What would be the appearance of the Moon if it nhk5n8i 1es q(:9kyi3tbz/ wd-m n9inhad
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the wholq x+/+cr a (3dybh;yuwe Roman fleet in the harbor of Syracuse by focusing the rays of the Sun with a huge spherical m urdc3y+(w; ab/yxh+q irror. Is this reasonable?

Although a plane mirror appears to reverse left and right, it doesn’tabv ,da su(6v5oyv:w - reverse up and down. E sva:5,o-ybavw vd6u(xplain.

If a concave mirror produces a real image, is the image nejpwdfwql.k w+/-py* ,k27 znwcessarily inverted? Exp*lw-/+ . j k2qwwdfp7ykzwpn,lain.

An object is placed along the princiu(obv(0v s2w ppal axis of a spherical mirror. The magnification of the object is -3.0 Is the image real or virtual, inverted or upright? Is thovpusv bw2 ((0e mirror concave or convex? On which side of the mirror is the image located?

Using the rules for the three rays discuseybb173 ro6 bssed with reference to (Fig. Below a), draw ray 23y6sbbo eb 71r for (Fig. Below b).
(a)
(b)

What is the focal length of a plane mirror? What is trowho.w c-in 6b (1,omhe magnification of a plane mioww1 ,r.h boi6mo(cn-rror?

When you look at the Moon’s reflection from a ripply sea, it appears elonu c)jqe qc1uu.,)*eshgated . Explain qesu1.qu h,ujc*)c e).

What is the angle of refraction when a light ray meets the boundary o,mw9jh nv x3tq*,jg5between two hg95v mj,oj 3nq*tw,x materials perpendicularly?

How might you determine the speed of light in a solid, rectangular, trg4bx ltfjppv; b kll1qe0ug;*3y9 /5lansparent objecx/k3*;l5f4 gl q1v;eg bujl0yplt9bp t?

When you look down into pv/qo 1 0ms4n ur5t+ vji)z4hga swimming pool or a lake, are you likely to underestimate or overestimate i)/ 4 z5hoq4+1mpv rnu ts0vgijts depth? Explain. How does the apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks bent when part of irm5 2jgh1qf u5t is under water (Fig.2juh 5g 5rf1mq Below).

Your eye looks into an aquarium and views a fish inside. One ray of li-tm ; or,ah im/sq5,aqght that emerges from the tank is shown in (Fig. Below), as well as the apparent position of the fish. In the drawing, indicate thesm,a,/i-hq;qmrat o5 approximate position of the actual fish. Briefly justify your answer.

How can you “see” a round drop of water on a table even though th pr8)*e i t(jfjt8aom*e water is transparent and colorlesstrmf t*ajj88i*o( pe )?

When you look up at an object in air from beneah/cfvgaseeejr 5q,ku2hm/.1m )sc 12th the surface in a swimming pool, does thm5/1mv s/, r .21hjs e)c qgehacku2fee object appear to be the same size as when you see it directly in air? Explain.

How can a spherical mirror have a m85,rtliwb5pctpdf31 u.. (ia yb/be negative object distance?

Light rays from stars (including our Sun) always bend toward the vebi 3 ar z;.8a9mtu2isljv2v8rrtical direction as they pass through the Ej.2ta8293azbrrv;m ius l iv8 arth’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 sm oo1;o4o1 grvharp image of an objec;mv 4oo 1gro1ot very far away?

What type of mirror is shown in (Fi) ; nikxdhj0uciqgf, )zs s504g. Below)? Explain.

A photographer moves closer to his subject and th xdt6xh j 2+6txcoxs7.7mkxi8en refocuses. Does the camera lens move farther from or clo8hj7 6cm i dxxo7k+2xt6sxt x.ser to the film? Explain.

Can a diverging lens form a real image under /wu(nqt h+eg 5any circumstances? Explain.

Use ray diagrams to show that a real image forei5 w 48iew5chmed by a thin lens is always inverted, whereas a virtual image ihe5e8wciw 45is always upright if the object is real.

Light rays are said to be “reversible y.k-u iy/, 6(phtazrs.” Is this consistent with the thin lens equation? Expla/u i.kpay zrts h(-y,6in.

Can real images be projected on a screen? Can virtual images? Can either be -k f7hw2:wore photographed? Discuw7k hrf:o2we- ss carefully.

A thin converging lens is moved closer to a nearby object. Does the real imak u788sqa ofsrf 38n+rge formed cq8s+ 83ukra8 ffo7 nsrhange
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index owvl i -lv 81vw*2nx-c2dlbcp/f refraction n = 1.30 In air, it is a ncl/v8l 2p2vl-1x wbw-d*i cvconverging lens. Will it still be a converging lens if placed in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands facing a converging lensdfhh1 (mu 4it(. If the nose and the tail are each focused on a screen im4 idh1thuf ((n turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facing a converging lens. Under whatr2il v;4wldk 0 circumstances (if any) would the image of the nose be virtual and the image of the tail be rw4;d2lil v0kreal? Where would the image of the rest of the cat be?

Why, in Example 13, must the converging lens have :n( hlls6dq sx w ovz:m155wd4a shorter focal length than the diverging lens if the lldm s5(wqv5zwd14:ohn l:x s 6atter’s focal length is to be determined by combining them?

Explain how you could ha6gus07.e k b6n)s(zr7ol nh kdve a virtual object.

  An unsymmetrical lens (say, planoconvex) forms an image vycu,5t+u+ k(f) dpox7b,u24dq x ,sbacav*q of a nearby object. Does the image qxy(d cf5savcq uvp +a24 kbuobd 7tu,,+,x)*point change if the lens is turned around? ----待选择----yesno 

The thicker a double convex lens is in the centerwmq:; 8+vkx2fsj og el5vl3c 9 as compared to its edges, the shorlxg582v9:3 klw fqcoe; vmsj+ter its focal length for a given lens diameter. Explain.

Consider two converging lenses separated by some distance. An object is placeg.nzv -kh o jmy4) m,t*kay6-zd so that the image from the first lens lies exactly at the focal point ofyy4nmt)h,-6 g o .kkj *zvazm- the second lens. Will this combination produce an image? If so, where? If not, why not?

  Suppose that you want to l2l hp 4dyg3i2take a photograph of yourself as you look at your image in a flat mirdl4y22lgh3p i ror 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 mwyrwh+y56,2ol(dvs l irror, 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 why this should be truly6yrl2,w 5dosv(h w+e.

  Two mirrors meet at ynf8 y*rpgypq+*ol,13v : l qia 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 fron uvgsnw/v .y.9t of a vertical plane mirror whose bottom edge is 43 cm above the floor, (Fig. Belouy./ .vswgn9 vw). 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 mirrowb.)8 7b*u raizbpqk2 r. What area of the mirror is used to reflect the rays entering onwb.2b8i rk *qu7)azpbe eye from 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 atr5mos*:lq ) op nk-9zs(xiz1w an angle $\phi$. a single ray reflected successively from both mirrors is deflected through an angle of $2\phi$ independent of the incident angle. Assume $\phi<90^{\circ}$ and that only two reflections, one from each mirror, take place.

  A solar cooker, really a concave mirror pointed at the Sun, focuses the Sun; s54iy a4to wpxckv y:lwc4c1+mq/l6’s rays 18.0 cm in front of the mirror. What is the ra;5t4lk6ms p:xaw +c14lq ywcc/v4i yodius of the spherical surface from which the mirror was made?    cm

  How far from a concave mirror (raq1lgzux tjh(;* qebh)1 z wf8i:bg:f2dius 23.0 cm) must an object be placed if its image is to be at i h 8f)1*q2:bui(wq ;z:xl1zfg jthbegnfinity?    cm

  If you look at yourselff.v;)/pyh bsl in a 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 sb vy)phf.l/;or virtual? Is it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusemen;.ggf g(z6 wab,e szj16q2gfnt park shows an upright image of any person who stands 1.4 m in front of it. If the image is three times the person’s height, what ;n 6ggg jfb s1e(gwz6f.qz2,ais the radius of curvature?    cm

  A dentist wants a small mirror that, when 2.20 cm from a ti puhogh;;m wh(e fu+ q.,-5doooth, 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 c7v* 7 ix2oi wvrn,wg8sars behind you that are smaller than they would be if the mirror were flat. Are the mirrors conog2iv,swnxrvw8 *77i cave 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 is pla rphwx2 o1)9rrgo5*vyced 20.0 cm from a convex mirror of radius of curvature2ywh o 1)r5go *xrvrp9 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 fromtn-hwmc c(51tmgjs 51 a convex security mirror in a store. You estimate the hw h tmtgc1sm5-c1j(5neight of your image to be half of your actual height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object be placed in fbbc2g *8craal8 c9 om7qx +n6dront of a concave mirror so that it produces an image at the same location as the object? 9c+ q cac* 8 76mlx2abdorgbn8
(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 lhm1b-7b)6lbhzxam: s;om 7m ml0uw8 is virtual and very small when viewed in a curved mirror. The image appears to be 18.0 cm behind the mirror. What kiwz 8lm7m7lob1-m xa;h h:mbb)usml 06nd of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techbf;bgf5) cd.f niques,
(a) a ray diagram,
(b) the mirror equation, to show that the magnitude of the magnification of a concave mirror is less than 1 if the object is beyond the center of curvature $C\left(d_0>r\right),$ and is greater than 1 if the object is within $ C (d_0 < r) $.

Show, using a ray diagram, that the magnification m of a convex mirror is .i+; ybwkndq 9$m=-d_\mathrm{i}/d_\mathrm{o},$ just as for a concave mirror. [Hint: consider a ray from the top of the object that reflects at the center of the mirror.]

Use ray diagrams to show that the mirror equation, Eq. 23–2, is valid fopdx ddbshjv /10w 94,:*rgfcor a convex mirror as long as f is consider4bs hgd w0:d, dvf91pc */jxroed negative.

  The magnification of ac,81i9zti 6lkwk1 +n8sr qglk convex mirror is $+0.65\times$ for objects 2.2 m from the mirror. What is the focal length of this mirror? $\theta_2$ =    $^{\circ}\,$

  A 4.5-cm-tall object is pla0 8o ypc6jv)fcj:xjd;ced 28 cm in front of a spherical mirror. It is desired c f6)j;:jdp8yj0xcov to produce a virtual image that is upright and 3.5 cm tall.
(a) What type of mirror should be used?  ----待选择----convex mirrorconcave mirror 
(b) Where is the image located?    cm behind the surface
(c) What is the focal length of the mirror? $f$ =    cm
(d) What is the radius of curvature of the mirror? r =    cm

  A shaving/makeup mirror is designed to magnify your face by a factor of 1.3gk-- uvo3yujb.zg/n u -dwxx l79w./a3 when your face is -x/gw.nkj/y uul3u-7xdwbzo. -vg9a placed 20.0 cm in front of it.
(a) What type of mirror is it?  ----待选择----convex mirrorconcave mirror 
(b) Describe the type of image that it makes of your face.
(c) Calculate the required radius of curvature for the mirror. r =    cm

  What is the speed of light in k1qy;)8 h8/iq wu7)y1thpbz wixsjr0
(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 if5 x7 5t.8dvsvkbc.e mce is $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a cer8f:i 8 h umeim5v;,ggctain substance is 89% of its value in water. What is the vf8c5;iigum 8g e,m:hindex of refraction of this substance? n =   

  A flashlight beam strikes the surface of a pane of glass (n = 1.58)2qjuk1dd.e ) q at a 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashlight upwa9hu b + ).wxey;s;x+fdn:qqwdco,a9d rd from beneath the water at a 42.5$^{\circ}\,$ angle to the vertical. At what angle does the light leave the water? $\theta_2$ =    $^{\circ}\,$

  A light beam coming from an underwaterfg4or6imr d+ , spotlight exits the water at an angle of 66g rm+ fr6d4o,i.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 31.c8pn- h p* 2g it2jodgs7vdp*/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 fl hexy5qwre zx 5t28 yvdezlrx(;o+/ 67at 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 angle of this light ray when it enters l5xr d;r(qt xhzo85 +6zew/e2xy evy 7
(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 wa,gx,mrgi7+ x8mdb y3ftchman shines a narrow beam of light from his flashlight, 1.3 m above the water level, onto the surface of the water at a point 2.7 m from the edge of the pool (Fig. Below). Where does the spot of light hit the bottom of the pool, measured from the wall beneat3g x+dg7rfbm imy,8x,h his foot, if the pool is 2.1 m deep?    m

  Light is incident on an eq9j 7y302bml6rq uvgib uilateral glass prism at a 45.0$^{\circ}\,$ angle to one face, (Fig. Below). Calculate the angle at which light emerges from the opposite face. Assume that n = 1.58.    $^{\circ}\,$ from the normal

  A beam of light in air strikes a slab of glass (n = 1.52) and iskux*1o0fwlnq:7 h n;k partially reflected and partially refracted. Find the angle of1knq ou7lwf:0hxn k* ; incidence if the angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam incident on a unifeo3) 4ucp/izz orm layer of transparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the incident beam, independentzceio z)4p/u3 of the incident angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on a fl/ksf29pb0 jnoff,0 o)6 /dtrm ej(nnn at piece of glass with index of refraction n as in (Fig. Below). Show tha) j2nf0o,n/60d(9psfknjeo b/mtnrft 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 for the interface between water and Lucite? To bil7vk1zo zo, 29mx(cce totally internall1zc xml9(,o 72ocv kziy reflected, the light must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–air surfac fy2.x*fj :zkq+ r,elte is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in a pool o 0d/q hf)tsv3-n3such f water from a depth of 62.0 cm. Where must it strike the air–water interface, relative to the spot directly above it, in order that the light does not exit th sdns/u3q h vt0)-c3fhe water?    cm

  A beam of light is emitted 8.0rs5 k8nxaohr97* 2nneo.*fig cm beneath the surface of a liquid and strikes the surface 7.0 cm from the point directly above the source. If total internal reflectionri5a7.oxnfhr8 n ns** e2gko9 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 prism in (Fig. B16b)k3 q5m qcqh9s/pors:q mselow) 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.:)gdkez;2b) weq te+ p Below). Show that we can guarantee total internal reflection a) et:qew pb;zd2+ kge)t 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 point a.

  (a) What is the minimum index of refraction for a glass or plasticya,i0y 7*;/ b anfqkkn prism to be used in binoculars (Fig. Below) so that total int kn*f,ka0 ;b7a/qniyyernal 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-length d g jj*imh5*zz;v h34)mxqk4t converging lens. Find thv3hm kxjh*qd4 jz*zg 5;t)mi4 e object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.5 cm behs9/ftiwcnwh*e qkfku4 )9*yu u n4;x5ind 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 o7)h zf4 0kujmr7 rze,o (ijlb1bject 2.75 m away as an image 48.3 cm on the other side of the lens. What type of lens is it and what is its f)mbuf hr7z ljjzir47(1 ,eo 0kocal 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-yu eao/:0xbub4 t2 v6ilength 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 lens27q,rvjc-2u zgi/ o sv with focal length 24 cm to view a stamp 18 cm in front of the lens,qjvsrg2i2 cv 7/u-oz .
(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 hprow8l5( ez s7igh. What are the position, type, and 7 8rwos5ep (zlheight of the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens zjr9g,m0 g86gmrk(xmis used to focus an image on the film of a camera. The maximum distance allowed betwmm08k9r ,m(xjggg z r6een 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 zfmk ehq8z*h.0h 3ny; factor of 2.5× when a book is placed 8.0 cm behihz n;0me*hy q3zh.8fknd 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. By how much does the image movq4hannb1ll, h;ex) 2me if the object is moved 1nelb2 am,nh;4lqhx )
(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 orl n.p+ r*db,pf 25 cm should an object be placed to produce a real image,p.bdr+ ln *rp which is the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length 7 5 8vbvbgf nll5fx3h+lens must an object be placed if its image is tln 3hbvg+lv5f85 f7xbo 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-length lens must an object be placed if its ima0gx pdjeei2up,20wj 3ge is tjg3dwx0j0ep 2p2, iueo be magnified 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 a 135-mm-focal-length lens. Wb/ (s12p-6*w-sfvahjubv zb )l url/fhere is the image, how high is it, and wsb)l/pfzh rv 62fw-l b *-uusj1vba/(hat 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 imagyy9 r-rw/m393 yhaps ue formed by a 75-cm-focal-length converging lens if the i r9ws /y-yh3mya3 up9rmage is 2.5× larger than the object and is real?    m

  A bright object and a viewing screen are separateylr+ .uggj7-hd by a distance of 66.0 cm. At what location(s) between the object and the screen should a lens of focal length 12.5 cm be pla -+ r7.hgjugylced 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 16.50ye ;lo1p:-ax ui eu8 7xr9tnr cm apart. An object is placed 36.0 cm in front of one lens. Where will the final image formed by the second lennp e 0lao7uyx :t rer;-u1ix89s be located? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens wit:i h+a:8mhe f,lgwpp 69ql)ng h $f=-31.5\mathrm{~cm}$ 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-lengthp2nv4ictgy/(e f2hp k +t s0e*m hf+5z converging lens is 21.0 cm behind a diverging lens. Parallel light strikes the diverging lens. After passing through the convergiv ppti+cf 5*h (kgny2z 40met fh+2/esng 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 Example 23–12 are now placed only 20.0 cm apart.c+pyr(f 1 5snb Thfsy(rc5p n+b1e 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 plcm3 8vuyoo w5+ rt:ux;aced 30.0 cm apart. The 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 155cumtw +oy:o;3v ux r8.0-cm-focal-length lens. A final image from both lenses is inverted and located halfway between the two lenses. How far to the left of the 15.0-cm-focal-length lens is the original object?    cm

  A diverging lens with a focal length of is placedn fi; ja7i (0ixdvl np9m(l48o 12 cm to the right of a convergi8 nx(7ovia4 mjfil d9n;i0(lp ng lens with 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 focal length 20.0 cm and one dikxi)5a( flc r;verging with focal length are placed 25.0 cm apart. An object is placed 60.0 cm in f c( r;il5k)faxront 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 convergin6ak wv en+ss h7ed *yji1q307bg 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 sur3r *j61z) b/ww qmryxpface radii of 34.2 cm and 23.8 cm. What is the focal length if n = 1.rz3q pr/ jx6 *1myb)ww52?    cm

  Both surfaces of a double convex lens have radiisr)js *2h18:3 xgwopgrl.ihu7wd b)39orv sr of 31.0 cm. If the focal length is 28.9 cm, what hu8rpg)7:l vh)o12.rso*w 3s d g ri sj9w3xrbis the index of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal g-1ue pb55gs blength of -23.4cm. What is the radius of the concave sur bbeus5g p-g51face?    cm

  A Lucite planoconcave vc*fa 2b;d1evtsm *t ys96cc, lens (see Fig. Below) has one flat surface and the other has R = -18.4 cm. What is the ctems91vf y2;tc*cs* v d6b,a focal length?    cm

  A symmetric double convex lens with a focal length ofqf3cdn z bxu229 +x6xu 25.0 cm is to be made from glass with an index of ref +xnd6qux2f3z9c2bx uraction of 1.52. What should be the radius of curvature for each surface?    cm

  A prescription for a corrective lens calls for +mk:wdt5mzd626 hy eb h1-vje61.50D. 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. Wh-mdj6m h: 26 hdee1wzv5yktb6at should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other:c 77d jdpuhv4 2.0 m apart as in (Fig. Below). You stand 1.5 m away from one of these mirrors jpud7c47 dv :hand look into it. You will see multiple images of yourself.
(a) How far away from you are the first three images in the mirror in front of you?
$d_1$ =    m
$d_2$ =    m
$d_3$ =    m
(b) Are these first three images facing toward you or away from you?
the first image is facing  ----待选择----toward youaway from you ;
the second image is facing  ----待选择----toward youaway from you ;
the third image is facing  ----待选择----toward youaway from you .

  We wish to determine;y7 kxh:e,axwqiic1- the depth of a swimming pool filled with water. We measure the width (xcekxh1iwaqy:7-;i , x=5.50m) and 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 aknblm93 4da6n m.yo)m certain 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 considl4-0h5 cb;m, + 2 hkqkj/dyyvs b,jjplered a limiting case of a spherical mirror. Specify what this limi5qcy+l ,b-j ds/4h;2 mb ,jk lk0hjpvyt is.
(b) Determine an equation that relates the image and object distances in this limit of a plane mirror.
(c) Determine the magnification of a plane mirror in this same limit.
(d) Are your results in parts (b) and (c) consistent with the discussion of Section 23–2 on plane mirrors?

Stand up two plane mirrors so they form a 90 wapl6evyp7l(x:px2 ;$^{\circ}\,$ angle as in (Fig. Below). When you look into this double mirror, you see yourself as others see you, instead of reversed as in a single mirror. Make a careful ray diagram to show how this occurs.

Show analytically that a diverging lens can never form a real image of a real obqq- v.m7 nw1ukject. Can you describe a situation in which a diverging lens can form a -7q1wuvm.q nk real image?

  Each student in a physics l1m/ uyq ip+so6 9g*xmhab is assigned to find the location where a bright object may be placed in order that a concave mirror with radius of curvature r = 40 cm will produce an image three times the size of the object. Two students complete the assignment at different times using identical equipment, but when they compare notes later, they discover that their answers for the object distance u*miq+6y/po g1 sh9 xmare 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 prip1 yh)g1hvb8yc - kd b7-+pfxmsm 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 cylindroh /8v0m1yh)fyii1hz ical 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 n3 pir*nqg6-gs2)h)0jtdyidxb u w* 8 focal length $f_1=15\mathrm{~cm},$ which in turn is 55 cm in front of another converging lens of focal length $f_1=15\mathrm{~cm},$ (see Fig. Below).
(a) Draw a ray diagram and estimate the location and the relative size of the final image.
(b) Calculate the position and relative size of the final image.

A bright object is placed on one side of a converging lens of focal length fw)o/kw0 zfoxy 9n 6g7b, and a white screen for viewing the image is on the opposiyb ow0 7kx6/)zw9ogfn te 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 the object whose image am*4 4w;eo nikis 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 from the lens should the slide be? If them oi 4ae4*kwn; 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 proje2o3yq: udi-jgcted on a screen 1.80 m by 2.70 m placed 7.50 m from the projector. What focal-length lens should be uso ygi2dq3u- j:ed if the image is to cover the screen?    cm

Show analytically that the imau 6 x.bwfhe8de *(;axlge formed by a converging lens is real and inverted if the object is beyondew(*; lx8d6fa .uhx be 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 shoo;x)i s+m/pdk ;exijk 2cpw d/6 lb3w;vting pictures of her at home. She claims the reporter was trespassing. To prove her point, she gives as evidence the film x/kdp3+ /2 bm 6;iwpsw)e ;ldik;vxjcshe seized. Her 1.75-m height is 8.25 mm high on the film, and the focal length of the camera lens was 210 mm. How far away from the subject was the reporter standing?    m

  How large is the image of the Sun on film used in a camerf 95 vtz:kpo8xa 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.