What would be the appearancez4 4mrcz)x* zjv);oe y of the Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burnedf6a 0u/( z lvh/:5cdadmj f uhc0o0uh) the whole Roman fleet in the harbor of Syracuse by focusing the rays of the Sun with a huge spherical mirror. Is this afoc:ua 5cf)(jhu uh06lm/vh d0z d /0reasonable?

Although a plane mirror appears *q y v0mest 80r aq2o8sdn//mhto reverse left and right, it doesn’t reverse up and down08 2 ta/res my qmv*/d08hqnso. Explain.

If a concave mirror produces a real image, is theal v6p4 lku:e+ image necessarily inverted? Ex u6pl+a4el:kv plain.

An object is placed g-g ziguf 1ei3nw3o ):along the principal axis of a spherical mirror. The magnification of the object is -3.0 Is the image real or virtual, inverted or upright? Is the mirror czfu 1:w)en3-ii gggo3 oncave or convex? On which side of the mirror is the image located?

Using the rules for the three rays discussed with reference to (Fi jw9eut4wgl1, g. Below a), draw ray 2 for (Figtj ,1le4 9wuwg. Below b).
(a)
(b)

What is the focal length of a plane mirror? What is luc(x::xk :x8ommkp0c8 2tcd the magnification of a plane mirroxm2u: dtm:l8( pk8ko ccxc x0:r?

When you look at the Moon’s reflection from a ripply (p(2g vn hrq+auh g: uyi3,)kqsea, it appears elongated .,y2q +vkui(r 3hup ng ag:q)(h Explain.

What is the angle of refraction when a light ray meets the boundary between -3sq7hve mnoo.h.o) 8w mmw0htwo materials p.en. om0w sqhmo7hwhmo3)-8 v erpendicularly?

How might you determine the speed of light in a sol7f5om n 42oynes, najyw: d*+cid, rectangular, transparent obje 2yaon f wnd5j: mc7+*y4o,senct?

When you look down igz,0h 6 1k ocl)di-t1lskwq x4g (eoi-nto a swimming pool or a lake, are you likely to underestimate or overestimate its depth? Explain. How does the apparent depth vari1w1 k oi tz-q-c60 s4ld)ok(h x,ggley with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks b u96nls4- lxyyent when part of it is under water (Fig. Belox4lylsn u 69y-w).

Your eye looks into an aquarium and views a fish inside. p:. 7,h q8 vb xk;cq nl22ncs1tp1sqb ksn5g(nOne 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 ;pkq8xvg7bq2kn sn1(hbsnt 2,. q: l5c c1pnsactual fish. Briefly justify your answer.

How can you “see” a round dro qacsw n*z(t1:yo syyo-x) ,4xp of water on a table even though the water is transpareoa:cwxt,sn y)z-yy4o *x s(q1 nt and colorless?

When you look up at an object in air from beneath the surface in ajqfh5 s ls57n (yhs,jjh phq.3p/8.o z swimming pool, does the object appear to be the same size as when phjhs3qno7.( ,pyh5zhj. fs58/j lqsyou see it directly in air? Explain.

How can a spherical 6qs.he/s nzk xp(3m/eiw)3*p g lgdbx+g0 + onmirror have a negative object distance?

Light rays from stars (including our Sun) al cts/fajbh*t7p4u; ;q3rw8k iways bend toward the vertical direction as thr ktpu c*/3s;wh4 qb8;a7ift jey 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 cam13(h ucxjyz. xera lens is to make a sharp image of an object very far away 3z(.xx1ujcyh?

What type of mirror is shown in6y3 rr .d -ezddu5dutagu1fd4/en,v; (Fig. Below)? Explain.

A photographer moves closer to hisrqfru tsh8: j,o)- *:*nczcax subject and then refocuses. Does the camera lens z c a*o*)q8h,junrcrs-x f:t: move farther from or closer to the film? Explain.

Can a diverging lens form a real image un)2w 5ja8 (pebg/.n2lpvra rl vder any circumstances? Explain.

Use ray diagrams to show that a real image formed by a thin lens is always invernu ibj5o9mms..1c62 zs kbd*u ted, whmbsb moi.*6kn5 d 9s.uuz j12cereas a virtual image is always upright if the object is real.

Light rays are said to be “reversible.” Is this consistent with the thiqfy8lip*j ,(hn lens equation? Explaqj (l,*8pyihfin.

Can real images be projected on a screen? Can virtual images? C-sqqtf;3dyl rv.u * j(an either be photographed? Discuss ca.uqfy(r-q;3 ts *jv ldrefully.

A thin converging lens is moved closer to a nearbufmv, 8/bnh9 w 5f(vney object. Does the real image formed chang9f/ b(uh en nf,v5m8vwe
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an5pt u6 96 a6h0fabzwob index of refraction n = 1.30 In air, it is a converging lens. Will it still be a converging au6bht6 9p05ofwa 6 bzlens if placed in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands facing a converhk3,q1(m:dbogg5 t ekging lens. If the nose and the taim3keqgdokb:g , 1t5(h l are each focused on a screen in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facing a converging lene3y t 7vpd6d ey(g:h9ys. Under what circumstances (ifv3 97 6dt:hye pdgyey( any) would the image of the nose be virtual and the image of the tail be real? Where would the image of the rest of the cat be?

Why, in Example 13, must the converging /5t tv,iwi30gf u t:vrlens have a shorter focal length than the diverging lens if the latter’s focal length is to b/ tvr0vutf i :it,3gw5e determined by combining them?

Explain how you could hasx h f uy8g8t3g:xh-(ife71dj ve a virtual object.

  An unsymmetrical lens (say, planoconvex) forms an image of a nearby object. Dq;s3 4,/,vrqpdey 4jexu w3-gimyxi/( v g3rpoes the image point change if the lens iyw -sv3xerypj44 m/ 3udqx3pigr ,q,(e;i v /gs turned around? ----待选择----yesno 

The thicker a double convex lens is in the center as compared to i8u*b8 bkr7qdgts edges, the shorter its focal length for a given lens diameter. Expla* r 7u8bqgk8dbin.

Consider two converging lenses separated by somekt-c) s:tgr ;r distance. An object is placed so that the imagesr-t tr)c;kg : 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 photograph of yourself as you look at your umc tc(3(ira(image in a flat mirror c(aiu( r3t(cm2.5 m away. For what distance should the camera lens be focused?    m

When you look at yourself inh42j6ls.5 + +rbcpelhpxt x;z a 60-cm-tall plane mirror, you see the same amount of your body whx+ jp5trpsz 6l;b.+c leh4 x2hether you are close to the mirror or far away. (Try it and see.) Use ray diagrams to show why this should be true.

  Two mirrors meet at a n 0miu:* .9assazesu* 135$^{\circ}\,$ angle, (Fig. Below). If light rays strike one mirror at 40$^{\circ}\,$ as shown, at what angle $\phi$ do they leave the second mirror?    $^{\circ}\,$

  A person whose eyes are 1.68 m above the floor stands 2.20 m in front of a vert g-ekv xd(a:luj7c4x, ical plane mirror whose bottom,jgca-lxve: 4ux 7(kd edge is 43 cm above the floor, (Fig. Below). What is the horizontal distance x to the base of the wall supporting the mirror of the nearest point on the floor that can be seen reflected in the mirror?    cm

  Suppose you are 90 cm from a plane mirror. What area of the mirror is used -hkcn368f)x 3 /jd 4w7jjwqyhod)om ito reflect the rays entering one eye fr3wjcnfd3h/mxhd 7)j-6y)o q o kiwj 84om 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 at asybh(8gtly 8l, 62pxo n angle $\phi$. a single ray reflected successively from both mirrors is deflected through an angle of $2\phi$ independent of the incident angle. Assume $\phi<90^{\circ}$ and that only two reflections, one from each mirror, take place.

  A solar cooker, really a concave mirror pointed at the Sun, focus eibiw(gg+()tj8.xs2;nrik pa wt 6j :es the Sun’s rays 18.0 cm in front of the mirror. What is the radius of the spherii kbep(2 6rstg:8i)j; gwj(+.iatx nwcal surface from which the mirror was made?    cm

  How far from a concave mirror (radius 2i.bv3o5clj2x5c k/e1: hg(q zi ao ml43.0 cm) must an object be placed if its image is to be at ini. e4ig:3h 5/jq2xbol 1mlkzvacc o(5finity?    cm

  If you look at yourself in a shiny Christmas tree ball wit-m +vqrqa*-bb h a diameter of 9.0 cm when your face is 30.0 cm away from it, where is your image? Is it real or virtuqrbbv-a -m+ *qal? Is it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shows an upright image of any person who stann+.:cjudjuj -3*ftf7g o ( prnds 1.4 m in front of it. If the imau 7+unj r*3t. (gjpofnj:f-cdge is three times the person’s height, what is the radius of curvature?    cm

  A dentist wants a small mirro 2leim0n 7-h5wlv) dmpr that, 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 produce images of cars behind you that ar(sap-q8r6 dq dz 1x84*ets iaqe smaller than they would be if the mirroq* spqa1 e8qad64t-x ( 8driszr were flat. Are the mirrors concave or convex? What is a mirror’s radius of curvature if cars 20.0 m away appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm h- q q k7d(9pa2 jngxhffzb3+q1igh is placed 20.0 cm from a convex mirror of radius of cuq9(jq2f71fa bn p+qhzg x-d3krvature 20.0 cm.
(a) Show by ray tracing that the image is virtual, and estimate the image distance.    cm
(b) Show that the (negative) image distance can be computed from Eq. 23–2 using a focal length of -10.0cm
(c) Compute the image size, using Eq. 23–3.    mm

  You are standing 3.0 m from a convex security mirror in /xik 0z a *w.f m1ve7v*/umq6jke1fdoa store. You estimate the height of your image to be half of your actual height. Estimate the radius of curva fxamvu1*j.evd f*1zm e6o7/q/ik0 kwture of the mirror.    m

  (a) Where should an object be placed in front of a concave mirror so that it prmpvpnk* xkmc4s*5 s38 oduces an image at the same location aspmv85 sx3m*cps* kn4 k 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 whuavh 6l+t :2 ez4mfy1gen viewed in a curved mirror. The image appears to be 18.0 cm behind th g 4fm uy2haetlv6z:+1e mirror. What kind of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniques,8t+g cveqh*lwoy. /+ rgp4x2y
(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 okr )hkhvw9:t 8f 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, isb71 6h7ph;lgcm1q gk x valid for a convex mirror as long as f is considerg cqlh7;khgx761mbp1 ed negative.

  The magnification of a convex miw c9be.a.h(px0*j vrwrror is $+0.65\times$ for objects 2.2 m from the mirror. What is the focal length of this mirror? $\theta_2$ =    $^{\circ}\,$

  A 4.5-cm-tall object is placed 28 cm in fn;ai mb. j-opfzg);h fqf 2+*front of a spherical mirror. It is desired panj fhfmf;;+).-b 2zgi*f qoto produce a virtual image that is upright and 3.5 cm tall.
(a) What type of mirror should be used?  ----待选择----convex mirrorconcave mirror 
(b) Where is the image located?    cm behind the surface
(c) What is the focal length of the mirror? $f$ =    cm
(d) What is the radius of curvature of the mirror? r =    cm

  A shaving/makeup mirror is designed to magnify your face by a factorqtm( m, b hi*,i6za9cr of 1.33 when your fac9qr(i,hi* mt azc,mb6 e 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 in fb x9eu zd*.t2yvq48 p
(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 ice is 5h mk15w:bwxzgj5 6cr / ae0jd$2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain substance is 89% of its value in water.r6+f hdxsjxza 1 y3tcx(y ,,f4 What is the index of refraction of this substaxyfz+s(6jd 31 xy,ar, f 4chxtnce? n =   

  A flashlight beam strikes the surface of a pa22hhup(jdqh1 pb/6*y2*z mihec1 pw xne 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 ath t3t1+z f7q,xbw;gqy 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 undc*qq1f 09gj,v lt me1perwater spotlight exits the water at an angle of 66*p0g1j vtemq9fc q l,1.0$^{\circ}\,$ to the vertical. At what angle of incidence does it hit the air–water interface from below the surface? $\theta_1$ =    $^{\circ}\,$

  Rays of the Sun are seen to make rzn8 gmg,8 z6kc;(3ag qi kd-ga 31.0$^{\circ}\,$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?    $^{\circ}\,$

  An aquarium filled wmer(5 -qy bh*l+ytp r7ith water has flat glass sides whose index of refraction is 1.52. A beam of light from outside the aquarium strikes the glass at a 43.5° angle to the perpendicular (Fig. Below)*5 b ph(mlyerqt -ry7+. 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 watchma+ug*l9 .fzzp7 j(aalzn 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). Wherz 9j(u+fa pg.la7z zl*e 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 equilater30t; z kdtf+r ;64ducwwv-tgeal 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 s kux ehxe b5t*;md; 0ep((tb)rlab of glass (n = 1.52) and is partially reflected and partially refracted. Find the angle k)ex edm(t; btphe r*u 5;x0b(of incidence if the angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam incident on aje4o/ jar m .+-exmb;)n2sa 9 qicdve* uniform layer of transparent material, as in (Fig. Below), t a2 *.er)acbe+/o mijx-m94j;dvenqs he 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 vvg, alydg vka*7 /3f+n as in (Fig. Below). Show that if the incident angl+vd vaagv/ gl*7, k3yfe $\theta$ 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 qztwo-0n (1hminterface between water and Lucite? To be totally internally reflected, the lighh1 mo(tqw0n -zt must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–air surfaov .xbg4)2d6shzr x/fce 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. Wheelt/m rag : )ictd-ieb tvd:1 yy2+.d:re must it strike the air–water interface, relative to the spot directly above it, in:i -ayb:t d)vdlcem :.dt 1gri2e/+ty order that the light does not exit the water?    cm

  A beam of light is emitted 8 r.7kl5jd dte5w4r+.3zqyfyi .0 cm beneath the surface of a liquid and strikes the surface 7.0 cm from the p ytd.5j7rq4i dy lwz3+ .5ekrfoint directly above the source. If total internal reflection occurs, what can you say about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face of the prism in (Fig. Beloa vi0uqj-fxyqur)du 277+h 4dw) 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 ock,8 ax vx4i1 bya27sbsbb)(qptic fiber as shown in (Fig. Below). Show that we can guarantee total internal reflection at the sideb4 xk7ix y8q (ba 2bc1,svbas) 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 refractionit z8,+ kdz ssvj-sz.1 for a glass or plastic prism to be used in binoculars (Fig. Below) so .jk+ z1-8 ssdszvz,t ithat 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 coc3 wn0i kh.jt:f ;2qehnverging lens. Find the object disf;q:3.whkh i0jcen2t tance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.5 cm * ;nudz0uzo xa*sj:+ s3/buikbehind a lens.
(a) What kind of lens is it?  ----待选择----converging lensdiverging lens 
(b) What is its power in diopters? P =    D

  A certain lens focuses lighs ra.r2cjje(a4icl2uf9e 2/ot from an object 2.75 m away as an image 48.3 cm on the othaialc9e(fesoj/42 2rrj2c .uer side of the lens. What type of lens is it and what is its focal length? Is the image real or virtual?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the power of a 20.5-cm-foca7xy ioq,r13z jtfa i*:l-length lens? P =    D  ----待选择----converging diverging 
(b) What is the focal length of a lens? $f$ =    cm  ----待选择----converging diverging 
(c) Are these lenses converging or diverging?

  A stamp collector uses a convergin// qakjcf/5mng lens with focal length 24 cm to view a stamp 18 cm in front of k/mjfq//n5 acthe 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 high. What are the positih5wyp 8ezfus.7g o3u1on, type, and height of7uwu51p ef83hygozs. 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 camera.d1;o7 a.xen h dd 9d .pg;62wyzs1kinf The maximum distance allowed bn;61k. id9.w2f edndg soza7hdy; 1xpetween 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 factor of 2.5× wyubsj /5al 4n7kw56g dhen a book is placed 8.0 cm uj5dwgy675n / abs4 klbehind 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 fr wge4.if+a7cg s ln.q0om an 8.0-D lens. By how much does the image move if the object ag0f+cq .ewng.s i4l7is 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 2lq9d;l+:mmufh c:1m+m2hua g5 cm should an object be placed to produce a real image which is the same siz2 +umg 9+l;amhl1uhc:dm:mq f e as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an object*z1p/gaqh w7 fq:a, rws)f)5tad xvqn:. y*vy be placed if its imageq : *x))y vapnfa/dta71 fw q:qwszr.,hv *gy5 is 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 an2yg9 r ;d)y7afa8qtn j object be placed if its image is to be magnifi)fgadna7yt yjr98 2 q;ed 2.00× and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm (formed by some other piece of optics).]

  (a) A 2.00-cm-high insect is biwd5 l2it7 rt 3 ejm.h;lj)e;1.20 m from a 135-mm-focal-length lens. Where is the image, erllhe)ji2jdwtt.m7;3 b; i5how high is it, and what type is it?
$d_i$ =    mm (real,behind the lens) $h_1$ =    cm (inverted)
(b) What if $f=-135\mathrm{~mm}$?
$d_i$ =    mm (virtual,in front of the lens)
$h_1$ =    cm (upright)

  How far apart are an objejn ,0fl* c5t pcf64ousct and an image formed by a 75-cm-focal-length converging lens if the image is 2.5× larger than t n4fot0sc*cu6fjp5l ,he object and is real?    m

  A bright object and a viewing screen are separated by a distance casxo0mgo-g r:r(*w /of 66.0 cm. At what location(s) between the object and the screen should a lens of focal ls- ag/0*cgromw(:ox r ength 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 converginggrr g; ;7ro d0uejp6o2p9m::.gyn tub( ozot 4 lenses are placed 16.5 cm apart. An object is placed 36.0 cm in front of one lens. Where will thdn:o490. o2rr :p ggtouu;ogpr zt yj7em ;6b(e final image formed by the second lens be located? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens wit*eb:59 forbzkky5vm . h $f=-31.5\mathrm{~cm}$ is placed 14.0 cm behind a converging lens with $f=20.0\mathrm{~cm.}$ Where will an object at infinity be focused?  ----待选择----realvirtual ,    cm beyond second lens.

  A 31.0-cm-focal-length converging lens is exep r8-sb09 h)4kjor 21.0 cm behind a diverging lens. Parallel light strikes the diverging lens. Af jek4e-p9bo hr0rsx) 8ter passing through the converging lens, the light is again parallel. What is the focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Example 23–12 .xdzdx+nh)1b,6d:er a j,8.shf nld9e s) gwiare now placed only 20.0 cm apart. The object is still 60.0 jr6ghfb) nd1zdxx+s)d8:eh .l 9,w eais .n ,dcm in front of the first lens as in (Fig. Below). In this case, determine
(a) the position of the final image,    cm
(b) the overall magnification.    cm
(c) Sketch the ray diagram for this system.

  Two converging lenses are placed 30.0 cmmkr,l0 *es 2sc 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 a*k2m0e ,lrssc nd 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 cm to the right of y*jru)x cuj0); z 3,lipd2bdha converging lens with a focal length of 18 cm. An object is place )jd p23id)rxl,uy;* jc0bzhud 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 witax9:.l( ojsri.g/nmf3kh+up w:c;xwh focal length 20.0 cm and one diverging with focal length are placed 25.0 chwcj9l wka(x+ .og/ :f3 sm;:p.nxri um apart. An object is placed 60.0 cm in front of the converging lens. Determine
(a) the position    cm to the right of the diverging lens
(b) the magnification of the final image formed.   
(c) Sketch a ray diagram for this system.

A diverging lens is placed i6df8j+arj8a 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 radii of 34.2 cm and 23.8 cm. What vn *x;l+twn+hd,7g,zd 1n kkg is the focal l+ d ,7n;v,1gwhdlnxkz+ ntg*kength if n = 1.52?    cm

  Both surfaces of a double convex len9)j6; cz ;my jgkqyt1hs have radii of 31.0 cm. If the focal length is 28.9 qc9z;k1jgth;6 y m )yjcm, what is the index of refraction of the lens material?    cm

  A planoconcave lens (n=1k rg+-hewvyp5owr 7n:ep*- a- .50) has a focal length of -23.4cm. What is the radius of the concg:r-yn- wwe h k7r*vopp+ 5-eaave surface?    cm

  A Lucite planoconcavexd3 pweie- yt1tk2,y f)w3-cfe c:k9j lens (see Fig. Below) has one flat surface and the other has R = -18.4 cm. What is the ffx-tw 9c, epiktwd2e e-3:cf y 3yj)k1ocal length?    cm

  A symmetric double convex lens with a focal length of 25.0 cm idlbveaz6 q1(n1 rz 31fs to be made from glass with an index of refraction of 1.52. What should be the radius of curvature fo(dn36 zr1 a1 qf1elzbvr each surface?    cm

  A prescription for a corrective lens calls for +1d(v fzj6(.j; vrwo6cp.50D. The lensmaker grinds the lens from a “blank” with n=1.56 and a preformed convex front surface of radius of curvature of 40.0 cm. What should be the radius of curvature of the other surface? z c(j v;wfv6.(6jpord   m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fi dxgvu1k1hu7 4g. Below). You stand 1.5 m away from one of these mirrors and look into it. You will see multiple im1u gdv47 kh1uxages 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 hth-/8 j1 of .7yl z(nuzirwn5filled with water. We measure the wo/5.1z- lj7 thrn(8nhu yfziwidth (x=5.50m) and then note that the bottom edge of the pool is just visible at an angle of 14.0$^{\circ}\,$ above the horizontal as shown in (Fig. Below). Calculate the depth of the pool.    m

  The critical angle of :fi -zd(fk4ma a certain piece of plastic in air is $\theta_{\mathrm{C}}=37.3^\circ.$ What is the critical angle of the same plastic if it is immersed in water?    $^{\circ}\,$

(a) A plane mirror can be considered a limiting case oflf00kuh29zuj jlpq;m4nu) d. a spherical mirror. Specify what this limku znl0h4j.pdu9q)jfl 20um ;it 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 st66;v0)6ig py egzu peo they form 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,b:f opf33 exthw,v,a diverging lens can never form a real image of a real object. Can you ao,v,33w bthfe: fx p,describe a situation in which a diverging lens can form a real image?

  Each student in a physics lab is assigned t5lv dh7l x(sq mo1z2,to find the location where a bright object may be placed in order that a concave mirror with radius of curvature r = 40 cm will produce an image three times the size of the object. Two students complete the assignment at different times using identical equipment, (slvmx hld 2oz,qt1 75but 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 p++s p: n)4qz jz*hmex(qv*vy erism 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 cylindrical *7 apzw m v,umefz.n*9ijj09 tx-c4tvglass 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 lenn13f)m7f bqpfp)( m/ kt:zl.dj6 caul gth $f_1=15\mathrm{~cm},$ 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 aoqdq sc01 g0 byhyyq.j9: walgl r*823 converging lens of focal length f, and a white screen for vieyl8b30.:yacdqws*yr9q0g j q g1l2o h wing 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 projector, the filmoe.1r gvyy :a5 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 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:orey a.y 1gv5 the screen? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (picture size is acyiq ,a 9g 2hlbkps+8u7tually 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 should be used if the 9q+8ih7 ,2agubsp lkyimage is to cover the screen?    cm

Show analytically that the image formed by a converbo d nq9elf57dp*4)rvonp e:e a8p,s1 ging lens is real and inverted if the object is beyfo95qdosr4bnp18 a v d7, enep)lp:e* ond 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 rux0,nhon f na 7(f(1jreporter shooting pictures of her at home. She claims the reporter was trespassing. To prove her point, she gives as evidence the film she seized. Her 1.75-m hejrnhxnfa0 (f 7(,uon1ight 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 thl+k c6c-nl0sa+ni;thq4+ ud /fcjx: ivnji(.e Sun on film used in a camera with
(a) a 28-mm-focal-length lens,    mm
(b) a 50-mm-focal-length lens,    mm
(c) a 135-mm-focal-length lens?    mm
(d) If the 50-mm lens is considered normal for this camera, what relative magnification does each of the other two lenses provide? The Sun has diameter $1.4\times10^6\mathrm{~km},$ and it is $1.5\times10^8\mathrm{~km}$ away.    for the 28 mm lens    for the 135 mm lens.

  (a) An object 34.5 cm in fr9e pdla10w( ns) ,vpnlont of a certain lens is imaged 8.20 cm in front of that lens (on the same side as the obnw()spe0 p9av1,ldln ject). What type of lens is this, and what is its focal length? Is the image real or virtual?    cm (diverging)  ----待选择----virtualreal 
(b) If the image were located, instead, 41.5 cm in front of the lens, what type of lens would it be and what focal length would it have?    cm (converging)

  When an object is placed 60.0 cm from a certain converginhmnb i ts(+ zp;7z--tqrat o1,g lens, it forms a real image. When the object is moved to 40.0 cm from the lens, the image moves 10.0 cm farther from the lenst 1zr,sm7z-at(iht+n ;q po-b . Find the focal length of this lens.    cm