensnrm,)4 f5, kgvizu xi- is turned around? ----待选择----yesno 

The thicker a double convex lens is in the center as com :dp tudz t::tyk 7rt4w.ag94a:kx/nvpared to its edges, the shorter its focal length fp47ta:g9tda:v:4n/dyt u.kr :k x wztor a given lens diameter. Explain.

Consider two converging lenses separated by some distj1vxj r 6vrg.+ance. An object is placed so that the image from the first lens lies exactly at the focal point of the second lens. Will this combination produce an imagejx v+ j6r.vgr1? If so, where? If not, why not?

  Suppose that you want th+.d0y mlxv/92gf;9r g+cu(t; hxqb dqhq p g9o take a photograph of yourself as you look at your image in a flat mirror 2.5 m away. For w9q 9+b hdx frgy2gg;qtpdm h.0;lc(+ /xuvh9qhat distance should the camera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mirror, youit-94j+g u , 7n* nxojptmjbv. see the same amount of your body whether you are close to the mirror or far away. (Try it and see.) Use ray diagrams to show why this should be tu 9+ngm.nj4jvpott,jx-bi* 7rue.

  Two mirrors meet at a 135fz(kn 0csr3v7;a9sgw $^{\circ}\,$ 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 abovervc9em3 c90: fhy wnd6 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 9ny fh:6rc930 wd vmcethat can be seen reflected in the mirror?    cm

  Suppose you are 90 cm from a plane mirror. What area of the mirror is used to ky; *(o wqs+gabs*1jhreflect the rays entering one eye frj ( s+h *1*w;kboasygqom a point on the tip of your nose if your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors meet at ann3*n , 9wi:xml-,zqbgrygt u4 angle $\phi$. a single ray reflected successively from both mirrors is deflected through an angle of $2\phi$ independent of the incident angle. Assume $\phi<90^{\circ}$ and that only two reflections, one from each mirror, take place.

  A solar cooker, really a concave mirror pointed at the Sun, mlu 44sp* rp-1e( galgfocuses the Sun’s rays 18.0 cm in front of the mi pp4 lgrg*4suale1-( mrror. What is the radius of the spherical surface from which the mirror was made?    cm

  How far from a concav-l0c9.vvb yoi3w 7 lace mirror (radius 23.0 cm) must an object be placed if its image is to be at in.-acb 9v0 lc yli7ow3vfinity?    cm

  If you look at yourself in a1ojwpr 2;l eqr)jun rs:b-0;n shiny Christmas 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? Isn1qrjs l n;)ob:wu0e2 r;rpj- it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shows an upright image of any person who stands 1.gs *0o.gwg3 u *bmzyq94 m in front o9w gm. z0gb*u3g qyo*sf it. If the image is three times the person’s height, what is the radius of curvature?    cm

  A dentist wants a smalcqh6/z4 m-tk,2h oyc yl mirror that, when 2.20 cm from a tooth, will produce a $\text{4.5×upright}$ image. What kind of mirror must be used and what must its radius of curvature be?
 ----待选择----convexconcave 
r =    m

  Some rearview mirrors produce images of cars behind you j8vbpxr lfrt92 1l*+s .6azjgthat are smaller than they would be if the mirror were flat. Are the mirror b1+*lprjzt96x2rlfag.sv 8 js 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 mm high v 7t1unmihftz 37njiz(ua72 6is placed 20.0 cm from a convex mirror of radius of cur1 vin7nz j7itmzh26u3tu7af(vature 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 mirryk ,4osluv(y3 or in a store. You estimate the height of your image ylky4u, v 3os(to be half of your actual height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object be placed in front of a conccqkl4:9 yse(xave mirror so that it produces an image at te9:4 sxc( qlkyhe 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 /hqdel 2uzsa4(ij ;j96r p3a wand very small when viewed in a curved mirror. The image appears to be 18.0 cm behind the mirror. What kind of mirror is it, and what is its radius of curvatu a49j3hq p(esjz/rw62li;a u dre?
 ----待选择----convexconcave 
r =    cm

Use two different techniv.ez vi8a -v39+jmnsdques,
(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, tm l 7-(qv,ndnvhat the magnification m of a convex mirror is $m=-d_\mathrm{i}/d_\mathrm{o},$ just as for a concave mirror. [Hint: consider a ray from the top of the object that reflects at the center of the mirror.]

Use ray diagrams to show that the mirror equation, Eq. 23–2, is vabzbq/fs-ha:lf 1zus jx 0f2) )lid for a convex mirror as lousa1z f)/j2s)fzl:b 0fx-q h bng as f is considered negative.

  The magnification of a convex mirror is6 i+.wu; 8 dt2v07hxxmjoxjgu $+0.65\times$ 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.ycapj u -vr/,z0zc1e05x9+t, b fwakf It is desired to produce a virtual image that is upright and 3.5 cm tallpxk1c/ywz-+a 90c u, btvr 05f fajze,.
(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 factor of* cywkt lar,:1 1.33 when your face is placed 20.0 cm in front of it. 1y:w,*ca rtkl
(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 iu5id)qf1iph 2ek 1 o3on
(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 i 9- m0ttc*j 5y geakdqyu(l.b*irw44vs $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain substance is 89% of its v3w2 ry8rccwa zfc*i0 1alue in water. What is the index of refraction of thi c0rr z fw328c*iway1cs substance? n =   

  A flashlight beam strikes the sub:q4r 1;vj ahrq jc67irface of a pane of glass (n = 1.58) at a 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a fla + n) -v.8v,e m8hc-pbczgjs5hhs xi:sshlight 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 f uti0z;.cfsn p,eajpfvo +d)va(3 3(yrom an underwater spotlight exits the water at an angle of 66.,a 3;0ycj e+z v3f(ftp).(v ouni spda0$^{\circ}\,$ 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 see6c+ q0(k udn8vyrpvo / jki42bn to make a 31.0$^{\circ}\,$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?    $^{\circ}\,$

  An aquarium filled with water has flat glass sides whose t;. 6mbzexuu4 index of refraction is 1.52. A beam of light from outside the aquarium strikes the glass at a 43.5° a uumzb6e4x;.tngle 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 )igxhc hr8b-ae;gc:xz *- pvsij o x745bad20pool at night, a watchman shines a narrow beam of light from his flashlight, 1.3 m above the water bdj*ixz7g-b )vae8 c0;-5ixc sga 2hropx:h4level, 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 wall beneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equilateral glass prism at a 45.0 gqv a1jm000 cz d+2gh 0z*8qktpni9ou$^{\circ}\,$ 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 iai2c-fk np:wc0 dl .0as partially reflected and partially refracted. Find the angle of incidence if the angle of reflection is twice th 02klai cpdw 0-:fna.ce angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam incident on ajbf6-*g*. ,av +mcjtp g -zstn uniform layer of transparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the incident beam, in jg s6+j fmvt*t,az-c*b g.pn-dependent of the incident angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on a fla;vgsn/pxh+ j0c9*o3 gmz2 go cv 3k0mjt piece of glass with index of refraction n as in (Fig. Below).ovov3g/h;+zmg030m j9sxpkj g2nc* c Show 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 angle 8wqk9kau*f0,n z*hcmbwox au :5h ++zfor the interface between water and Lucite? To be totally internally rebnhqkz*a+8u,*0:9c uawmkhw+x fz 5o flected, the light must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certainvf09w n,go3v :vea;- genwm1z elu-in:ld 5 9f 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 pok7( s c2;yoh.bdmr xy(ol of water from a depth of 62.0 cm. Where must it strike the air–water interface, relative to the spot directly above it, in ordeb7(cx h;yoy( .2rd mksr that the light does not exit the water?    cm

  A beam of light is emitted 8.0 cm beneath the surface of9./eg zxcx bn- m/4fof a liquid and strikes the surface 7.0 cm from the point xgzb.ec o/-x/f9fm4n directly above the source. If total internal reflection occurs, what can you say about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strike 7j4cfzo7.rgh s the left face 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. Belowwxbxh u5/oq pjdoxg72;/z,4l). 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 of the angle the light beam reflects back into the material at po, l4;jwqph uo/xd2gxzx75o/b int a.

  (a) What is the minimum index of refraction for a glass 1zyrh ex,87-zp cnc2v/ wss6j or plastic prism to be used in binoculars (Fig. Below) so that total internal rsz 7c2 -6xwe/ny8,zchsjp1v 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 mkf kw((c/v:va 65.0-mm-focal-length converging lens. (:w k /kcv(vfmFind the object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a pointyp7bzffb) ;nu(a) o57luq0 q y 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 frolcv72tj //4:1lupr*a kzjvccm an object 2.75 m away as an image 48.3 cm on the other side of the lens. What t: z 1cvr*74lcpkj atu2/vjcl/ype 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-cm-focal-length lens? Pje emj:6wj9 wfg 67yam6ws6.i =    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 ca1 (stt,q veb89qa*gd6+ tyenonverging lens with focal length 24 cm to view a stamp 18 cm in front ontasedbq y, e*8tq 61+9g tva(f 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 r/sxc.jabumult n c :(lp*+1,14.0 cm from an object 4.0 mm high. What are the position, type,/ltc:1r +,usc. bnm*axluj(p and height of the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens i3rwwe +)1a.8een;p gr,9pq 6rb sr fvh o8wvd.s used to focus an image on the film of a camera. The maximum distance allowedd9q rr )e r8wa.3pno6wvswgr8ephe ; b +,1.vf between the lens and the film plane is 120 mm.
(a) How far ahead of the film should the lens be if the object to be photographed is 10.0 m away?    mm
(b) 3.0 m away?    mm
(c) 1.0 m away?    mm
(d) What is the closest object this lens could photograph sharply?    mm

  It is desired to magnify reading material by a fac4 /g9lf(m txu.edo gd*tor of 2.5× when a book is placed 8.0gm (l*d4g.9f dx/ueto 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 ffn2iq2e.l.baoy c. k2ugz5)jp,i wz97b0 xiqrom an 8.0-D lens. By how much does the image move if the objectz5 e072l,iwb2 )f.q. ibu. cgojq xpzk i2nya9 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 c o t mfl0uc.zv.j)vr5v 9(v7llens with a focal length of 25 cm should an object be placed to produce a real image which is the same size as th v.7jzvflc.c9 )v rv0lm5u( toe object?    cm

  (a) How far from a 50.0-mm-focal-length lensa)-sr to vbmzav-t130 must an object be placed if its image is to be magnified 2.00× and be real? m v 3b-t1aor )0szavt-   mm
(b) What if the image is to be virtual and magnified 2.00×?    mm

  (a) How far from a 50.0-mm-focal-leng;vw2y 8od5 ygnth lens must an object be placed if its image is to be ma8oyv; 2ywng5dgnified 2.00× and 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)rkd)xt+ ue/qp28c in a 135-mm-focal-length lens. Where is the image, how high ic)enkti2du8+ r) x/pq s 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 image formed byxwyl, xg /j21o a 75-cm-focal-length converging lens if the image is 2.5× lax/,go1x2y jwl rger than the object and is real?    m

  A bright object and a viewing screen are separa8982/0)hkr megswz a+ wreyqg ted by a distance of 66.0 cm. At what location(s) b rhw)e8 y/a0m+zq2kr8 9sggweetween 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 should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length converging lenses are placed )i*o yh0 e)yac16.5 cm apart. An object is placed 36.0 cm in front of one lens. Where will the final o *eyac)y0ih)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 with4v(hd pz+qeu8ye + e5f $f=-31.5\mathrm{~cm}$ 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 divergpoqd3) c.2c laing lens. Parallel liq) l3p. 2occdaght strikes the diverging lens. After passing through the converging lens, the light is again parallel. What is the focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lens hy:7;na.f qvkxt4 r+7zx9*va.bt y jses of Example 23–12 are now placed only 20.0 cm apart. The object.y4.*a;7:+hfbjtzv kxqn a 9vxrs7 y t 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. Th6dv ka48zdpcz1 k6-p0 ubcv6 he focal length of the lens on the right is 20. vkvuk8 cazp 16hzcp6- 0d6db40 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. How far to the left of the 15.0-cm-focal-length lens is the original object?    cm

  A diverging lens with aow, 0 s0/3gt,xazzhfg focal length of is placed 12 cm to the right of a converging lens with a focal length of 18 cm. Axoz/zg h0sw, g0ta3,fn 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 2aams2z4pl, l kh2 5fcigxw6 +)0.0 cm and one diverging with focal length are placed 25.0 cm apar6p swa,+ kfzagl22cm 4h) x5lit. 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 mss4gu;. o/lxof focal length $f_C$ as in (Fig. Below). If $f_T$ represents the focal length of the combination, show that the focal length of the diverging lens, $f_D$, is given by
$\frac{1}{f_\mathrm{D}}=\frac{1}{f_\mathrm{T}}-\frac{1}{f_\mathrm{C}}.$

  A double concave lens has surface radii of 34.2 c2mkar qtb2, rfiva)ah 4*):rem and 23.8 cm. What is the foca)m irrfe4 bav2aqt*k, r :h2a)l length if n = 1.52?    cm

  Both surfaces of a double convex lens have radii :-gxj(t dx bt-of 31.0 cm. If the focal length is 28.9 cm, what tbxtj- (:-dgx is the index of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm. What is th-i+)ybkwxss3 z mc+l8e radius of the lsk ws yc)3i-+xzbm8+ concave surface?    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat surfze21 . ncx;jtz8s bhao6ml99yace and the other has R = -18.4 cm. What is the focal length? s1.bh2 z8zjl ;6tyan9xomc9e    cm

  A symmetric double convex lens wic1iy(ot h67 ym1px5hpk2f tq(th 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 curvatur o1(pqxtt52ycym(ph1h7k6ife for each surface?    cm

  A prescription for a corwv4s;2 ccw3x frective 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 tw;c f34vx sc2whe radius of curvature of the other surface?    m (convex)

  Two plane mirrors facp e,ya 7g/4jatsw(j)fh)x;z h vx;1 yde each other 2.0 m apart as in (Fig. Below). You stand 1.5 m away from one of these mirrors and look into it. You will see multiple f)4(txy dxj/ h,pyvj1ahea7;s;)w g z 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 with water. We measure nlxd;qb39wt d4q/ 3jl the width (x=5.50m) q ;/nbdl43j 3 lwq9tdxand then note that the bottom edge of the pool is just visible at an angle of 14.0$^{\circ}\,$ above the horizontal as shown in (Fig. Below). Calculate the depth of the pool.    m

  The critical angle of a cecea2*shh lr uo66am 1dixf,8 6rtain 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 c*a ,bmib* i9cnwsri ;-onsidered a limiting case of a spherical mirror. Specify what this limit ii-aimnrb** 9 i,w;sbcs.
(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 th:e knpre j z-j ,*ns9iy2fs5a))n1povey 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 tha8,9ya3 sb ipk wguv p,wbt394tt a diverging lens can never form a real image of a real object. Can you describe a situation in which a diverging lens can f3a,ikbu4gp9 y8sw t,tb pwv 39orm a real image?

  Each student in a physics legy 1lpc+ z w+u8pm+ 6e4o9evqab is assigned to find the location where a bright object may be placed in order that a concave mirror with radius of curvature+qzo 86e cuvelwm4+yp1p 9+g e r = 40 cm will produce an image three times the size of the object. Two students complete the assignment at different times using identical equipment, but when they compare notes later, they discover that their answers for the object distance are not the same. Explain why they do not necessarily need to repeat the lab, and justify your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of ab6s 9ecid3d3f/;hvc ckx x m x(5db) -gvd-yk/ 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 cylindric1a lg7z z;5ejq4xt+qz5w kv:w al 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 lej2v 7 6ail r2iio26)rw cht0kgngth $f_1=15\mathrm{~cm},$ 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 focal length f,oyb6om j+oeh2s: um8, and a white screen for viewing the image is on the opposite side. The dissobmy8j h +:e,ou6mo2tance $d_T=d_i+d_o$ 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. p;r: -msdspc is projected on a screen (Fig. Below). If a 105-mm-focal-length lens is to project an image on a screen 8.00 m away, dp;-pc: r.mss 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 pr3llkjsxp. s 22ojected on a screenxljssl. k232p 1.80 m by 2.70 m placed 7.50 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 convery2rk8lq8j63 :ahce b kging lens is real and inverted if the object8kyahb6jq er 83lkc:2 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 rep nv-ku8p6y/ gvorter shooting pictures of her at home. She claims the reporter was trespassing. To prove her point, she gives as evidence the film she seized. Her 1.75-m height is 8.25 mm high on the film, and the focal length of the camera /-kg6vp y8vnu lens was 210 mm. How far away from the subject was the reporter standing?    m

  How large is the image of the Sun on qdjm:m /1unscsxm v7l 0k6dp:m7 .cu.film used in a camera with
(a) a 28-mm-focal-length lens,    mm
(b) a 50-mm-focal-length lens,    mm
(c) a 135-mm-focal-length lens?    mm
(d) If the 50-mm lens is considered normal for this camera, what relative magnification does each of the other two lenses provide? The Sun has diameter $1.4\times10^6\mathrm{~km},$ and it is $1.5\times10^8\mathrm{~km}$ away.    for the 28 mm lens    for the 135 mm lens.

  (a) An object 34.5 cm in front of a certain lens is imaged 8.20 cm in f8nm0 p4vwuah i;f ,w7d*(jhvgront of that lens (on the same side as the object). What type of lens is this, and what is its focal length? Is the imageh;0 pwijn m8vhv*f7a(4dw , gu 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 fro5 ra7j; inbe+dm a certain converging lens, it forms a real image. When the object is moved to 40.0 cm from the lens, the image moves 10.0 cm farther from the lens. Find the focal length of this lens.+; d r75naeijb    cm