What would be the appearance oftk1zg : dg(f2x the Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fleet in the harbo/*p/rb o9gn1kl0s z x6e swrxd/nt54pr of Syracuse by focusing the rays of the Sunzn96skr/rbng/pe s0 wo*4x5 x l/d1pt with a huge spherical mirror. Is this reasonable?

Although a plane mirror appears to reverse left and right, it doesn’t r t1h(9o;)njxv dgy66(wt xkgieverse up anwg;6jgy9it hxovk td(16x(n) d down. Explain.

If a concave mirror produces a real image, is the image necessar9:yn39v bjy if4fw- vrily inverted? Expv- iw4v f:r3ynjy9 bf9lain.

An object is placed along the principal axis of a spherical mirror. The magnific f:3j*(wgpx7m rc6oio ation of the object is -3.0 Is the image real or virtual, inverted or upright? Is the mirror concave or convex? On whiromx:j7w * 6i f(3gocpch side of the mirror is the image located?

Using the rules for the three rays dj/fqon(r1b vpwn/x8x;8g a -fiscussed with reference to (Fig. Below a), draw ray 2 for (Fig. Bel /g x-af ox1; rbj8np8(fwnqv/ow b).
(a)
(b)

What is the focal length of a plane ma8i,1- mp x.. 7gz-chd jmkifcirror? What is the magnification of a plane mcdjipghcx,-k . 1 fz8i-.7am mirror?

When you look at the Moon’s reflection from a ripply sea, it appears elongate;1 a9slfo+tnz d . Explaols19z;n a+ ftin.

What is the angle of refraction when a light ray meets the boundary betweenvftivj )9+foh31co (c m n7kh5 two materials pe)vf1ft +5kiv(o 3hh7cocjm 9 nrpendicularly?

How might you determine the speed of lqy3 u),u2pqu eight in a solid, rectangular, transparent object?,qu23e u qu)py

When you look down into a swimming pool or a lake, are you likely to underesttoixx/m b,1m1 fgj9 (gimate or ov1b9tm /gmjo1(,xgxi ferestimate its depth? Explain. How does the apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks bent when part of it is under p1s;zduwv)qn3, -mnywater (Fig. zyw3nq ,)dvusm n1; -pBelow).

Your eye looks into an aquarium and views a fish inside. One ray of ligkp j)xodt0/ po *fb20tht that emerges from the tank is shown in (Fig. Below), as well as the apparent position of the fish. oxpk/t0b2)o0dtjf p* In the drawing, indicate the approximate position of the actual fish. Briefly justify your answer.

How can you “see” a round drop of water on a table even though th7xl h zqa)3q*we water is transparent and c)al7*h zqwq3xolorless?

When you look up at an object in air from beneath the 0tm1vabje q5t-) 9fn5 6kpe wbsurface in a swimming pool, does the object appear to be the same size as wh)nqa 61- 0 jbb9ep5 tkfwmt5veen you see it directly in air? Explain.

How can a spherical f.m 7ic)um-uemirror have a negative object distance?

Light rays from star. )ch6 wxop+fkp;ior9z:eo+qhrm48m s (including our Sun) always bend toward the vertical direction as t9i6h p px kwofo;+z.8cr)qeo m4m :+hrhey 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 fdpt4s: kse i j2y4j 8je*i(4lplaced if a camera lens is to make a sharp image of an object very far away?s:42jt(kliye *jd 4j efsp48i

What type of mirror is shown in (Fig. Below,dq xkd8+ -ftqkioo(0)? Explain.

A photographer moves closer to his subje;m1.0 oa;vcimvimt1+d q v2wwct and then refocuses. Does the camera lens cm0mv v.i mq+ ;a11wi;2vwtdo move farther from or closer to the film? Explain.

Can a diverging lens form a real image -s 8gcvn3:40 me xmrimunder any circumstances? Explain.

Use ray diagrams to show that a real image formed by a thin lens is always mkg;xfc( 0 wo8kh3 ;tdn bit4:inverted, whereas a virtual image is always upright i hom:8; kw ;tcgd3btin( f40xkf the object is real.

Light rays are said to be “revo4e t xbhl2u(a:be7u3 u 6l5wqersible.” Is this consistent with the thin lens equation? Et( el qew2b5huba6l : 473xuouxplain.

Can real images be projected on a screen? Can virtual imu: kj1mcby1 :qages? Can either be photographed? Discuss cay:kmbuq cj11 :refully.

A thin converging lens iagn/rve;;np y)udkf8+b7 cuj3gnh 2 2s moved closer to a nearby object. Does the real image formed cg 3g;dy)eb7nnfa2vk;p2r+n8 u hj uc/hange
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material witt8cd 2s1ql6esh an index of refraction n = 1.30 In air, it is a conv sql e68dt21scerging lens. Will it still be a converging lens if placed in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands facing a converging lens. If thee1j4ar6vsz4ylxco9oz17a v - nose and the tail are each focused a9jorvx z1ye 46v1zc7a-ls4 o 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 conv8 ok+x2u4ls 5y;qwgge erging lens. Under what circumstances (ifgxq le5g ;284ysuwo k+ 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 lens have a shorter focal lengu u:( m7oaz*bjjdh42 hth than the diverging lens if the latter’s focal length is to be determined by combining thez7hd4u2a m j(b*ho: ujm?

Explain how you could have a viretnqa rh n1g uj/;:u):tual object.

  An unsymmetrical lenn/kmziqw 7st1ib7 dpr9 ..m;ss (say, planoconvex) forms an image of a nearby object. Does the image poikq it9 midb.77s sm r1p.w/;nznt change if the lens is turned around? ----待选择----yesno 

The thicker a double convex lens -c8/ :t) zwolcokr8w bis in the center as compared to its edges, the shorter its focal length for a given lens diameter8 -: t wwro8bz/lok)cc. Explain.

Consider two converging le hz.08g d sgh4eo,k /8upjl0xgnses 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 produce an image? If so,sh0heo ugl88z. d04xk p,ggj / where? If not, why not?

  Suppose that you want to take a photograph of yourself as you look at yo wl y /hm2mg:rbd3m*pt;fi0y5ur image in a flat mir2gdp mmmlib / y;w5y:hr0t *f3ror 2.5 m away. For what distance should the camera lens be focused?    m

When you look at yourself in a 64wfc(jm-r6 jf 0-cm-tall plane mirror, you see the same amount of your body whether yo- wj46jfrcf m(u 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 ioe3ek 62:kvdrq:nr 5 135$^{\circ}\,$ 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 aboveaq3/ + /8pfr9sjeng (ofzk4nh54wiq u the floor stands 2.20 m in front of a vertical plane mirror whose bottom edge is 43 cm abovq84oe 3 wfqph/r9k u /g4j+zafnn5s(ie 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 areayonl 9wk3qv -j9l-v ym (d9/ip of the mirror is used to reflect the rays entering one eye 3v9y n/9-mji(kodl- qvyw lp 9from 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 mirr0au7d)nuo-ouz2g2(pfu 6vd8jl l u 7g ors meet at an angle $\phi$. a single ray reflected successively from both mirrors is deflected through an angle of $2\phi$ independent of the incident angle. Assume $\phi<90^{\circ}$ and that only two reflections, one from each mirror, take place.

  A solar cooker, really a concave mirror pointed at the Sun, focuses the Sun’s rc-:9tf xa,hvvays 1fh a,-tv v:c9x8.0 cm in front of the mirror. What is the radius of the spherical surface from which the mirror was made?    cm

  How far from a concave mirror (radius 23.0 cm) must an object be placed if i ze8pc9 f0msz8ts image is 908pz8ezs m fcto be at infinity?    cm

  If you look at yourself in a shiny Christmas tree ball with r 9b cjj7aj8(oa diameter of 9.0 cm when your face is 30.0 cm away from it, wherea jj 8(7obcjr9 is your 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 park shows an upright image of any person who stanl1,/co6(bh dxzq* wegds 1.4 m in front (o/w ge6hldzq1*x,bc of it. If the image is three times the person’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror that, when 2.20 ,/: j nfpna2 l)hva9jacm 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 are smaller s*s3m9 ai6s ag 0jjf(ythan they woul3 s9jsga*ms ayf(0ji6d be if the mirror 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 high is placed 20.0 cm from a conv+/d * f0wzk m./vlitseex mirror of radius of cur/idmf*sk+l/t zwev .0vature 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 syq 9)cts ywp).b6 rg.convex security mirror in a store. You estimate the height of your image to be half of your actual height. Estimate the radius of curvaty wc )..qg9styrpsb6) ure of the mirror.    m

  (a) Where should an object be placed in front of a concave mirror so that 0lw.fkf ah7)j +m*rv vit promj)7v*wf.kal0 +r fh vduces an image at the same location 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 ve:vy2t/anm*tj kr34u s ry small 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 radiuyn4*a k/2j3v us:ttrms of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniquen. cm e3zr/g+hs,
(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 suoq *f8-1gbe 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 mirroc3/q xxvr:nbdx5c z9,;j p1ga p5fq0fr equation, Eq. 23–2, is valid for a convex mirror as long as f is considered n rfp9q x 1/fv;cxgcp0aj,b:xn5dzq35 egative.

  The magnification of p vrz hvluufs-p7/zhq301b) .a convex mirror is $+0.65\times$ for objects 2.2 m from the mirror. What is the focal length of this mirror? $\theta_2$ =    $^{\circ}\,$

  A 4.5-cm-tall object is placed 28 cm ir*xu1ya+ 1oj p -da *(tfz1jeroe9u*xn front of a spherical mirror. It is desired t+1oo*xduz9*(-jfee a1a xr ptu*r1yjo 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 mirrorntpaj.ci 7t.u* pnrq ;z33wi7 is designed to magnify your face by a factor of 1.33 when your face is placed 20.0 cm in front nc.pu 3. rqz7tp7t3 ;iawji n*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 inbg - 8la8e3kzd
(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 i7-q nis:8kavh ce is $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain substance is 89% of its valuk*g ,ioeb.yz uflg.b9-kgm(r; n*pz6 e in water. What is the igyzurz.f,gbnbgk;o* k* e6 9 m-ip(.lndex of refraction of this substance? n =   

  A flashlight beam strikes the surface 1qzzfgm.7 t 1w92.uxn jvnm52:vxylt 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 upwar-*pb;(zh/v22o1lcnkjrg xw8 e1 bejd,i.f p nd 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 underwate ot q; e;rd(fmh thfn)k+)(7gsdyr8/er spotlight exits the water at an angle of 66.mr7 +t/) e (fnresdfog;ht8y)dh; qk (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 seeniw7x;/g+e6oz zkts 2+vz+vsm 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 refra61wu8ga48 xcfhgsa4+tll0u - w)aepiction is 1.52. A beam of li-6lgw cs+ u4pi81l xgeaua8t hw0 f)a4ght from outside the aquarium strikes the glass at a 43.5° angle to the perpendicular (Fig. Below). What is the angle of this light ray when it enters
(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 nighthx n9nehr 3.0,ur x3gi, a watchman shines a narrow beam of light from his flashlight, 1.3 m au3 ngr3einx 09hxh ,r.bove 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 beneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equilateral glass prism at a yp)jgv0k amc5u 2oamc4z aa 3 i6aa,(: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 o f8111qkoy hxof glass (n = 1.52) and is partially reflected and partially refracted. Find the angle of incidence if the angle of reflection is twice the angle 1ox1 o1y8fkhq of refraction.    $^{\circ}\,$

Prove in general that for a light beam incidenj l-8h4ch1upwz5e2pm9rht jmy7+b qsa)70r y t 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 inciden 4y )jh7q 8we7hbputl9 5rhasp0czy m2rm+1j-t angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on a flat piece of glass with index of refra)rjnh t.)omnz87l lg. ction n as izn 7on)r. lmg lj8h.t)n (Fig. Below). Show 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 critical1 qi9g c0ty3zl angle for the interface between water and Lucite? To be totally internally reflected, the liz1 tcyqig9l 03ght must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–air surface 7 1l-yxp9:s(s /w u2upxhjxtcis 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in a po nqqx k ,disu231yevfg8u3)f5 ol of water from a depth of 62.0 cm. Where must it strike the air–water interface, relative to the spot direct,fdqyg8vu53sn ) q1iu3ex2f kly 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 akv7w ccb-)jxsl mvpb3z * h3qa6 5:t21n1r xfp liquid and strikes the surface 7.0 cm from the point directly above the source. If total internal reflectionb-tlbchx cv)j2pvsaz5 nm1q3x3k 16rf:* 7 pw 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 gfk,ev;m rf85(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 aq1pwc0bnt o .6qm56lqn1l .vl*g-q eqs shown in (Fig. Below). Show that we can guarantee total internal reflection at the side eb5l 0q6.twcg qnomvq6-pql1. n*q1lsurface of the material (at point a), if the index of refraction is greater than about 1.42. In other words, regardless of the angle the light beam reflects back into the material at point a.

  (a) What is the minimum index of refraction for a glass or plastic priqh xqfqkg7, ug-.0e.osm to be used in binoculars (Fig. Below) so that total internal reflection occurs at khxg q.f7-goqq0e,u. 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 convergingx(m;xo 0 jzd6i95z bq4ffhdj7 lens. Fi4h;569 b(mzjxziff 0jx ddoq7nd the object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.5 col*t2yyyh8q (wb/bj 8m behind a lens.
(a) What kind of lens is it?  ----待选择----converging lensdiverging lens 
(b) What is its power in diopters? P =    D

  A certain lens focuses light from an object 2.75 7 wt7kdoq ;b*yc 4g98 :uysdaxm away as an image 48.3 cm on the other side of the lens. What type of lens is it and what is its :g7t97dd*c a xyk4wbq 8so;u yfocal 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-length lrq*8u qw,v9sr ens? 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 conv rwg n5j6-7fyw +qm+ondq63o t+anz) ierging lens with focal length 24 cm to view a stamp 18 6qwgda3o+qom fj tnnr6+5in)7 -+ywz cm in front of the lens.
(a) Where is the image located?    cm behind the lens (virtual)
(b) What is the magnification? m =   

  A -5.5-D lens is held 14.0 cm from an object 4.0 mm high. What are the po5,wa*s(p a av z2 v0bquhe oq.9wpyt7js7xn60sition, type, and height of2v9asy5(vp q * 7axeozth 0j.,s q6bu70nwpaw 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 89q p6 c7xchh.zwkpi-8dpd p,a camera. The maximum distance allowed be 6,x.ppi8q9-zpd7hkw chd8pctween 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 nzg; 8*rexpx00cfe 0 kreading material by a factor of 2.5× when a book is placed 8.0 cm behink0fc8z xgpe0r nx0;*ed a lens.
(a) Draw a ray diagram and describe the type of image this would be.  ----待选择----realvirtual 
(b) What type of lens is needed?  ----待选择----converging lensdiverging lens 
(c) What is the power of the lens in diopters? P =    D

  An object is located 1.5 m from an 8.0-D lens. By howpfk+savx ax z,. ml3za,sm-02 much does the image move if the objemsxmk zl-3zvp2x,a0a a,.s f +ct 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 od(k1gae8ai7 t/n1a bp f 25 cm should an object be placed to produce a real im te1g8/aa dni7b1a(kpage which is the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens7z, . ulldo7vg must an object be placed if its image is to be magnified 2.z uodg, vl7.l700× 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-fojjzkhhj);)6wuu gw8fdcr8 ; 3 cal-length lens must an object be placed if its ima jhdg );fu;h)jw6wcrj88 zk3u ge is to be magnified 2.00× and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm (formed by some other piece of optics).]

  (a) A 2.00-cm-high insect is 1.20 m from a 6bnd pv-1(1xh: wikim135-mm-focal-length lens. Where is the image, how high is it, and whvxm1di1p-n:(6 hwibkat 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-cm-focal-len3g hu 8 a:mltgdfx1l-7gth converging lens if the image is 2.5× larger than the obj3a 17m ug8fhldlt: -xgect and is real?    m

  A bright object and a viewiz9vbtz29 ql c a)y9ad.ng screen are separated by a distance of 66.0 cm. At what location(s) between the object and the screen should a lens of focal length 12.5 cm be placed in order to produce a crisp image on the screen? [Hint: first draw a diagram.] lens should .tq9dl2a z)zay9bcv9be placed    cm or    cm from the object

  Two 28.0-cm-focal-length converging lenses are placed 16.5 cm apart. An objecty* 13,suzzmt dm9o)lg is placed 36.0 cm in front of one lens. Where will the final image formed by the second lens be located? Wumz1myl t*z3 )dg,so 9hat is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens with w 1je gbc zrn(9zqrqdr1mbi:)55 4k (x$f=-31.5\mathrm{~cm}$ 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 diverging lens. ; hom acu.sy2pvk)4*j7 gte5tParallel light strikes the diverging lens. After passing through the converging lens, the light is again parallel. Wha*ptth k5)y .2s;amcu j4gov7et is the focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Example 23–12 are now placed only 20:ps7d ka4 -npi.0 cm apart. The object is stppnk:7 is-ad4ill 60.0 cm in front of the first lens as in (Fig. Below). In this case, determine
(a) the position of the final image,    cm
(b) the overall magnification.    cm
(c) Sketch the ray diagram for this system.

  Two converging lenses :il 1a) -;w o5d,2thvmfuip ezare placed 30.0 cm apart. The focal length of the lens on the right is 20.0 cm, and the focal length of the lens on the left is 15.0 cm. An object is placed to the left of the 15.0-cm-focal-length lens. A final image from both lenses is inverted and located halfway betwee uzh l ;5oaep,wi2-1it:d)fv mn 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 focalz(eamt ng z;57 length of is placed 12 cm to the right of a converging lens with a focal length of 18 cm. An object is placed 33 cm to th5(z ;gmte7nza e left of the converging lens.
(a) Where will the final image be located?    cm to the left of the converging lens
(b) Where will the image be if the diverging lens is 38 cm from the converging lens?    cm to the right of the diverging lens

  Two lenses, one converging with focal length 20.0 cm and one diverging with f,m*xos vkrv1xpoj9z +fnh95 c)/ hw-local length are placed 25.0 cm apart. An object is placed 60.0 cm in front of the converging le519 +* ms-fp cvk,w9o r hnhx)xvjz/olns. 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 placb sv:(bdbsjo09h5* k fed 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 is the focah qcm;-6o(xnjym9s e0 l length if n = 1.(q xsmm n;60o-yjc9 eh52?    cm

  Both surfaces of a double convex lens have v+ig(5tc swi/ radii of 31.0 cm. If the focal length is 28.9 cm, what is thecs +g 5witv(/i index of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm. What is the rau a:582espd(p6m yj sadius of the concave surfac 8 d(aeu5:amjyspp6s2e?    cm

  A Lucite planoconcave lens (seam z*7r0ls,7k 3wscg9ahqsk, e Fig. Below) has one flat surface and the other has R = -18.4 cm. Whrkwl, ss0ag3 7a q,smh z79*kcat is the focal length?    cm

  A symmetric double convex lens with a focal length of 25.0 cm is toyq 2ze/b 6blxiz3 :qw7 be made from glass with an index of refraction of 1.52. x2qz7/l ieqwy 3bb:6zWhat should be the radius of curvature for each surface?    cm

  A prescription for a corrective lens calls for +1.50D. The lensma15n ) dipg3gbpj d9+i7 ujdfa*ker 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 curvap da3uj7gi1i5d)njd f9p b+*gture of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart aspb4 8sfd3d 4wh in (Fig. Below). You stand 1.5 m away from one of thesp w4 bddf3h8s4e mirrors and look into it. You will see multiple images of yourself.
(a) How far away from you are the first three images in the mirror in front of you?
$d_1$ =    m
$d_2$ =    m
$d_3$ =    m
(b) Are these first three images facing toward you or away from you?
the first image is facing  ----待选择----toward youaway from you ;
the second image is facing  ----待选择----toward youaway from you ;
the third image is facing  ----待选择----toward youaway from you .

  We wish to determine the depth o,gf-rovh l*b2s0f pq2 f a swimming pool filled with water. We measure the width (x=5.50m) and then note that the bottom edge of the pool isq2s rg,fhb*2l-pf 0vo 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 certait*zgcpa 8/0in5))u xdi mewcad3;f6 i n 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 casqzx , 60 me-)hd rffo6n6n9deyfbb-s .e of a spherical mirror. Specify what thb6fnx0b,e.9 -dryos-6 )fmnqfe6dhzis limit is.
(b) Determine an equation that relates the image and object distances in this limit of a plane mirror.
(c) Determine the magnification of a plane mirror in this same limit.
(d) Are your results in parts (b) and (c) consistent with the discussion of Section 23–2 on plane mirrors?

Stand up two plane mirrswbq, ,czbu21k-eiq 5ors so 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 diverg*u 89m4genw *gr:uzgxw yzy8*ing lens can never form a real image of a real object. Can you describe a situation i *g*genuz*9mz 8wrygx4u wy8:n which a diverging lens can form a real image?

  Each student in a physics lab is asbemgs a 554 tmwf( nss:j0nb6:signed to find the location where a bright object may be placed in order that a concave mirror with radius of curvature r = 40 cm will produce an image three times the size of the object. Two students complete the assignment at different times using identical equipment, but when they compare notes later, they discover that their answers ft0:bss g:majws f 5n6n5meb(4or 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 a2y2c- tk-au5qi11 oecb nd8as prism is $\phi=72^\circ$ see (Fig. Below), what is the minimum incident angle for a ray if it is to emerge from the opposite side (i.e., not be totally internally reflected), given $\mathrm{n=1.50~?}$ $\theta_1$$\geq$    $^{\circ}\,$

The end faces of a cylin0 pn +cwdui61wdrical 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 j2 kisz e bozayf +5r0+)8x5kocm in front of a converging lens of focal length $f_1=15\mathrm{~cm},$ which in turn is 55 cm in front of another converging lens of focal length $f_1=15\mathrm{~cm},$ (see Fig. Below).
(a) Draw a ray diagram and estimate the location and the relative size of the final image.
(b) Calculate the position and relative size of the final image.

A bright object is placed on one side of a converging lens of foc4,fkto l+:98 z3 zohtr* k0*ueymtk aial length f, and a white screen for viewing the image is on the 4* tokt, u ya0*i hrz8zmkot9+f:3lekopposite side. The distance $d_T=d_i+d_o$ between the object and the screen is kept fixed, but the lens can be moved.
(a) Show that if $d_{\mathrm{T}}>4f,$ there will be two positions where the lens can be placed and a sharp image will be produced on the screen.$d_T$>4$f$
(b) If $d_{\mathrm{T}}>4f,$ show that there will be no lens position where a sharp image is formed.
(c) Determine a formula for the distance between the two lens positions in part (a), and the ratio of the image sizes.

  In a slide or movie projector, the film actdmxsw,w/s)bjd ,wp50hflg y)3cas ,8 s 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, ho ,pghm)s30 yx) ,d , cwa/lww8sbsjdf5w 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) ives-kt*b5/fehu 6 (ass to be projected on a screen 1.80 m bbfs/s6he5vk*et (au -y 2.70 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 ths/q;yu; /jwk1f xmhxj-4 h j1bat the image formed by a converging lens is real and inverted if the object is beyonb1/yuwq14 -x;s jk jmf/hhx;j d 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 herca** /(df vwve at home. She 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 lengthf( d wc*evav*/ 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 ax 56zr,v:xwjfilm 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 imaged 8.20 cm in front of , 1da9mhjt sk2f wwtw/ l3c39gm1 cy+tthat lens (on the same side as the object). What type of lens is this, and what is its focal length? Is the image real or virtuc wgt3c w ya9k9j12lt13w,+sh mft /dmal?    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)