What would be the appearance of the Moon if it hllwikb*k1tgq2 1a-sj:/ hq7 nad
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the wh wo16wr 943hyp)zl)k sar-mnjole Roman fleet in the harbor of Syracuse by focusing the rays of the Sun with a 9o a4 y)n3w zjkwrrhp16)m-slhuge spherical mirror. Is this reasonable?

Although a plane mirror appears to reverse left and righa a4-l/fvgt o8t, it doesn’t reverse up and/lt f a-o4a8vg down. Explain.

If a concave mirror produces a real image, is the image nece4*arftsglx .oq. 0x8rssarily inverted? Expla*gf. lxs0.4qrr t oxa8in.

An object is placed along the princil;. udf to5 lr-z/,qutpal axis of a spherical mirror. The magnification of the object is -3.0 Is the image real or virtual, inverted or upright? Is ulfz,t u-/;l rodq. t5the mirror concave or convex? On which side of the mirror is the image located?

Using the rules for the three rays disuupcc-ww) .gf14v n(w cussed with reference to (Fig. Below a), draw ray 2 for (Fig. Belogun u-4w1( ). fcvwpwcw b).
(a)
(b)

What is the focal length of a plane mirror? What is the magnification of a pl9c4hqq7+i: oq3dyfqk ane mf7:qyqq9+d3 hci k4qoirror?

When you look at the Mokeh3kf;u//8)ag qr m jon’s reflection from a ripply sea, it appears elongated . Expla/ rkuj qe/;fm)h3kg8a in.

What is the angle of refraction when a light ray meets 4ysv ul da37:mxj:ia,the boundary between two materials: v 4yjx3au:d,m7lasi perpendicularly?

How might you determine the speed of light in a solid, rectangular, transp5/ 4pgx3 rg v;c+ih* uhw,svx muy:,mnarent om cg r;v sh4gu, ym+wuv5xn:pi*,3/xhbject?

When you look down into a swimmi ncequnu59z7 rg1tryb 061) nang pool or a lake, are you likely to underestimate or overestimate its depth? Explain. How does the apparent deptcny)ntue5 167bq1r9g rn z 0uah vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks bent when p2dv6 pc;)vf lxk;:1cej, xmzxart of it is under water ( xm:k;p l)cvxxvzd6f1 ce;,j2Fig. Below).

Your eye looks into an aquarium and,6 ab 2fvx1q t;7)et srwuw:jz views a fish inside. One ray of light that emerges from the tank is shown in (Fig. Below), as well as the apparent position of the fish. In the drawing, indicate the approximate position of the actual fish. Brief tt;wqb67)u :jea 2sxfvrwz1,ly justify your answer.

How can you “see” a round dropjtxr l-3;1lz i of water on a table even though the water is trans-3 ltr;jz1ixlparent and colorless?

When you look up at an object in air from beneath the surfaxvbr4 skd35 hfenr ,*0ce in a swimming pool, does the object appear to be the same size as when you see it directly in ah5 b,r*4dr 3kes0nvxfir? Explain.

How can a spherical mirror havevt+b x eag9x3o8urn3: a negative object distance?

Light rays from stars (including our Sun) always bend toward the vertical direct82kx yu )v(+ jfkq4sfrion4r jkfyskv8 2x(fq+)u 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 lharlr:ji,r/)h p)7ov *d:vcwens is to make a sharp image of an object:7rorl:v ,pv/i)) dwc ar h*jh very far away?

What type of mirror iutx1gnis2h9e 9, xtq7s shown in (Fig. Below)? Explain.

A photographer moves close ijd:-va,h3mf r to his subject and then refocuses. Does the camera le3h jdvi:,f-am ns move farther from or closer to the film? Explain.

Can a diverging lens form a real image under a4gm gm;0ms /lp3wg ee6ny circumstances? Explain.

Use ray diagrams to show that a real image formed by a thin lens is a ryh atl 2ds5-*aj0e1clways inverted, whereas a virtual image is alwayh1ec*-tda 0rj2 sl5y as upright if the object is real.

Light rays are said to be “reversible.” t/4r60)f6fxuima b ch8 fycj o ag69p(Is this consistent with the thin lens equation? Expluaftx 6fb46(hpi oc)6m a 9rg8 fyc0/jain.

Can real images be projectejsytc:/3mk ;dmv5)u ed on a screen? Can virtual images? Can either be photographed? Discuss carefull) :kj ;yuse3vm mt5dc/y.

A thin converging lens 9/knegqw *g z4 22lthris moved closer to a nearby object. Does the real image formed change rg2kl/2hn4tzqe* wg 9
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of rezk f1h (h4xfnk 17k)gvfraction n = 1.30 In air, it is a converging lens. Will it still be a converging lens if placed in wate4ng 11hkxz (h7f)vfkkr? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands fpnt 0b0z*r4sjacing a converging lens. If the nose and the tail are each focused on a screen in turn, which will have the greanr *p0j40bt szter magnification? ----待选择----nosetail 

A cat with its tail in the air stands facing a converging lens. Un5p1 -q 0tqn5uzoc.uc. 1as6zuwew3ixder what circumstances (if any) would the image of the nose be virtual and the uzc6i351q . unstop-czq wua1ew05.ximage of the tail be real? Where would the image of the rest of the cat be?

Why, in Example 13, must the converging lens have a :l9dh c+r;sbw shorter focal length than the diverging lens if the latter’s focal length is to be determined by combininh9ws l:+dbr ;cg them?

Explain how you could haveecb/z y q9h.uxae4/p 74,w iec a virtual object.

  An unsymmetrical lens (sc zk,cd8gk6 1ray, planoconvex) forms an image of a nearby object. Does the image point change if the lens is turned 16 kck,g8z rcdaround? ----待选择----yesno 

The thicker a double convex lens is in the center as compared to its edges, tk 1o7e:3 t0:-ubcj0od evaetm he shorter its focal length for a given lens diameter. Explain-eacj0o1ot:ev 7ebm0: 3u tdk .

Consider two converging l3g xt,xo2bzj 9v:8po *g ej3hhenses separated by some distance. An object is placed so that the image from the first lens lies exactly at the focal point of the second lens. Will this combination proo*8egjjv:x3,ghbz23x oth 9pduce an image? If so, where? If not, why not?

  Suppose that you want to take a photograph of yourself as you low9xgdjk) ,+sershjl6r 9p;5 gjx/+ unok at your image in a flat mirror 2.5 m away. For what distance should the c;kdlj x/+ r jjgh +sp96se5 nx,9gw)uramera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mirror, you see the same (zf qsyi q(w;6amount of your body whether you are close to the mirror or far away. (Try it and see.) Use ray diagrams to sho;6(izq qfwy (sw why this should be true.

  Two mirrors meet at a 13uuw9 q4u2l 5/ :yhzmpn ur*fr65$^{\circ}\,$ 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 from84 uozeo1yo1h57lw r2f7nx r fg +.tont of a vertical plane mirror whose bottom edge is 43 cnf8ymf+ozut l4g1e5wr r oox217 .7hom above the floor, (Fig. Below). What is the horizontal distance x to the base of the wall supporting the mirror of the nearest point on the floor that can be seen reflected in the mirror?    cm

  Suppose you are 90 cm from a plane mirror. What area of the mirror is used to regkjc:.v 7)tinflect the rays entering one eyejigvnt :k7) c. 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 mq 09h/ ppi;hvd4ik:j oeet 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 pointedqgf aazg5ky.,k s85i9 at the Sun, focuses the Sun’s rays 18.0 cm in front of the mirror. What is the radius fa98 . giy,55kzsqgkaof the spherical surface from which the mirror was made?    cm

  How far from a concave mirror (rxn wc 9de3vat/vg.)iy4 22tdtf7w qq0 adius 23.0 cm) must an object be placed if its image is to be at infinity? c.3q7wfxgvv) 2n/ w9d2 ait te4yq0td    cm

  If you look at yourself in a shiny Christmas tree ball wid 9e8eiznn5v0th a diameter of 9.0 cm when your face is 30.0 cm away from it, where is ye9n 0n5dze iv8our image? Is it real or virtual? Is it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement. 8tc3o oy/tjw park shows an upright image of any person who stands 1.4 m in front of it. If the image is three times the wt/o.83to yjc person’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror that, when 2.20 cm from a toothhgf;n4lb:( le, will produce a $\text{4.5×upright}$ image. What kind of mirror must be used and what must its radius of curvature be?
 ----待选择----convexconcave 
r =    m

  Some rearview mirrors produce images of cars behind you that( hqjlemi:yi)wi*7g0+ap- fa are smaller than they would be if the mirror were flat. Are the mirrors concave or convex? What is a mirror’s radius o0w(iy m)a:a*7ihgepjil + -fq f 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 20.003w *h ufm8ndx cm from a convex mirror of radius oxw 8*ufm03h dnf curvature 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 s1vvj(,gd0ncymwu7 4n ecurity mirror in a store. You estimate the height of your image to be half of your actual height. Esj,40vcdm gnu yw n7(v1timate the radius of curvature of the mirror.    m

  (a) Where should an object be placed iq iqxgz2o3b8 2n front of a concave mirror so that it produces an image at the same loc2ziqg82 3 boqxation as the object?
(b) Is the image real or virtual?  ----待选择----realvirtual 
(c) Is the image inverted or upright?  ----待选择----invertedupright 
(d) What is the magnification of the image?   

  The image of a distant tree is virtual and very small w 6js y(bmf57 ;o6ugqufhen viewed in a curved mirror. The image appears to be 18.0 cm behind the mirror. What kind of mirror is it, and what is q7g6 ffom b(y;ju us65its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different te8)ouhdzx/a,v / sw6duchniques,
(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 2 jqp35d3o7peotfdr/ew f*q7 m of a convex mirror is $m=-d_\mathrm{i}/d_\mathrm{o},$ just as for a concave mirror. [Hint: consider a ray from the top of the object that reflects at the center of the mirror.]

Use ray diagrams to show that the mirror ea/qvuknfeda6g481: lw zg b/,quation, Eq. 23–2, is valid for a convex mirror as lo :/g,n/ew zvqakb1df8ga4l u6ng as f is considered negative.

  The magnification of a con-homo vfy +uh,-,ay4 fvex 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 c.6ad/cescd/ +ac9e;za n yxt8x *2 ditm in front of a spherical mirror. It is desired to produ//tdac+ x*c e9ist26a dy de8x;. anzcce 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.i,1y4ql(d d ad33 whenyld,d14d qa( i your 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 light ot*j ea/m-4ix 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 ice4w6y :br: owtuocw,)djoi l9,cjj), b is $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a crtt e4 w 9+(ww-n ;x;pxlorlb/ertain substance is 89% of its value in water. What is the index of refraction of this sulw9/ r;4xtenb;xl w+p o(t- wrbstance? n =   

  A flashlight beam strikes the su2ecv-( hllgt;b;jp64t j 7up lrface of a pane of glass (n = 1.58) at a 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashlight upward from beneath the water at a 4mw : 1)8yqmef/ w;mlh 4yeu0dd2.5$^{\circ}\,$ angle to the vertical. At what angle does the light leave the water? $\theta_2$ =    $^{\circ}\,$

  A light beam coming from an underwater spotligv3a/x ggxuqx63s7 7;iv7o xbj6e 7vb eht exits the water at an angle of 66.sjxebiev7o6 ;7 g7v3ax7xv3x bqgu/60$^{\circ}\,$ 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 see.*-ga 6qwze ion to make a 31.0$^{\circ}\,$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?    $^{\circ}\,$

  An aquarium filled with water has flat glass sides whose index of (7t/wi cj)vphrefraction is 1.52. A beam of light from outside the aquarium stri7/i)c hj wpv(tkes the glass at a 43.5° angle to the perpendicular (Fig. Below). What is the angle of this light ray when it enters
(a) the glass, $\theta_2$ =    $^{\circ}\,$
(b) the water? $\theta_3$ =    $^{\circ}\,$
(c) What would be the refracted angle if the ray entered the water directly? $\theta_3'$ =    $^{\circ}\,$

  In searching the bottom of a pool at night, a watchman shines a narrow betf w8tx42;nh/ ka:wdx t22u wlam 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 beneax2a4t k8:x ;l/df2hwu wn2ttw th his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equilaterja4 op wvsk/4tff6 .wy s4-q*lal 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 ishdt-h02za : ncpg/ x2s partially reflected and partially refracted. Find the angle of incidencegsp n2 xa/h0z-2dtch: if the angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam inci yhrd m-dnr7jrkwphcw ) 627)4dent on a uniform layer of transparent material, as in ( -jcnwrdy4ph6 ) 27rwh7 k)rdmFig. 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 a flat piece of glass with index of refraction nfj k.1cueo66r3jupe0 e8 wl/m as in (Fig. Below). Show that if the in 0eeu81r cojleu6p/j 63km f.wcident 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 betwer xz:tm1o)q9ndio a()en water and Lucite? To be totally internally reflected, the light )q mdo 1nrao x(9ti:z)must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–air surface iv9 1 3ve 8z*r-3ognjkq0h/o o ua/zlexs 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted i tw6vrkzdtzo;:) h :i0n a pool of water from a depth of 62.0 cm. Where must it strike the air–water inter0:: dthzzi)w 6t;vork face, relative to the 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 surface of a liquid and strikeqq//iai i5:gy s the surface 7.0 cm from the point directly above the source. If total internal reflection occurs, what can you sqg a/y: iq/5iiay about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikestpm rs;jq5/ s4 the left face of the prism in (Fig. Below) at 45.0$^{\circ}\,$ as shown, but is totally internally reflected at the opposite side. If the prism apex angle (at the top) is $\phi=75.0^\circ,$ what can you say about the index of refraction of the prism? $n \geq$    (retain three decimal places)

A beam of light entersumpf.*k1iiyjo701rks .cgg b96s :vg the end of an optic fiber as shown in (Fig. Below). Show that we can guarantee total internalkigujrsg .. f9k: *6m1pybc1 vg07si o reflection at the side surface of the material (at point a), if the index of refraction is greater than about 1.42. In other words, regardless of the angle the light beam reflects back into the material at point a.

  (a) What is the minimum index of refraction for a etxm2ld:pn 6 z1.yfk/pz c /f,glass or plastic prism to be used in 6p e mkzpc/12f:yt,. nzlfxd /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-length ceung+ ba;vpbj-g/1q1z,4 a 2t vs- msionverging lens. Find the object distagnem 2v-- qs,sgb/ ;au pz1i+a4b 1vtjnce
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.5 cm behind a lens.(nv kthd2(e6vmm g q48
(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 obigv3 2*kxi2*6hz j aowvvfo1 io (o-p6ject 2.75 m away as an image 48.3 cm on the other side of the lens. What type of lens is i*(a k6 -iig i3*xvowfpoz6vooj2 21 vht and what is its focal length? Is the image real or virtual?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the power of a 20.5-cm-focal-.n, dv0k 6;ktstmahcc3c71yzk 9t ;vclength 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 focal leng -9* d9lmg8 drmdql8cp,ka-.pcihk1eth 24 cm to view a stamp 18 cm in front -8 c9dk8lq pk9e1plha* dg,-mmi.rcd 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 hi xsar4 ds/o22ngh. What are the position, type, and height of th dasno2srx42/e image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length len7)z .ja bz/vujs is used to focus an image on the film of a camera. The maximum distance allowed betjjz)zv bau/ 7.ween 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 re t)7x(vrl 5ettading material by a factor of 2.5× when a book is placed 8.5r(ttv)7l e xt0 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 frd 45q)tzs 2ayjom an 8.0-D lens. By how much does the image move if the 5)yqts 4zd2ja object is moved
(a) 1.0 m closer to the lens,    cm away from the lens
(b) 1.0 m farther from the lens?    cm cm toward the lens

  How far from a converging len ,tlqbpmw25-uy 4. ixu s/;vu;xod5pm s with a focal length of 25 cm should an object be placed to produce a real image whi w;by u5st/q5mo-pmu, xv dupl4.2 xi;ch is the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an object be-t5ckfml1k 5pdf5/3dw.ku m u placed if its image immwu3l5dkf 5td kpk/ .- ufc15s 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-length lens must an object x)(, mverhac2sjlx- 4be placed if its image is to be magnified 2.00× and be real jar,-vehlc(4 x )2msx?    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. Where is tcs4; 7vy nyss;he image, how high nvcs;7sys4;y 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-cmp c4(xw/;n: pm-qfibl( dtz y0-focal-length converging lens if the image is 2.5× larger than the object andpxndli 4m;b/pq(ftwy:(0 cz - is real?    m

  A bright object and a viewing screen are separated by a distance of 66.0 cm. Ax5d8q3jt-w me4;z amb x/sah kfn2h+l *8ts/ ft what location(s) between the object and the screen should a lens of focal length 12.5 cm be placed in order to produce a crisp image on the screen? [Hint: fh- tex+ 3 q42ssmakwfntz*hja/b5 8;l8d/m fxirst 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 c08o); u)-ustgw m zakh ).ak3*shte lvrv(0lhm apart. An object is placed 36.0 cm in front of one lens. Where will the final image formed by the second lens b)h0rlmuv()wa3g-;eau .ovt*h8sz)tk l s0khe located? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens wit8dep (c5nqs i cow0cl.92cmr aksc : t*d(i2e9h $f=-31.5\mathrm{~cm}$ 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-jkdx 0pe d,)ztky 1u5 lens is 21.0 cm behind a diverging lens. Parallel light strikes the diverging lens. After passing through the converging lens, the light is againd)ykdpzk,ut0 -xe1 5j 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 p z,9s h1bvzu0 : b*5*xnlgdzoplaced only 20.0 cm apart. The object is still 60.0 cm in frond5vz:u9* b ,0gzhxzs *o1p bnlt of the first lens as in (Fig. Below). In this case, determine
(a) the position of the final image,    cm
(b) the overall magnification.    cm
(c) Sketch the ray diagram for this system.

  Two converging lenses are placed 30.0 cm apart. The focal j(ip22 jur+ dglength of the lens on the right is 20.0 cm, and the focal length of the lens on the left is 15.0 cm. An object is placed to the left of the 15.0-2 j(j +2gdruipcm-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 ls9 dqh6p/,c9 wom ;sn(x1 unt4i 6tsiyength of is placed 12 cm to the right of a converging lens with a focal length of 18 cm. An object o1im( h9sn;xq6/ndc4is6 utp yw 9st, 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 le wx+,qvwvui9struh2u-l :d . -ngth 20.0 cm and one diverging with focal length are placed 25.0 cm apart. An object is pla-lx 2h +u, :isvuwd9twuvrq-. ced 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 co6oq1*iwmwgcd0( j .1:dj wkipnverging 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 radii of 34.2 cm and 23.8 cm. What is the foca*u* kr6v b9gqhl length if n = 1.h b uvgk**q69r52?    cm

  Both surfaces of a dom j jm+gp4he4-uble convex lens have radii of 31.0 cm. If the focal length is 28.9 cm, what is the index of refraction of the lens pejmg4hmj+- 4 material?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm. a(o 7xmj2e3v imn8q;las2d*0jvq *k cWhat is the radius od2 7n(v l32q* o 8;xsjmvam 0k*eqcjiaf the concave surface?    cm

  A Lucite planoconcave lens (see Fig. Below) has one flag,;;yc-c iec q,ptzc8 t surface and the other has R = -18.4 cm. What is the foca8, -ctczyp,ecc;gqi; l length?    cm

  A symmetric double convex len a;i faj ,3in./(kgpfwcer:m)s with a focal length of 25.0 cm is to be made from glass wianc;f( .agje / fkmwip)r 3,:ith an index of refraction of 1.52. What should be the radius of curvature for each surface?    cm

  A prescription for a correctd25h fii3l :.jx-p gajive lens calls for +1.50D. The lensmaker grinds the lens from a “blank:a5ijdp 3-gx. lihjf2” with n=1.56 and a preformed convex front surface of radius of curvature of 40.0 cm. What should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fika ( y-zkd jy23csp;5eg. Below). You stand 1.5 m away from one of these mirrors and look into it. You will see k (y2;e3- 5akzsdcpyjmultiple images of yourself.
(a) How far away from you are the first three images in the mirror in front of you?
$d_1$ =    m
$d_2$ =    m
$d_3$ =    m
(b) Are these first three images facing toward you or away from you?
the first image is facing  ----待选择----toward youaway from you ;
the second image is facing  ----待选择----toward youaway from you ;
the third image is facing  ----待选择----toward youaway from you .

  We wish to determine the depth of a swimming pool filled witc 77z0gid upw :x/xxg.h water. We measure the width (x=5.50m) and then note that the bottom edge of the pool is just visible atg7cpx0 w i:ud 7gzx/.x 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 mxo 6p9 g ob.v6n7d8racertain 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 limitingky3 9/hqcbxbz. :be 6g case of a spherical mirror. Specify what this lim6yh9: /qb e bz.3kgcbxit 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 9oltu -uox:p ng9x1d z* xkz/q+7)ku3 t0$^{\circ}\,$ 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 can5f pji4tl .pd.7u;esr never form a real image of a real object. Can you feut i dplr47.sj; 5.pdescribe a situation in which a diverging lens can form a real image?

  Each student in a physics lab is assigned to find the location where a bright 5yqkm-gx h;r+v*x.yagw.p r pe- xg(5object may be plqa grx+-p.w(m5xkx5e*hy-g;p yr .v gaced 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 necessarily need to repeat the lab, and justify your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of a prismdb l,i/s7ey0;kx * bm7zf6ymi 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 cywzwx2qela 81gk6t + 1hlindrical 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 cond7 *::vgd llykverging 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 convergizxj- a*)n6zx11q gwa6m sar;dng lens of focal length f, and a white screen for 6z-;za ag61as*nwx jdq)mxr 1viewing the image 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 u8s cybrzc tr r;jgot0k-g ,+3d:qi.9 projector, the film acts as the object whose image is projec+cok ;.8iyrt3d:u gr j-r ,sgtb 9c0zqted 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 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 vcl/xrt/5kn n:6d.bx 36 mm) is to be projected on a screen 1.80 m by 2.7lkx.nx/vt:c r6/ bn 5d0 m placed 7.50 m from the projector. What focal-length lens should be used if the image is to cover the screen?    cm

Show analytically that the image formed by a converging lens is real mb7n+ygj+vwhok/;p f tsp3 8 3and inverted if the object i bfsn hg+wt;7+p/jv3op 8k3yms beyond the focal point $(d_0>f),$ and is virtual and upright if the object is within the focal point $(d_0>f),$ Describe the image if the object is itself an image, formed by another lens, so its position is beyond the lens, for which $-d_0>f$, and for which $0$<$-d_0$<$f$.

  A movie star catches a reporter shooting picturesn 6gv-5dzbn * pj06md9uhhg8j of her at home. She claims the reporter was trespassing. To prove her point, she gives as evide*6 u0j h8nddzbhm -pggnvj569nce 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 image of the Sun on film used i)qpb +-segf4nlk/*s n n 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 1ng/ypw:g f3dhq.t (hcertain lens is imaged 8.20 cm in front of that lens (on the same side as the object). What type of lens is this, and whyn(:gg f wtq3. /1hhdpat is its focal length? Is the image real or virtual?    cm (diverging)  ----待选择----virtualreal 
(b) If the image were located, instead, 41.5 cm in front of the lens, what type of lens would it be and what focal length would it have?    cm (converging)

  When an object is placed 60.0 cm from a certain converging lens, it forms a +pzx z7s jrt:5real image. When the object is moved to 40.0 cm from the lens, the image moves 10z r:jzpsx7t+ 5.0 cm farther from the lens. Find the focal length of this lens.    cm