What would be the appearance:x oz4ss: cs t*4e5hfb of the Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fleet rcyk. lxzg jkq*a. z v6-;c+y7in the harbor of Syracuseg r.zz 7k-xc k*yva6yl.;jc +q by focusing the rays of the Sun with a huge spherical mirror. Is this reasonable?

Although a plane mirror appears to reverse left3yk: fg5.trz f8wxu,j and right, it doesn’t reverse up and down. 5jt 38uz.,kfwgyxr :fExplain.

If a concave mirror produces a real image, is the image necessarirts89;mj9a wnkv1qh,zj3 z-+-q qvhqly inverted? Exh3wt 9q vj+snqz ,a--zv1qmh9q;j 8 rkplain.

An object is placed alonz 65a 06cgudht:h 5qftg the principal axis of a spherical mirror. The magnification of the object is -3.0 Is the imagauh 6:fqt0t5dz 5chg6e real or virtual, inverted or upright? Is the mirror concave or convex? On which side of the mirror is the image located?

Using the rules for the three rays discussed with reference qw6r,n+p- jh 9h91 wwnsje hrt22+dozto (Fig. Below a), draw ray 2 for (Fig.hwdrhwtn2+ws nj9p+6zq - 219h , eojr Below b).
(a)
(b)

What is the focal length of a plane mirror? What is the magnification ofcodht*v*0q 4f a plane d t*0 qfv4*hcomirror?

When you look at the Moon’s reflection fr3u3*gqmmet z+ojku44: xx li4 om a ripply sea, it appears elongated . j43xetum +gi4qx:z34u*ok m l Explain.

What is the angle of refraction when a light rah-avm 5m/:gml1 33+eq qre uhby meets the boundary between two materiam /q:+ 1 me3-b5hum3vrql ehagls perpendicularly?

How might you determine the speed of light in a solid, rectangular, tranrims +;di+g9m sparent ob;im9rs+m+ digject?

When you look down into a swimming pool or a lake, are you lf c16crz i:ov yg6qpw(ay(a 9/ikely to underestimate or overestimate its depth? Explain. How does the:c(if( 6yoc/ 6qzpra vga1wy9 apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks bent wh;) irc6 uta0s )y5zcoken part of it is under water (Fig. Belotscc ozkau) )5; y06irw).

Your eye looks into an aquariu* 9wxd2mpl0i q9hj j7eb;)frz dl h9p2m and views a fish inside. One ray of light that emerges from the tank is x)*7frl2h 9pqjd9b 09d2jlhwzi;p e mshown in (Fig. Below), as 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 rounyw .5 g8mewk .*gox kjxlzjdg:5f,5)b9z ;uifd drop of water on a table even though the water is transparent and col* gbofjlg; .:xky9zjdg,iwu x)8 fez 5m5 wk.5orless?

When you look up at an object in air from beneath the zce ;bdn7xd5( surface in a swimming pool, does the object anc( dz xd;eb75ppear to be the same size as when you see it directly in air? Explain.

How can a spherical mirrawjduc ;1h;,j dz,*5j3uq cgtor have a negative object distance?

Light rays from stars (including q4u8zvph;(on, mg3mxour Sun) always bend toward the vertical direct,pmxhz3v;ng 4 u8 omq(ion as they 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 w dz f3*.sota8make a sharp image of an object very far awaz*wt s3.8 foady?

What type of mirror is shown in (Fig. zql*m j6w5oo 2i7wsl +Below)? Explain.

A photographer moves closer to his subject and then refp gm+p(:m 5; bikhbhu;r, t+ebocuses. Does the camera lens move farther frbr5:;mbhgb i;u+m ,k+(e tpphom or closer to the film? Explain.

Can a diverging lens form v/ag4nue34*6 hxqw p xa real image under any circumstances? Explain.

Use ray diagrams to show that a real image formed by a thin lens is alwaysm +gg9bq8y 2cwmaoa/ms g3o00 inverted, whereas a virtual image is aawa3m2/bg0c o0o+ qm gs8ym 9glways upright if the object is real.

Light rays are said to be “reversible.” Is this consiste/ +eb gpc10 pozq9y+aapr7o a/nt with the thin lens equation? Explain.0preaq b7 1z9gp/yp oao+ca+/

Can real images be projected on a screen? t9ncmn/ .-st qCan virtual images? Can either be photographed? Disct.cnsm /n-tq9uss carefully.

A thin converging lens is moved closer to a nearby object. Does the real image + l7,v+jwwsr/jbhbg1formed,lwwrh7sj 1+b bg v+j/ change
(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 Im(0 nn /7*zsk(ezpnlcn air, it is a converging lens. Will it still be a converging lens if0(zn(/kl7nz*s enpc m placed in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands facing a convergk :ze enssyt8vt9h,g4h/ir7:ing lens. If the nose and the tail are each focused on a screen in turn, which will have ,yz/e9e:i htn:sgrs t v7k4 8hthe greater magnification? ----待选择----nosetail 

A cat with its tail in the air sta*1hc0py+ k 1(ds l pkovvov-x6gd 2aa+nds facing a converging lens. Under what circumstances (if any) would the image of the nose be virtual and the image of the tail be real? Where would thep11 p6kl+ cyadhdv o vkx2a*(+-o0vsg image of the rest of the cat be?

Why, in Example 13, must the converging lens have a sho - kkn) dbh2:58tcqt1 tf;nv-k;ai1sd9ydqev rter focal length than the diverging lens if the latter’s focal length is to be de- qdf 1dqi)dtt 9 n8tkcke5 sn-by1 2v;:;ahkvtermined by combining them?

Explain how you could have a virtual o9s5jiv qjnv, 9bject.

  An unsymmetrical lens (say,rod*ty (aw pzd26it/m x;dl, 2 planoconvex) forms an image of a nearby object. Does the image point change if the lens is turned around? iox6rp/2d*t2;z y,a d l(mwdt ----待选择----yesno 

The thicker a double convex lens is in the center as compared to its edges, tijxnh n3uc9,0he shorter its focaln 3xj,9h nu0ci length for a given lens diameter. Explain.

Consider two converggshx3 y6rjr na2 i6 jj3cc7f48ky+ *oking lenses separated by some distance. An object is placed so that the image fr 6*k3hfny7+2gjkycscjrri 38 x6oaj4 om the first lens lies exactly at the focal point of the second lens. Will this combination produce an image? If so, where? If not, why not?

  Suppose that you want to take a photograph of yourself as you look at your im480aw ax6 edf9dz7x uoage in a flat mirror 2.5 m zwuf6da78 oaxxd0 4e9away. For what distance should the camera lens be focused?    m

When you look at yourself in a 60-cm-taugjak 8i6fs3h263 bi ds;u6 gall plane mirror, you see the same amount of your body whether you are close to the mirror or fs;hs23ga86 uj6u ga ikbf6i 3dar away. (Try it and see.) Use ray diagrams to show why this should be true.

  Two mirrors meet at apu l1hmzc9 p6)92otyl 8hkn:v 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 (w.is x:x)u wjm 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 xu.x:)ijsww (that can be seen reflected in the mirror?    cm

  Suppose you are 90 cm fromna9qed3x 3qmm:sc 2c4 a plane mirror. What area of the mirror is used to reflect the rays entering one eye from a point on the tip of your nose if your pu ceq:nqmmcd 43a3x 92spil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrork;kb 1ihbc9;ht2i m/w6lhsbt 1gd1 4ws meet 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 a concave mirror pointed atxrg ; g8wc-)wl the Sun, focuses the Sun’s rays 18.0 cm in front of the mirror. What is the radius of the spherical surface from which the mirrorx-r)w l ;wc8gg was made?    cm

  How far from a concave mirror (radius 23.0 cm) must an object be pla/1 fky m zh767bgfoxm.ced if its image is 7 ob6y/.g7mxfk1z m fhto be at infinity?    cm

  If you look at yourself in a shiny Christmas tree ball i/+gqwayy4kz2 xir1zq;p /k- with a diameter of 9.0 cm when your face is 30.0 cm away from it, where is your image? Is q gy4ai r-z1pykkzi wqx+/2;/it real or virtual? Is it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shows agct5dn47v +0p c uga/cn 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 is thegna gcp u4c5v/ c+0dt7 radius of curvature?    cm

  A dentist wants a small mirror that, when 2.20 cm froz4,z6 z; j55cgp *ruufkcg ro9m 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 behint tee.mgf.s55 :vmpsa* htw )1d you that are smaller than they would be if the mirror were flat. Are tg.ev:p 1mts.ta 5e*5f w) mtshhe mirrors concave or convex? What is a mirror’s radius of curvature if cars 20.0 m away appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is placed 20.0 cm from a convex mirror of radius o b*yl8/ tyha;rf curvb8y/ ayt *r;hlature 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 sa,8,*(3a7ncu 0fnqteymm7/ t;srv tx 3mgmq from a convex security mirror in a store. You estimate the height of your image to be half ofu8n3 a/ tt0;37ces f*x(vtqq,am,mm nsr g7ym your actual height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object be plarh -he ,q. mo /h3zg5cuyx55ecced in front of a concave mirror so that it produces an image at the same l -ocz 5xmhu,.qc/ yh5g53 erheocation 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 an66y3s-piu.a 4tg tp wed very small when viewed in a curved mirror. The image appears to be 18.0 cm behind the 4i.6p- getspay3t6uw mirror. What kind of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different tecpigq*whice* 8( r7f 1, uxrj2qhniques,
(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 owf*; s mzqipbw, 7jn;1f 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 valhsfw ea9w yv7jd 4m+15xv8 jf4id for a convex mirror as long as f is considera4 shw8jv w e j+5d749vmyff1xed negative.

  The magnification of a conije s.dj1 xs19vex 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 ct)du,ypj5ah txxg(lh5)fz. 4(p8p s mm in front of a spherical mirror. It is desired toa,zp) xl p(umpt 4hd(5y85 tg.x)jhsf 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*1j4ulqerf17qk n ft2 by a factor of 1.33 when your face is placed 20.0 cm in front ojnfl 2 17*qurqk41etf f 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 lig,ht-fs7 e- xvfht 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 iciw /1tv nefi q9)(d9wxe is $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certaym/ yh;+f6 paxin substance is 89% of its value in water. What is the index +6mfa;pyh /yx of refraction of this substance? n =   

  A flashlight beam strikes the surface of a pane of glass (n = 1.58) at aruj w(z* c5h;jca n1z; 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashlfylka ,dj9i4 nzv ++gp0um e699p2z yaight upward from beneath the water at a 42.5$^{\circ}\,$ angle to the vertical. At what angle does the light leave the water? $\theta_2$ =    $^{\circ}\,$

  A light beam coming from an undx1 7s k0xj/rrp g,zt3kerwater spotlight exits the water at an angle of 6g31k,r/ k 0 trxxsp7zj6.0$^{\circ}\,$ 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 sr 5sjmqb+r:+;kagq8u6 u(jd)lhkq *reen 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 d61ts)c8t wj a.ekot;yms-z-whose index of refraction is 1.52. A beam of light from outside the aquarium strikes the glass at a 43.5° angle to 6s)okemw c.-y8aj tt d-z1 s;tthe 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 botb tn97j4yb u 3 7y7yn(oia+yxbtom of a pool 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 pool (Fig. Below). Where does the spot of light hit the bottom of the pool, measured fryn7yi7 uyj79y no 3b+xbt4ab(om the wall beneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equilateral glass prism at a.8 7q aknw0qf2m) v ;kps-ycmn+k;aml 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 fc vkkt01c7d s s8ufxvf6b h.7+j(af+is partially reflected and partially refracted. Find the a +a+ f16 vs.fjkub7hc8k70svftfcxd( ngle of incidence if the angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for+ct- 9mrih/ qk a light beam incident on a uniform layer of transparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the incident beam, independent of the incident /k thcm+qi-r9angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on a flat piece of glass with indafjiu7 :e py tjc(,egku+ 3 .i0yx2w5cex of refraction n as in (Fig. Below). Show that+ayuip 3(fcctwjg5i2e7u0 kj:x,. ye 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 waterov+0uuly5x. u2qtnxh(iu,4 y and Lucite? To be totally internally reflected, the light must start y q2uoni(lx0yu ,uh+u.v5tx4 in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle foxg9k9r0 (5ms w-di nlfpem8-zx x(cq1 r a certain liquid–air surface is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in a pool of water from a depth o-b:.mg9wrfdcna 9jceehyyrso+-/8 )6s1f t h f 62.0 cm. Where must it strike the air–water interface, relative to the spot directly -1aw bthfng9e+chcsj o)e r: fs 9y68.m-rd/y above it, in order that the light does not exit the water?    cm

  A beam of light is emitted 8.0 cm beneath the surface of a liqui1 v5rmw*y gd1q7nv xd,31sdlu(d .ce xd and strikes the surface 7.0 cm from the poi*e sndx ,rdxd35d(w1mqluv c.vg11y7nt 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 tn99t8tj z0, i(nzivmd he 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 shown2dm)b+ rj52w0v dwr zs sccjo4/lhx9; in (Fig. Below). Show that we can guarantee total internal reflection at the side surface of the material (at point a), if the index of refraction is greater than about 1.42. In other words, regardlessl) wm0xzo4dsjw/5b 9jvrc+;2rhs2 dc of the angle the light beam reflects back into the material at point a.

  (a) What is the minimum index of refractfeb7l7) braxm*v /2mn ion for a glass or plastic prism to be used in binoculars (Fig. Below) so that total internal refl /*xevbr2n7a)7mmbl fection 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+ (r dhbdg)ndef* (a:k mm behind a 65.0-mm-focal-length converging lens. Find the object distanceka ) g d:r(*bdhendf+(
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.5 cm behind a lens/;cpln5q/j bmbbm+bj /0kr 2z .
(a) What kind of lens is it?  ----待选择----converging lensdiverging lens 
(b) What is its power in diopters? P =    D

  A certain lens focuses light from an object 2.75 m awayl/8hdq x*jm 6j as an image 48.3 cm on the other side of the lens. What type of lens is it and what is its focal length? Is the image r *jjx6lqd/h 8meal 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-ljdzef-,d1sur- o zpks ;c 4b:5ength 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 kt(ylf2q2niwe gr9/q90 h(gv with focal length 24 cm to view a stamp 1g2lk9 g(/2efiqr(qv9yh wtn08 cm in front of the lens.
(a) Where is the image located?    cm behind the lens (virtual)
(b) What is the magnification? m =   

  A -5.5-D lens is helv9b b boi+zf9*d 14.0 cm from an object 4.0 mm high. What are the position,bvzo9+bfb * i9 type, and height of the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to focus an image on the film of a ca3a9/ cfvuh0jf ( 4rjygmera. The maximum distance alvc(r93fga j4y hu/0 fjlowed 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 materiald t2ec(r2ism 4 by a factor of 2.5× when a book is placed 2 r2eim 4stcd(8.0 cm behind a lens.
(a) Draw a ray diagram and describe the type of image this would be.  ----待选择----realvirtual 
(b) What type of lens is needed?  ----待选择----converging lensdiverging lens 
(c) What is the power of the lens in diopters? P =    D

  An object is located 1.5 m from an 8.0-D lens. By how mucha;kv+y ag7;uo o1xg8f does the image move if the object io;7+f 1ykxagguo v8;as moved
(a) 1.0 m closer to the lens,    cm away from the lens
(b) 1.0 m farther from the lens?    cm cm toward the lens

  How far from a converging lens with a focal length of 25 cm should an object 6ry*8yikwq a: 4 tqn7 z 9hyqidlb09x2be placed 9:wn7*9yy4d iiq0h2 x abklyr t8 qq6zto 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 it5mto67lsvw/jf2l sl ( adeku6a*9 v0 b;he4c ms image is to be magnified 2.00× and b0e 49l* ms2 kwm(d;/665a7lub hovcaj fltevs e 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 7pzl jin 3kipu8x.b edy86lc/x5 5dw-if its image is to be magnified 2.00× and be re5j7x3il nkbdl-86p/5 dp .i 8cxze uywal?    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 tqwoug4 ;2:zt1.20 m from a 135-mm-focal-length lens. Where is the image, how high is it, and what type is :qo ;t t42wgzuit?
$d_i$ =    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 fo8w*o6v4yts j:kef33:lfm h nfkdm *8 ormed by a 75-cm-focal-length converging lens if the image is 2.5× larger than the object and is real? fyk*4k8o*s:l83emmfo6f: t wnh3v d j   m

  A bright object and a viewing screen are separated by a dib5 pwlr:e:kq,k *yc p0stance of 66.0 cm. At what location(s) between the object and the s,wbp 5ce ::k0qr* pylkcreen 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 16.5 cm apart. An ofuw wkxsq9b /y782u;u bject is placed 36.0 cm in front of one lens. Where will the final image form;u wxbs/w9fu8 u q2y7ked by the second lens be located? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens with j)tx .qm+ -dyh$f=-31.5\mathrm{~cm}$ 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 div(ijdwq3sw3 v*erging lens. Parallel light strikes the diverging lens. After passing through the converging lens, the light is again parallw(jq 3wd3*v isel. 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 go 47el1tcdy). The object is still 60.0 cm in front of the first lenst7o) e ldg41yc 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 ar jq:v1e3 k3hg1e k.adke placed 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 15d kkk3e.gaq1vhj31 e:.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 placed 12 ca *(s3+msorpzm to the right of a converging lens with a focalozs( +*mp 3sra 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 ks,i:: mr :h*;z gqep:gb zwx6focal length 20.0 cm and one diverging with focal length are placed 25.0 cm apart. An pr:x; gg6: ,sb:zh:zmke wiq* 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 plav 2ggi:xsmve s hz70ce xq255;ced next to a converging lens of focal length $f_C$ as in (Fig. Below). If $f_T$ represents the focal length of the combination, show that the focal length of the diverging lens, $f_D$, is given by
$\frac{1}{f_\mathrm{D}}=\frac{1}{f_\mathrm{T}}-\frac{1}{f_\mathrm{C}}.$

  A double concave lens has surface radil leoc7 *c (*gaj8rkl;i of 34.2 cm and 23.8 cm. What is the foca8*gll(*o j cac k;r7ell length if n = 1.52?    cm

  Both surfaces of a double convex lens have radii of 31b1 -b t-lxx0fy.0 cm. If the focal length is 28.9 cm, what is the index of rebl-yx1f- xt0 bfraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm. What is th1 g8 dcyabo;v8e radius of the cb;8davg1cy8o oncave surface?    cm

  A Lucite planoconcave lens (see t23vtkx1tbknu 38g 0j/crgl1er-5 tc Fig. Below) has one flat surface and the other has R = -18.4 cm. /gk8gn ek bcv1r50t32r -1x3l tuc tjtWhat is the focal length?    cm

  A symmetric double convex lens with a focal length of 25.0 cm isv;vre) ng2ru2pnu p1+ to be made from glass with an index of refrac)e p 2 nrvpgu+ruvn1;2tion of 1.52. What should be the radius of curvature for each surface?    cm

  A prescription for a corrective c gqyn* /)h9oqg6e.gxlens 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. W eyg./xo6*gq gcqh9)nhat should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fig. wi: /z--hov8, d5k7bje; ynck- dazyqBelow). You stand 1.5 myd-ne-zaj/bqki8hy -k d 7w ;co z5v:, away from one of these mirrors and look into it. You will see multiple images of yourself.
(a) How far away from you are the first three images in the mirror in front of you?
$d_1$ =    m
$d_2$ =    m
$d_3$ =    m
(b) Are these first three images facing toward you or away from you?
the first image is facing  ----待选择----toward youaway from you ;
the second image is facing  ----待选择----toward youaway from you ;
the third image is facing  ----待选择----toward youaway from you .

  We wish to determine the .msg(r)yxnr / avd ;-kdepth of a swimming pool filled with water. We measure the width (x=5.50m) and then ./ )rkar gvs; yn-xd(mnote 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 certain piece of plastic in-dj,u)ig4o yf air is $\theta_{\mathrm{C}}=37.3^\circ.$ What is the critical angle of the same plastic if it is immersed in water?    $^{\circ}\,$

(a) A plane mirror can be considered a limiting case of a spherical mirrocfo-; qq;,8es62m qgwd2l dxkr. Specify 2gqw6l8oc ks;-qdfd,ex 2mq; what this limit is.
(b) Determine an equation that relates the image and object distances in this limit of a plane mirror.
(c) Determine the magnification of a plane mirror in this same limit.
(d) Are your results in parts (b) and (c) consistent with the discussion of Section 23–2 on plane mirrors?

Stand up two plane mirrors so they fok 0mg1, 4vrjdzrm 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 fog8qk-; bgjngoha+9; krm a real image of a real object. Can you describe a situation;a89;ggk + hkgj o-qbn in which a diverging lens can form a real image?

  Each student in a physics lab is assigned to fin p0(lpt+v*9 (xmcjgfeka( 8c bd 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 completetlm b(8pgcc0p k9(vxj ea(f+* 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 aond6,v2 5vkyuild1lc v2+ 5 ft 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 cylindricap,ap1 dxlap* 6l 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 convergi7nnxtj3kte jlu 0s *.1ng lens of focal length $f_1=15\mathrm{~cm},$ which in turn is 55 cm in front of another converging lens of focal length $f_1=15\mathrm{~cm},$ (see Fig. Below).
(a) Draw a ray diagram and estimate the location and the relative size of the final image.
(b) Calculate the position and relative size of the final image.

A bright object is placed on one side of a converging lens of focal length fype;:b:1ofhdi 7 b8u wjxq 81g, and a white screen for viewing the image is on xgh u8b:p7 wj:; eq1 o1dib8yfthe 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 pz*2/3t7zmetl:lo b8f5o fbc as the 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 m7ll 5 b/:zzbtpo om8tec3 f2*f away, how far from the lens should the slide be? If the slide is 36 mm wide, how wide will the picture be on the screen? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (picture size is a v w :059w (lcecv7oi,; l)u)uadhfwvgctually 24 by 36 mm) is to be projected on a screen 1.80 m by 2.70 m placed 7.50 m from the projector. What focal-length lens c v0hawlu g)9dil)u,5f7v(ov c:w;e wshould be used if the image is to cover the screen?    cm

Show analytically that the image formed by a mfa3rzw3(ls 1 converging lens is real and inverted if the object is beyond the foc31(a mls rzf3wal point $(d_0>f),$ and is virtual and upright if the object is within the focal point $(d_0>f),$ Describe the image if the object is itself an image, formed by another lens, so its position is beyond the lens, for which $-d_0>f$, and for which $0$<$-d_0$<$f$.

  A movie star catches a reporter shooting pictures of her at nf.x6vm.m g6h/ lrn 0shome. She claims the reporter was trespassing. To prove her point, she gives as.h6/n lmsm rfgn.xv60 evidence the film she seized. Her 1.75-m height is 8.25 mm high on the film, and the focal length of the camera lens was 210 mm. How far away from the subject was the reporter standing?    m

  How large is the ima. )gtwz/g a;poge 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.