What would be the appea;uvi3zy d5r :prance of the Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman f7k4jsctzy26 xleet in the harbor of Syracuse by focujk 4czx6 y7s2tsing the rays of the Sun with a huge spherical mirror. Is this reasonable?

Although a plane mirror appears to reverse left and right, it doe0oso rko rk1 j5z,u:u(sn’t reverse up and down. Expus1ko0rou,z 5(o :rjklain.

If a concave mirror produces a real image, is bca23c0/txtq8wnh5g;- y/md 3w e wlqthe image necessarily inverted? Exp; /g5aq thnww2 em8 yb3t-w0/l3dcxcq lain.

An object is placed along j7g-b0,zvug:a fcb8 2pe4kdc3 +afer the principal axis of a spherical mirror. The magnification of the object is -3.0 Is the image real or virtual, inverted or upright? Is the mirror conca2, ck4c g bejuarvfb 0fdea+:zg38-p7ve or convex? On which side of the mirror is the image located?

Using the rules for the three rays e il;15,nk 1nkgegfm/discussed with reference to (Fig. Below a), dkm/ e11efi gkng; 5,nlraw ray 2 for (Fig. Below b).
(a)
(b)

What is the focal length of a plane mqy( f/y4p b /o.y ceswq*3qb/mirror? What is the magnification of a planeb/pqy f3 4w yqq(/.oe b*smc/y mirror?

When you look at the Mof:14dn -flcgz on’s reflection from a ripply sea, it appears elongated . Explai 1f:fnd-lcg 4zn.

What is the angle of refraction when a lighzhy2mo z84t2q4(,hqgt em gk/t ray meets the boundary between two materials perpendicularlytqgo g q2,2m(kzmz4te4hh8/y?

How might you determine the speed of light in a solid, z g4(,h/bvrijo/ r2uhrectangular, transparent objebz rv2(igoj hhu/r 4,/ct?

When you look down into a swimming pool or a lake, are ,xn ewgg0x 8/ryou likely to underestimate or overestimate its depth? Expla,rwg xe/n08g xin. How does the apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why/ k.k3ao agop: a stick looks bent when part of it is under water (Fig. Bea og 3okk:p.a/low).

Your eye looks into an aquarium and views a fish inside. One ray of lic-u +-g3w oalvwyq2e/rx2ywcy6u6 2xght that emerges from the tank is shown in (Fig. Below), asy 2c- + x-y3/6rqc6woauxelwuyg v22w 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 roucxh1o6;*sk nbyo 9, zr 6o7ainnd drop of water on a table even though the water is transparent and o 6x1oh ic,6bna;on9 szk*ry7colorless?

When you look up at an object in air from beneatht3 l-ztp41bjv the surface in a swimming pool, does the object appear to 3tp1z lbjv -4tbe the same size as when you see it directly in air? Explain.

How can a spherical mirror have a negamdnthrd vp i3,,yh4/4n wp6k 9tive object distance?

Light rays from stars (including our Sun) always bend toward the vertical direc1lnufel y41 1 5*a3kjnx ;osqbtion as 4k1a5lf*u xl;3nybs qo11en jthey pass 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 make9sjx0 b/o sv3+/i 05o b0phslc0rdldmm fa3. u a sharp image of an object very far 903/lpxd ubi v0 /mlsr0hajs s 5dboo3fc.0+maway?

What type of mirror is shown in (Fig. Below)?+qpsg;3 g d* qh88gkfs Explain.

A photographer moves)dyzt.lpi d/+ , i;lws closer to his subject and then refocuses. Does the camera lens move fas.zlip+,; id l/)dywt rther from or closer to the film? Explain.

Can a diverging lens form a real image under any d ojs+5lz,ainucmw+ p.g+ ,+x )i3at tcircumstances? Explain.

Use ray diagrams to show th :g hy:y ;klje*8sut06g1y1l 4 uktbkhat a real image formed by a thin lens is always inverted, whereas a virtual im je hlgkt8gl;:h6kty1u*1b:k 0yus4 yage is always upright if the object is real.

Light rays are said to be “reversible.” Is this consg;2/iuy+1 dvu:wmpe q istent with the thin lens equatim+pwe/yu gv1;2d:uq ion? Explain.

Can real images be projected on a screen? Can o sbu bd)a.vv+;nh 5*1bpl6wx virtual images? Can either be photographed?bvp)s*lv . +obxnhw6d5b ; 1au Discuss carefully.

A thin converging lens is moved closer to a nearby objr ;kl epo/11 qu(oe-1rpo.k kmect. Does the real image formed changkpokkr1 erel oo .q (11;-up/me
(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**68qd ydizd c, it is a converging lens. Will it still be a converging lens if placeddqi6d*dcz* 8y in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands facing a converging le3ksxizqd5, r)ngj5e vp u7my+5 4t(j7ri+rinns. If the nose and the tailni)u45dj+zt57j7gkv y,r r sn ipemq+r(xi 53 are each focused on a screen in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facing a convergin dtu, c+2rhul3g lens. Under what circumstances (if any) would h + cd2tl3u,ruthe 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 t2tsb 3jmj+5xj he converging lens have a shorter focal length than the diverging lens if the latter’s focal length is to be determined m3+ b52 jjtjsxby combining them?

Explain how you could have a virtual objectlfbw.,n* +yuf zo/n)me6nd u7.

  An unsymmetrical lens (say,gruyb ia6v-+ ,q5 o3)m:pqgmm planoconvex) forms an image of a nearby object. Does the image point change if the lens is turned aroqmr+5:u gg)a-i3m,yv b po6m qund? ----待选择----yesno 

The thicker a double convex lens is in the center as cor/;3/avh i h46jzxh)jmko fdf22 1pne mpared to its edges, the shorter its aoej h;23 hnp fk4f1x/dzh vri)/6jm2focal length for a given lens diameter. Explain.

Consider two converging lenses separated by some distance. An object is qji;xl 8fvpv :q2 uos16vm-nwc .f;h- placed so that the image from the first lens lies exactly at the focal point of the second lens. Will this combination produce an image? If so, where? 8vf.xlq; vuvmf q-n-2 w6j1;cpi: hos If not, why not?

  Suppose that you want to take afikm1;zmgiof 7,c-4gk.d xn4 photograph of yourself as you look at your image in a f,fizkn7i dmggofm- k14x.;c4lat mirror 2.5 m away. For what distance should the camera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mirror, you(x6 fqsg2bf d) 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 bfg6x) dqf( s2should be true.

  Two mirrors meet at 49 js)uzl2)g55pu ze n/cd9bquuvvi + a 135$^{\circ}\,$ angle, (Fig. Below). If light rays strike one mirror at 40$^{\circ}\,$ as shown, at what angle $\phi$ do they leave the second mirror?    $^{\circ}\,$

  A person whose eyes are 1.68 m above the floor stands 2.20 m in front oblf 6)zl:3ybft)p (t zf a vertical plane mirtb3 6zbtp(): yflflz) ror 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. Whaq0y;v q b,zb. ahyz,-xsd* x/u 2lwl+zt area of the mirror is used to reflect the rays entering one eye from a point on the tip of your nose if y w ,s+llzxza/h bu,zqx. 0vydq2 b*-;your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors mez3 b fe),a wcmnq)z.; 0grdn.q ef/sc)et at an angle $\phi$. a single ray reflected successively from both mirrors is deflected through an angle of $2\phi$ independent of the incident angle. Assume $\phi<90^{\circ}$ and that only two reflections, one from each mirror, take place.

  A solar cooker, really z ymd,jij::i /a concave mirror pointed at the Sun, focuses the Sun’s rays 18.0 cm in front of the mirror. What is the radius of the spherical :j,imz: jdi/ ysurface from which the mirror was made?    cm

  How far from a concave mirror (radius 23.0 cm) /m01y5lqmffle4 5wd p(vhu * xmust an object be placed if its image is to be at infuw 5v/ 4 ephy5(m1ldff*0lmqx inity?    cm

  If you look at yourself in a shiny Christm,e b6g0l 0,udpn:qcf *7uqltfas 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 ue0,c l,6:ubqt qgfp *dnlf70 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 whob x8siuw) xr6 ;gqvs02 stands 1.4 m in front of it. If the image is three times the person’s height, what is the r6sxxr8gu sbv;0w) 2iq adius of curvature?    cm

  A dentist wants a small mirror that, when 2.2; lev6ce 2d 5u.8saedd0 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 wd t*:s: ;srz9avv9t2f hjx m8behind you that are smaller than they would be if the mirror were flat. Are the mirrors concave or convex? What is a mirror’s radius of curvature if cars 20.0 m away appear 0.33× their normal :rad9jt8 : tv*w sxh2;v mz9fssize?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is placed- dyzjh7r6d 4k 20.0 cm from a convex mirror of radius of currjd7yzk hd46-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 mirror in a store.qfz8ms ul/z1he,aq s1h,bnk f-i 0p00 +p)ulh You estimate the height of your image to be half of your actual height. Estimate the radius of curvature of the mil,u fl 0qkhs) hs0p-+m 1f0a81 ez/hiq pzbnu,rror.    m

  (a) Where should an object be placed in front of a c 1d 8+bkzj0t sv7un wloc,7mv(oncave mirror so that it produces an image at the same locatio0s c,m7 1(+vbtvkujd o nlw78zn 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 treemjx6:g2m,l*v e ad fz/ is virtual and very small when viewed in a curved mirror. The image appears to be 18.0 cm behind the mirror. What kind of mirro jd*mlmafveg :z62/ ,xr is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniqumw(1a se2gpnu,qrb+ /es,
(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 conv 2p9tm0+ )qhs4bjz zibex 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 t rw:q5c/hy(n yu/ ,wcjhe mirror equation, Eq. 23–2, is valid for a convex myjqcy w /(,n/r:5uchw irror as long as f is considered negative.

  The magnification of a co qh,f +vj+/v5iot6t rxnvex mirror is $+0.65\times$ for objects 2.2 m from the mirror. What is the focal length of this mirror? $\theta_2$ =    $^{\circ}\,$

  A 4.5-cm-tall object is placed 28 cm in front of a spherical mirror. It is descjot1ki vt6:i) uy5e5e gz*d6ired to produce a virtual image that is upright and 3.5 ckide:6tzv * o51 5t uie6jgyc)m tall.
(a) What type of mirror should be used?  ----待选择----convex mirrorconcave mirror 
(b) Where is the image located?    cm behind the surface
(c) What is the focal length of the mirror? $f$ =    cm
(d) What is the radius of curvature of the mirror? r =    cm

  A shaving/makeup mirror is designed to magnify your -yz) *ul ryywup*e:*hface by a factor of 1.33 when yo:)-eyy*p y**zlu hu wrur face is placed 20.0 cm in front of it.
(a) What type of mirror is it?  ----待选择----convex mirrorconcave mirror 
(b) Describe the type of image that it makes of your face.
(c) Calculate the required radius of curvature for the mirror. r =    cm

  What is the speed of l vi w)e7f;po,v k+eya5nyb +/tight 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 i ce0b5dm)ru w(ce is $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain substance is 89% of itsr7w/lb/fg9z 1+ )x2 darjqxm s value in water. What is the index of refrawsxm/rx 2d 1+z9qlj/f g)7a rbction of this substance? n =   

  A flashlight beam strikes the surface of a pane of glass (n = 1.58) a:c.cq vd 0b o*xpg7w5gt 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 water atie4gug: 5ra (g 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 spotlem35zhki)z2( uovj 0q2 * qhasight exits the water at an angle of 66e5sh v3qk ju qo)az(*mzi2h 20.0$^{\circ}\,$ 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 a8i)ux wwo; ro+ 31.0$^{\circ}\,$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?    $^{\circ}\,$

  An aquarium filled with wateiufww/:;a +-imr l+y,g-dh xjr has flat glass sides 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 ;iglr ,diyw+h --wx mj/+ fa:uangle 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 im)bd /r4el-o at night, a watchman shines a narrow beam of light from his flashlight, 1.3 m above the water level, onto the surface of the water at a point 2.7 m from the edge of the poolo-db /)lemr 4i (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 atpv:6l) 8l f2whay8y0oh 7nxeq 5f8yka 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-fj+x8r wbrg tmkb)4+5*shsu partially reflected and partially refracted. Find the angle of incidence if the angle of reflection is twice the angle ofg wkt+b+ fub)8r5r m4*h -xjss refraction.    $^{\circ}\,$

Prove in general that for a light beam 8yz t) p;fvaz6aer:)+l) hqaz incident on a uniform layer of transparent mz:)aazv)ftq8h ly ;) +6zpaeraterial, as in (Fig. Below), the direction of the emerging beam is parallel to the incident beam, independent of the incident angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on a2 3c,5mwoeit 9o9owlu flat piece of glass with index of refraction n as in (Fig. Below). Show that if the incid9, ilot35o2meuwco w 9ent 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 intqtea*ghpmj 0 lxga7:/o+7 sp8or b0 b/erface between water and Lucite? To be totally internally reflected, the light must start in which m0e*:am sr+/7obqapgb /j gp 08txoh 7laterial?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a cer66)nd+q 1xke8esfk, ypnu7-n zdbm* stain 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 fromqzcw 8tbvj 0)8 a depth of 62.0 cm. Where must it strike the air–water interface, relative to tjcz 8tqbv 8)0whe spot 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 8ubmft5i7 y/4vpe w,t surface of a liquid and strikes the surface 7.0 cm m,ie458fwy t /ubt vp7from the point 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 strikes the left face of the prismzlea1 q-dm.n azs5. w)i-7f hy 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 (Fi7hm,y:q (2siearg55( zqf:kam sk k,fg. Below). Show that we can guarantee total internal reflection at the side surface of the materi5 krz :( sg,7m h(kifs5kya2qefqm,:aal (at point a), if the index of refraction is greater than about 1.42. In other words, regardless of the angle the light beam reflects back into the material at point a.

  (a) What is the minimum iso (r0gy8lx .g6eu+)hu kv*cq ndex of refraction for a glass or plastic prism to be used ince o+6khv lu0* gur8sg(.)yx q binoculars (Fig. Below) so that 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 65.0-mm-focal-lengt qwt7n-q+c/v- .qbebs h converging lens. Find the objec+7qnb vwsecq -bt/. q-t distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.5 cm behin z) svh*lrl3*w. *qmrqcg m,9wd 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 2af* 3xr).2qiuq u/jz,tb 5uxf.75 m away as an image 48.3 cm on the other side offa*zx5u3fr, u2 /t i)qujx.b q 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-cm- jo syjub+0u.+focal-length lens? P =    D  ----待选择----converging diverging 
(b) What is the focal length of a lens? $f$ =    cm  ----待选择----converging diverging 
(c) Are these lenses converging or diverging?

  A stamp collector uses a converging lens with od )n/segvggm(i39. o/ttm arb70x . ffocal length 24 cm to view a stamp 18 cm i/t90dgn/oabmr tief3.vgm o( )7xs.gn 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 dyc+m ea ;d 1ckyzjk+4508vhwhigh. What are the position, type, and height of the im1c0yamyvk 5j8k+4h ; +d weczdage?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to focus an image on the film of a cameram4 z0ifxbx k(3. The maximum distance allowed between the lens and the film plane ix0z34kmxf i b(s 120 mm.
(a) How far ahead of the film should the lens be if the object to be photographed is 10.0 m away?    mm
(b) 3.0 m away?    mm
(c) 1.0 m away?    mm
(d) What is the closest object this lens could photograph sharply?    mm

  It is desired to magnify reading material by a factor of 2.5× when a book is pz5com o0u xq(4laced 8.0 cm behind a lens.ozocu540qxm(
(a) Draw a ray diagram and describe the type of image this would be.  ----待选择----realvirtual 
(b) What type of lens is needed?  ----待选择----converging lensdiverging lens 
(c) What is the power of the lens in diopters? P =    D

  An object is located 1.5 m from an 8.0-D lens. By how much drr)*o+ai aeqj 7n;hq 5l -m0xnoes the image move if the object is moved 5-nha lqrr)0o e7 +nx;qiam*j
(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 czoq-8 /3qbbl pe4u;fom should an object be po; qf 4l-ebub p/q3oz8laced to produce a real image which is the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an object be placed if its im52 b+q 6cimb ef;+4;czzlcjxs age is 5f 2jz+c;ezbxicmqc sb; l64+to be magnified 2.00× and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm

  (a) How far from a 50.0-mm-focal-lengc z8pcgq4 wn+ rmuy (m+6uc3l:c9smz 6th lens must an object be placed if its image is to be magnified 2.00×:+6+ q 4umclzmcu mpnrg6 yw(zc s983c 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 a 135-mm-focm4 urg5d :zbq*p *tmn)al-length lens. Where is the image*4b):zd5mpgqmur* tn, how high is it, and what type is it?
$d_i$ =    mm (real,behind the lens) $h_1$ =    cm (inverted)
(b) What if $f=-135\mathrm{~mm}$?
$d_i$ =    mm (virtual,in front of the lens)
$h_1$ =    cm (upright)

  How far apart are an object and an image formed by a 75-*(sy wa0neahkupyoa7x 5 iu ;0i,z9-q cm-focal-length converging lens if the image is 2.5× larn -;up 9(yx7iu yq ,as0kzh0we5aio a*ger than the object and is real?    m

  A bright object and a viewing screen are separated by a distance of y5 1r,*btqfkt66.0 cm. At what location(s) between the object and the screen should a lens of focal lekbq51tf,yr* tngth 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 1xw17k8k0ncsa r t6gj.jk7 ; qx6.5 cm apart. An object is placed 36.0 cm in front of one lens. Where will the final image formed by the second0w; ka.crj6 x1xg8snqj7k7tk lens be located? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens withbwrpmb18k 1f 0 $f=-31.5\mathrm{~cm}$ 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 divergincq+p3d8 8feopgdd 8 yhef14t:g lens. Parallel light strikes the dtfo pchfpd 4 y83+qed:ed188giverging 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 lenses of(hphzfrw132t6q l9esek . 4iw Example 23–12 are now placed only 20.0 cm apart. The object is still 60.0 cm in front of the fi ths ke.3p16ir4fzhe l(9w2 wqrst 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 focal length 6zuc dh d5zetbcw9) 4to:v,l(of the lens on the right is 5dhd, ut(ebwczlo 4zc)vt9:620.0 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. How far to the left of the 15.0-cm-focal-length lens is the original object?    cm

  A diverging lens with a focaw pi+-w(j6i:sc h-xq s .;gzbkl length of is placed 12 cm to the right of a converging lens withkbg-+:wx;jps(.zi6h c q ws -i a focal length of 18 cm. An object is placed 33 cm to the left of the converging lens.
(a) Where will the final image be located?    cm to the left of the converging lens
(b) Where will the image be if the diverging lens is 38 cm from the converging lens?    cm to the right of the diverging lens

  Two lenses, one converging with ia*jo)9p.1nznm2 3 vtva/uoh focal length 20.0 cm and one diverging with focal length are plac1 j*zu.p a vn n9oahi)v2t3/moed 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 lensbum3*fdi ou 3- 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 sl.szf:vf 6e57cau/7: l celgnxki55n urface radii of 34.2 cm and 23.8 cm. What is the focal length if n = 1.52? 75ce5:xf/ zu:aliv fk lel6s 7ngc5 .n    cm

  Both surfaces of a double convex lens have radii of 31.0 cm. If vlf-yrlap( n f 89r8r+the focal length is 28.f-plya f+9lvrrr(n88 9 cm, what is the index of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm. Won 8h/ d( wrad),cbjz:hat is the radius of the con n/c w j()d8ad,zorbh:cave surface?    cm

  A Lucite planoconcave lens ucwuzg x t it*:+-+pnj;9sp.py7 wwo2(see Fig. Below) has one flat surface and the other has R = -18.4 cm. Wh+2: tw9gn-+*px yz wispj.tpc7uwu;oat is the focal length?    cm

  A symmetric double cwo h/9-o8rvy honvex lens with a focal length of 25.0 cm is to be made from glass with an index of refraction of 1.52. What should be the radius of curvature for each surfv hw/8o-ry 9hoace?    cm

  A prescription for a correcti .uteu8b0ymiz 0tju*,4 civu3, .h xnzve 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 m8jy uceu z0h, zt. ub xui4*i03,.nvtradius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fig. Below). You stand k:mp/m.fn0/3ag:adr2q gn* l4sah v s1.5 m away from one of these mirrors and look into it. You will see multiple imagekm.:/gng hnl*ar/:vasa0 d 3 mfps42qs 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 swimmi wj(d1b ,pia8ung pool filled with water. We measure the width (x=5.50m) and then note that the bottom edge1p,ujd w i(8ab 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 certa+ l3y-b yjhmfpzh0: 1zin 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 considered a limiting case of kojyb73h n)vd41s9 v ia spherical mirror. Specify what this limit is. 1sbn7kyovh9 ) v3dji4
(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 for) me-0 nnh)htqm a 90$^{\circ}\,$ angle as in (Fig. Below). When you look into this double mirror, you see yourself as others see you, instead of reversed as in a single mirror. Make a careful ray diagram to show how this occurs.

Show analytically that a diverging lens can never form a real image o - j7cvgnmx-ta9fg +c5oqh2km2 8t8egf a real object. Can you describe a situation in which a diverging lens can form a real imagcn gg+va 2j5-ttcmh9k o f828 g-mqex7e?

  Each student in a physics lab is assigned to find the location where a bright eu7/*lv 3sd3wx0cof2v yg v 6wobject may be placed in order that a concave mirror with radius of curvature r = 40 cm will produce an image three times the size of the object. Two students complete the assignment at different times using identical equipment, but when they compare notes later, they discover that their answers for the object distance are not the same. Explain why they do not necessarilyw d7evxwv*s33lg6v/ufc2o0 y need to repeat the lab, and justify your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of 1q . s o rp*;uqay gsks:m5/dc/7-sdhsa 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 cyuvyzfgzua 68qp ;.g4)lindrical 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 fo7lius svbzrru37y3y8 (b/.4llnt mz 7cal 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 placejij -fsy-a 25bac jn12co,q- md on one side of a converging lens of focal length f, and a white screen for viewing the 5cb12qm aycjj,oaji -nf--s2image is on the opposite side. 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 projector, the film acts as tohg.k c.-2dt12 ohjeohe object whose image 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, how far frt ho ood.1j.ghe2 2ck-om 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/w rj )uxxuel.y.-7ku 36 mm) is to be projected on a screen 1.80 m b. 7-.uxuxlyuw r)/jke y 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 formekum.)u so7 ,tz93pis rd by a converging lens is real and inverted if the object is bt,pisrs7uz u)k9 m.3o eyond the focal point $(d_0>f),$ and is virtual and upright if the object is within the focal point $(d_0>f),$ Describe the image if the object is itself an image, formed by another lens, so its position is beyond the lens, for which $-d_0>f$, and for which $0$<$-d_0$<$f$.

  A movie star catches a reporter shooti5jr yb*o6 5tseng 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 lens was 210 mm. How fart os6 j5ryeb*5 away from the subject was the reporter standing?    m

  How large is the imasy3 iu54; .z (fcdmmpuge of the Sun on 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 len4g02 eni rj8p9o2wh xws is imaged 8.20 cm in front of that lens (on the same side as the object). Wx2 0irjw4n 9hgweo2p 8hat 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 ce3lm+f,f4 ,: dkgi qs0i mmn6zsrtain converging lens, it forms a real im 3+mg z,d6fns0:, sfli4 kqimmage. 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.    cm