What would be the appej-; kylmoz.fd:yqqj ;-l+)xn arance of the Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to hvt6ke)fx0 ek.ej ,p f9ave burned the whole Roman fleet in the harbor of Syracuse by focusing the rays of the Sun with a huge sphef,9)txek f. ev ekj06prical mirror. Is this reasonable?

Although a plane mirror appears to reverse left and right, it doesn’t( tr7s,eoeznv8pb x1(p +: ij8)fypr v reverse up pvrovp,t) i7b( (8 yepxfn1erjsz :+8and down. Explain.

If a concave mirror produces lrwtfo e9x534a real image, is the image necessarily inverted? Exlf5t94x er3owplain.

An object is placed along the principal axis of a spherical mirror. Thjg crs 8zckwtw :j2 -:q-;7xtye magnification of the object is -3.0 Is the image real or virtual, inverted or upright? Is the mirror concave or convex? On whij tg yw: w2qjcts-8 r;cxkz-:7ch side of the mirror is the image located?

Using the rules for the three rays discusseigz770pr8 olipc zw-- d with reference to (Fig. Below a), draw ray 2 for (Fig - 7i z87-0pcgzrlwopi. Below b).
(a)
(b)

What is the focal length of a plane mirror? What is the m6v. k7ilod t3q+riek2 agnification of a plane miroleq7ri3 v. + id2tk6kror?

When you look at the Moon’s reflection from a ripply sea, it appearw75vyr8lt fq) x6mfhk 62z5 bds elongated .fzh2wlb ) dvk6tx5q68y75m rf Explain.

What is the angle of refraction when a light ray me .5f2fb fdo*2iflcc+5 ogn*2 zab:zniets the boundary between two materials perpen5b ifd i2gf fczfz.2l2 *o*:c5ab+nondicularly?

How might you determine the speed of light in a solid, rectangular, transpar -0b-cgeam/hi9-lz eqwa;3olent object?9 ;zeaohlg/3m w-0ql-e- abci

When you look down into a swimming pool or a lake, are you likely to undero)ea21e .b6j*5y creiviqpg 3 estimate or overestimate its depth? Expleer6i 35 b.* je1iy)goqcpv2aain. How does the apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to shoo. ib kumxma2314:i(hpzrs 9f w why a stick looks bent when part of it is under water (Figao9k( 4i1zp bisf : 2u.3mhmrx. Below).

Your eye looks into an aquarium and views a fish insiya7,fw 9zq*50 f,oye6 s zlicude. 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. Briefly jqyof79 z* s,,awfz5ey0ilc 6uustify your answer.

How can you “see” a round drop of water on a taxe3 lju 1du,qn .-enn4ble even though the water is transparent and colorl qd3.jn4-1n le,uenxuess?

When you look up at an objectdthl4wls,2 -h in air from beneath the surface in a swimming pool, does the object appear to be the same size as when you see it directly in air? Exp t-2ldw4l, hhslain.

How can a spherical mirror have a negative objehvg 4t)nv ngkq 2 5h6.a,nw*puct distance?

Light rays from stars sdh; :-.)o +dt+wibtsj.jez w(including our Sun) always bend toward the vertical direction as they pass through the Earth’s atj-dwsstibh +.eo;j) :d.w+tz mosphere.
(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 28xvemgk 4xed rrwo -jes+)6,a camera lens is to make a sharp image of an object very+dx-s, o vr2 8eewm egxk4rj6) far away?

What type of mirror is shown in (Fqh-di 1 je3t lm)9d9s,fwce f0ig. Below)? Explain.

A photographer moves hoz:m 1fzz1)9(oz obkcloser to his subject and then refocuses. Does the camera lens move farther fromzzhzmz9fb:ko) 1(o1o or closer to the film? Explain.

Can a diverging lens form a real image uea(iarz913 w .)rksg7 dm;vho nder any circumstances? Explain.

Use ray diagrams to show fx sv-+s(y9mc that a real image formed by a thin lens is always inverted, fss(+-vy9xcm whereas a virtual image is always upright if the object is real.

Light rays are said to be “reversible.” Is this consistent with tev/-z )n0uv qfhe thin lens equation? Explan0-)/ fveuvzq in.

Can real images be projected on uis5vyn79:1(e ylnab a screen? Can virtual images? Can either be photographed?19nvs7 5 e yuly(aib:n Discuss carefully.

A thin converging lens is moved closer to a neicy ekhv:39 *larby object. Does the real image formed changhl i cek3:*v9ye
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of rjcy z8bb ci y,wt;am:co y r.o2h45s+*efraction n = 1.30 In air, it is a converging lens. Will it still be a converging lenwiy msy2+trz. ah 58*c,by4 :ocjbc ;os if placed in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands facing lg t3 oxhuu5*+a converging lens. If the nose and the tail u5u xgh+o*tl3are each focused on a screen in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facing a converging lens6si7y06ldcg;g did82 9 hg-r-mttai z . Under what circumstances (if any) would the image of the nose be virtual and the image of d g2i8r0iyt 6d h6s;mt-giczgdl7 -9athe tail be real? Where would the image of the rest of the cat be?

Why, in Example 13, must the ccx0mgj::(c x8wvi/jnonverging lens have a shorter focal length than the diverging lens if the latter’s :m0n8vjw c(xg ji/x:cfocal length is to be determined by combining them?

Explain how you could have a virtual object.u3 wn-pijefy9jioc pf3:b( .(

  An unsymmetrical lens (say, planoconvex) ,0hkoziw4bq 0l i7yo- forms an image of a nearby object. Does the image point change if the lens is turned q0ih4-y7i lo0 kobw,zaround? ----待选择----yesno 

The thicker a double convex lens is in the center as compared to i:1fo etzlw495wv za/hts edges, the shorter its focah wa5l491: vfetzz/ wol length for a given lens diameter. Explain.

Consider two converging lenses separated by some distance. An y y7i/+l0.nh r.rfatg- o*ofxyd5p7 jobject is placed so that the imagh ny r-a* +5.t ofx/7ifyro7.ydlp0jg e from 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 wcomnw b/s*.m za/v6,photograph of yourself as you look at your image in a flat mirror 2.5 m,v/6w mo mnw*s. /bcaz away. For what distance should the camera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mirror, rkxn0idc w9/a) 59e 2gsd*qtu you see the same amount of your body whether you are close to the mirror or far away. (Try it and seeu cd*kxd wie 0gt 9s/q2ra)n95.) Use ray diagrams to show why this should be true.

  Two mirrors meet at tm rmo1smzz+kc: r4 1gynq-7/ a 135$^{\circ}\,$ angle, (Fig. Below). If light rays strike one mirror at 40$^{\circ}\,$ as shown, at what angle $\phi$ do they leave the second mirror?    $^{\circ}\,$

  A person whose eyes are 1.68 m above the floor stands 2.20 m i rgha3.2rf n3zn front of a vertical plane mirror whose bottom edge is 43 cm above the floor, (Fig. Below r2.3r gzfa3hn). 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 pl+u,r4txx45w.kpnip// dn uf sane mirror. What area of the mirror is used to reflect the rays entering o4 , p n.k/tpn4duuxwir+x/ s5fne 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 u81absowgd b5r+3 ;hgat 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 mirkzp-g;2 okqav4(c4m jror pointed at 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 mirror wask p (-vgkz442ojmac ;q made?    cm

  How far from a concave mirror (radius 23.0 cm) krb 4s--e2r ramust an object be placed if its image ie-r-4 bs2rarks to be at infinity?    cm

  If you look at yourself in a shiny Christmas tree b y 1cj-d9gj:7tn ks5fuall with a diameter of 9.0 cm when your face is 30.0 cm away from it, where is your image? Is it real or virtual? Is it upright ors-57jcu d j1n9fk gty: inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shows an upright image .m; ez0 7 gspi)vwf5 zcap1ao0of any person who stands 1.4 m in front of it. If the image is three s0g.1oea a7c5pwmvpf 0 z;iz)times the person’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror that,4e+wrm, 6g non/ wirt;zhc2bjj ..pu) when 2.20 cm from a tooth, will produce a $\text{4.5×upright}$ image. What kind of mirror must be used and what must its radius of curvature be?
 ----待选择----convexconcave 
r =    m

  Some rearview mirrors produce3 pap/ u dyf3l9ko+cx4 images of cars behind you that are smaller than they would be if the mirror were flat. Are the mirrors concave or convex? What is a mirror’s radius o f adc3p9yxlok/3up4 +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 20.0 cm frgxt;9 luoy,(lz9o3rj0x) qpbom a convex mirror of radius of curvature 20.0 cm.jzr9,p lo x3yo90;u)lt gbx (q
(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 0rnfsxat::*s e9 98ci hozcc/ convex security mirror in a store. You estimate the height of your image to be half of your actual height. Estimate the radius of curvature of * fctc8:r: a9ezi90sh s nxoc/the mirror.    m

  (a) Where should an obg nzxqgw4+vdv12 i 1 x;wvnj8:ject be placed in front of a concave mirror so that it produces an image at the same location as the object+nw8nvzgvdi vgw:2 41xjx;1q?
(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 s2 5jnn90xa wt smg6a-qmall when viewed in a curved mirror. The image appears to be 18.0 cm behind the mirror. What kind of mirror is it, and what is its radius of curvature?x mnsqwna a0g96j25 t-
 ----待选择----convexconcave 
r =    cm

Use two different techniqueytlf u q0*s.l )(y7dyes,
(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 mik3c wuwf c1o)y8kqucrgf2+v( ;m*ib. rror 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 equati 4 tt;xmabw,9y;f 2zbau-/)l*: t5c dpf ayswlon, Eq. 23–2, is valid for a convex mirror as long as f ixaw54-cy;:y ,) s d; atfzb9lt 2pwlbmu*a/ft s considered negative.

  The magnification of a con)w , :dowbf) 3zsaud)uvex 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 isqar6xan47x nqy) v ,y.i2 5msn placed 28 cm in front of a spherical mirror. It is desired to produce a virtual iyynq x)vi5 n.as76r 4x2namq ,mage 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 magiwyrs,w3zig+m1tc o a p,30a :nify your face by a factor of 1.33 when your face is placed 20.0 cm in fr z+i g3,ta,mcpy1 w3w sro0:iaont 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 if +khlahov8d 9ya ,e:(n
(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 ic;cjv+)mcw/vd- xy ,yt(6f 0sll r y1bre is $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain substakb +omhp3y 8y l7t(mw8nce is 89% of its value in water. What is the index of refraction of this substance? n =hb+ owpmkyt3ly 8 (7m8   

  A flashlight beam strikes the surface of a pane of glass (nh+mra+ 5 dylr, = 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 zdd i3 ;*sfa0gz/b jd.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 underwater spotlight exits the water at an angle o idjj;i;j/za8 f 66ijj; ;aji8z/ d.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 2 ))gail 6oq+ekr sc6mmake 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 refraf.qt68ds qer,( xvnr 1ction is 1.52. A beam of light from outsir.e(qsd f ,r6xv8qt n1de 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
(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 bei m(2vu ;;qja 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;m i2u(;jeqbv pool (Fig. Below). Where does the spot of light hit the bottom of the pool, measured from the wall beneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equilateral glass prism at a5l;-xkjy+mw, gpxl 7/ e3;slqhh czv: 45.0$^{\circ}\,$ angle to one face, (Fig. Below). Calculate the angle at which light emerges from the opposite face. Assume that n = 1.58.    $^{\circ}\,$ from the normal

  A beam of light in air strikes a slab of glass (n = 1.52) and is partia*a-tui)n*tcd)pxrlg j o* -;r lly reflected and partially refracted. Find the angle of incidence if the angle of reflection is twice the angle of al x) t-orj*;tp* ic*n d-ugr)refraction.    $^{\circ}\,$

Prove in general that for a light beam incr)cp c2/ +lmzoident 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 incidp)+2/clz co rment angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on a flat piece of glass with indeqg4i1+vbdcfp2 ; g-odx of refraction n as in (Fig. Below). Shicd b+p21;4fdg -oqvg ow that if the incident angle $\theta$ is small, the emerging ray is displaced a distance $d=t\theta(n-1)/n$ from the incident ray, where t is the thickness of the glass and $\theta$ is in radians. [Hint: for small $\theta,\sin\theta\approx\tan\theta\approx\theta$ in radians.]

  What is the critical angle c9s0ici +4 ttrfor the interface between water and Lucite? To be totally internally reflected, the light must start in wcr9ti + t4s0ichich material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certaih8y m -1) p))/ad hugkv hee3css*yg*tn 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 of 62.0 cm. W jy2y5-noiln +- xlbr(here must it strike the air–water interface, relative to the spot directly above it, in order that the light does not xl +lyi-r25nn-yj bo( exit the water?    cm

  A beam of light is emitted 8.0 cm beneath the surface of9urqwdnec11 1 a liquid and strikes the surface 7.0 cm from the point directly above the source. If total internal reflection occurs, what can you say about the index of refraqwc 1du11r 9enction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face of thc;6+/l cvcsgle 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 shwyg.uy wmr6)h3a/ 9k yown 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, regardless of the angle thew)6/gka ym. rhuyyw93 light beam reflects back into the material at point a.

  (a) What is the minimum index of refr)x1-(mtb+vx*5 g(lg x rcak wpc*v7nsaction for a glass or plastic prism to be used in binoculars (Fig. Below) so that tt) p5v +rxc*xgnxmalb* (1 7 (c-wvksgotal 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 32 mg gus.ahyj;3z/rfmm behind a 65.0-mm-focal-length converging lens. Find the3 m2hau;gy.fr/ z3gj s object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.5 cm behind a ledze8f x0hm1; bns.
(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 l1vz- 7eaq8w flight from an object 2.75 m away as an image 48.3 cm on the other side of the lens. What type of lens is it and 1lqze8 wa7f -vwhat 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-lengt- wf *x2dpm1kxh 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 lensbtg w7)km a 3q0epx14kuc c3)o with focal length 24 cm to view a stamp 18 cm in frontp3gwe107 uock)cmx)t4a3q bk 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, :2zm vav0c5r(dukqn.0 cm from an object 4.0 mm high. What are the position, type, and height of the ima 0kra:v(q 5n2mzvd,ucge?
   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 camera. Tc p0h9afeld,0he maximum distance0fp ca0e9lhd , allowed between the lens and the film plane is 120 mm.
(a) How far ahead of the film should the lens be if the object to be photographed is 10.0 m away?    mm
(b) 3.0 m away?    mm
(c) 1.0 m away?    mm
(d) What is the closest object this lens could photograph sharply?    mm

  It is desired to magnify reading material by a fabq(jjm c;i*r c+ scvui35o6 a* zi*k-xeoz(4wctor of 2.5× when a book is placed 8.0 cm behind a lena6( ioc b(w 5xrocm*q*ez jj+4;kvuc *3i-iszs.
(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 1.5u*h f 4j,llma.i,g)l /8ofdvw bby 37l m from an 8.0-D lens. By how much does the image move if the ob7 /fm.4 v38obh,aduw*bl,ijylf )l lg ject 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 lens with a focal length of 25 cm should an objecc62 .xb) mn rn9hvr+ylt be pv l9b)r6cx 2r+.h nynmlaced to produce a real image which is the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an object be placed ifnla wrwoh d 5 )nsxy7b3vn4y1a;)v- 0e its image is to be magnifiyynb7 -h 1d0 s)wnw4 or;nxavlv e5)a3ed 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 i b.i* 5szi,tlm9fx 6lxs89hoh. loe(if its image is to be magni.zf( *l9 lhme.9obxoiit,568l s xsihfied 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 insezpjw , d8r0,nel.la n1ct is 1.20 m from a 135-mm-focal-length lens. Where is the image, how high is it, and what type is nr.8zn,aje ,w1 d 0lplit?
$d_i$ =    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 ;icux w(h9k d,and an image formed by a 75-cm-focal-length converging lens if the image is 2.5× lar9i(c;ud whk,x ger than the object and is real?    m

  A bright object and a viewing screen are separated by a distance of 66.0 cm.mfbyzq2b- l0.qlt -yo jegv43apmk:48b* a2l At what location(s) betwb2-e.a by mpak y ql4lbv0gjm lzo-3q 2tf48*:een the object and the screen should a lens of focal length 12.5 cm be placed in order to produce a crisp image on the screen? [Hint: first draw a diagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length converging lenses dq9d,ueec.+m are placed 16.5 cm apart. An object is placed 36.0 cm in front of one lens. Where will the final image formed by the second lens bem.+eq, ddu 9ce located? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens with ;y*+i4 s2 rct8yhg wlqm ie(+c$f=-31.5\mathrm{~cm}$ 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 dijgsmjrw 3;c33 (r,k tf/qs)ud verging lens. Parallel light strikes the diverging lens. After passing through the converging lens, the light is again parallel. f3 3rg /3jwst )u,cd(;r qkjmsWhat is the focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Examfb;ri-vpaf1; e3hz ;n5 t2 llnple 23–12 are now placed only 20.0 cm apart. The object is still 60.0 cm in front of the first lezlpnn; 2av te 3l;;hi5 ffb-1rns 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 cw.tnxkz;w9 o0mli3b2 m 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 15.0-cm-focal-length lens. A final image from both lenses is inverted and located halfway between the two lenses. How far to the lnb;0.izk t9wlxmo23weft of the 15.0-cm-focal-length lens is the original object?    cm

  A diverging lens with a focal length of is placed 12 cm to the righ6i( 5 v ;bxyhf6vvwumfk6zi/ )t of a converging lens m/if(;yv wh)k6xzb5 u6ivf6vwith 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 converl82zi5hwv7+n rwa g2e ging with focal length 20.0 cm and one diverging with focal length are placed 25.0 cm apart. An object is placed 60.0 ra2 8 5ghww 7+vz2eilncm in front of the converging lens. Determine
(a) the position    cm to the right of the diverging lens
(b) the magnification of the final image formed.   
(c) Sketch a ray diagram for this system.

A diverging lens is placed next to a converging lens of focal leu(1y8/ruki vc0 zcoa(+ai 2uongth $f_C$ 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 lenssxpki4n- )l4 3pybt:c has surface radii of 34.2 cm and 23.8 cm. What is the focal le )nk-cp3x :syip 4l4tbngth if n = 1.52?    cm

  Both surfaces of a double convex lens have radii of5u.tq-+g)hanx i4-jki 4h6 nq)dufob 31.0 cm. If the focal length is 28.9 cm, what is the index of refraction of the lens materialifgb j- 5i6qxk +qd4h4nno tau-)u.)h?    cm

  A planoconcave lens (n=1.50) has a focal rg 1j9t89qo-e/kaikn length of -23.4cm. What is the radius of the/ret8qg a jk-k199 oni concave surface?    cm

  A Lucite planoconcave lens (see Fig. lfd: : wwbsba 88xhr1:Below) has one flat surface and the other has R = -18.4 cm. What:wbr:wbd1 x:sa 8h fl8 is the focal length?    cm

  A symmetric double convex u4scmt)qo 8lb2;:slq lens with a focal length of 25.0 cm is to be made from glass with an index of refracq2ql:4 s;oblc )t8ums tion of 1.52. What should be the radius of curvature for each surface?    cm

  A prescription for a corrective lens w.bc :c)hbf2lre6(hx calls for +1.50D. The lensmaker grinds the lens from a “blank” with n=1.56 and a preformed convex front surface of r r(b) l :ef.hwchbxc62adius 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 ap9oh q t2hzx:,h .qeww4z,un,xart as in (Fig. Below). You stand 1.5 m away from one of these mirrors and look into i ,9wh zhz ehwtx ,x42q:q.,unot. 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 depth of a swi+fd ob0;zs h+,ry)uiamming pool filled with water. We measure the width (x=5.ifr;0us+ b,o d+)zh ay50m) 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 a certain piece of plastic in airi 2o +5 gpsr6xh0o0f q -0pz(4dzvdwy ir1vgd1 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 mi2yim58t7ol ,i7fa gjy itq o-0rror. Specify what this limit is. i7y8 0qty5loit,7 igmjf-2oa
(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 90q/b r(abdba 8rj *8;um$^{\circ}\,$ 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 nec jq6*po7j3if ver form a real image of a real object. Can youj6 3q 7cpjofi* describe a situation in which a diverging lens can form a real image?

  Each student in a physics lab is assigned to find the location whew h. 0,5msiv95 vii5ukyvbk yib6dn.)re 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 are not the same. Explain why they do not necessarily nee.5bkb ,w5n5y 9s iy u 0ihiv).vkdvmi6d to repeat the lab, and justify your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of a prism is r xk fao4jse7z3m6; ;a$\phi=72^\circ$ 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 cylindrical glass0l1tz+dsf3b5- mnii z5 j mnw9 rod $(n=1.54)$ are perpendicular to the sides. Show that a light ray entering an end face at any angle will be totally internally reflected inside the rod when the ray strikes the sides. Assume the rod is in air. What if it were in water?

A lighted candle is placed 33 cm in front of a converging lens of focal lengil a0ug f v zoqtmhb/:c(2x15/ux ;o-uth $f_1=15\mathrm{~cm},$ 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 placs /)qw2niw0, gc1kvgn hid .3qayd k0cc)a8f8ed on one side of a converging lens of focal length f, and a white screen for viewing the image is on the opposite /ygi i,kd8f1.kd cw qvc03n hs)n8)aw gq20ac 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 ty2af* wrhi+j2 a/:e *v6tvlvprojector, the film acts 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 stviy vj+/h2:ea* tw *v2alrf 6creen 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 36 mm) is to be proje366 0mntavvx-stu 0ddi.be.icted on a screen 1.80 m by 2.70 m placed 7.50 m from the projector. What.v e30 vni66dx i.t0-dambsut 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 and invertw/: + oq fb)mrspqd 6qjtg8n,.ed if theo/qp.bwm tqd:rf,jgsq 8+n )6 object is beyond the focal point $(d_0>f),$ and is virtual and upright if the object is within the focal point $(d_0>f),$ Describe the image if the object is itself an image, formed by another lens, so its position is beyond the lens, for which $-d_0>f$, and for which $0$<$-d_0$<$f$.

  A movie star catches a reporter shooting pictures of her at home. S, -dtryz 55pulh:ze1nhe claims the reporter was trespassing. To prove her point, she gives as evidence the film she seized. Her 1.75-m height is 8.25 mm high on the film, and the focal length of r5,zny5 l e-p:1tduhzthe 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 frhc3p29-urmq/ xld1f)tzdqk 4g( ( t qilm used in a camera with
(a) a 28-mm-focal-length lens,    mm
(b) a 50-mm-focal-length lens,    mm
(c) a 135-mm-focal-length lens?    mm
(d) If the 50-mm lens is considered normal for this camera, what relative magnification does each of the other two lenses provide? The Sun has diameter $1.4\times10^6\mathrm{~km},$ and it is $1.5\times10^8\mathrm{~km}$ away.    for the 28 mm lens    for the 135 mm lens.

  (a) An object 34.5 cm in front of a certain lens is iknvwd*r2uns7 cj6g /(maged 8.20 cm in front of that lens (on the same side as the object). What type of lens is this, and what is its focal lengt r /ju7wc62(*kvndsg nh? 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, itaxau5u7+*e7;x k chau forms a real image. When the object is moved to 40.0 cm from the lens, the i xu+ c57uha;ua7e* axkmage moves 10.0 cm farther from the lens. Find the focal length of this lens.    cm