What would be the apkx. 6o c wyrg *2tpzrr8g(tuu)yh6; y(pearance of the Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Romamx- n /0vfrv-*qte1fx . ve+x fuhg)6an fleet in the harbor of Syracuse by focusing the raysvt*vx a-6gxrnh1 mxfqe/ve-f.+ ) uf0 of the Sun with a huge spherical mirror. Is this reasonable?

Although a plane mirror ( bpph0mszb mwwwq9q5ec; ,v +k4,ye;appears to reverse left and right, it doesn’t reverse upvhkb;5m,;4ew 9s(,c eww0 y qqpzmb+p and down. Explain.

If a concave mirror produces a real image, is the image necessarilym:1 yvfuk26 2udltd -c6c g.poco(ll 9 inverted? Exdcdc9yg :2lv t 6 2pol kc6f.-m1uluo(plain.

An object is placed along the principal axx .jf(3zz6 k 5pvxmd0hplmr)7 is of a spherical mirror. The magnification of the object is -3.0 Is the image real or virtual, inverted or upright? Is the mirror concave or convex? On 6 d3j(7hpz5mx zxrp)vkm0 f .lwhich side of the mirror is the image located?

Using the rules for the three rays discussed with 0,qs) h*l0 japf8me ycw(w3urreference to (Fig. Below a), draw reh * ( cwwm03p,0r 8s)fluayqjay 2 for (Fig. Below b).
(a)
(b)

What is the focal length of a plane mirror? What is the magnific1g j w;mded;pev h*2d*ation of a plane mirrord;*;w1 jgdee dv hp*m2?

When you look at the Moon’s reflection from a ripply sea, it appears elon+b80nbrty/n 9h 3tfnc:h)sg hgated . Explai9 tbn:tcb8+0 yn hs nh/3f)ghrn.

What is the angle of refractionr ;0eox,v 6t:z w+h2*tsufv dg when a light ray meets the boundary between two materials pevhf z +t*6ts0dxv,we;og: ru2rpendicularly?

How might you determine the speed of light in a solid, rectangular, trandv7 t :lb0ar7ssparent object?tbs :7vd0r 7la

When you look down into a swimming pool or a lake, are you likely to unde 2rwl7r 0gw+;ba0n eqerestimate or overestimate its depth? Explain. How does 0b w; l7a+ergenrwq20 the apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why zg:71w/v ftpzac34ydu+rv:ca stick looks bent when part of it is under water (Fig. Be74 p+z c3dcftvg /:rvz:1yauwlow).

Your eye looks into an aquarium and views a fish inside. Onkay ;f dwt n ;k*voph*pu:.,+tt yb6.3vyxg,ne 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 approximu;aokpyxn ,6t f3tn.hg,:pb;vwy*dt k.+ v y*ate position of the actual fish. Briefly justify your answer.

How can you “see” a round drop of w i3s(.fc z sw148s,sq;x -zqqmrlma j2ater on a table even though the water is transpa.;1qrmcsj 2 isx(wlf s8sma,4-3 zzqq rent and colorless?

When you look up at an object in air from benea3 h-b.5gmj 4ovvzco,c:6c kg c( suud.th the surface in a swimming pool, does the object appear to be the saoz jsucm:h k( bo.vgdgcv.u-346c 5,cme size as when you see it directly in air? Explain.

How can a spherical mirror have a5z kufjr91gutvl( 9y o d3 iw5uk/-: d,9kiwra negative object distance?

Light rays from stars (including our Sun) always bend toward the verti5 prq i*zwu7m3cal directurwp5 * 3mi7zqion as they pass through the Earth’s atmosphere.
(a) Why does this make sense?
(b) What can you conclude about the apparent positions of stars as viewed from Earth?

Where must the film be +.ml bb, -myq ol;tj,eplaced if a camera lens is to make a sharp image of an object very far awaytq -l,mj;l oym ,+b.be?

What type of mirror is shown in (Fig. hakej70e( el ;;j4f4zn.ba zfBelow)? Explain.

A photographer moves closer to his subject and then refocuk6u; gwt+ ne6vkx(j6gc ua9), gna7h fses. Does the camera le9;agkk,gau(6vufnxt h 6j) 7 ceg6w+nns move farther from or closer to the film? Explain.

Can a diverging lens form a re3si vz3frd(-;(jz gqaa kb31wp c9ut6al image under any circumstances? Explain.

Use ray diagrams to show that a real image formed by a thin lens is always inrxo 6h.n,i6 chverted,ci ,onhh.xr66 whereas a virtual image is always upright if the object is real.

Light rays are said to be “reversible.” Isj 8dz9;--fdo wx,.o xff zph-s this consistent with the thin lens equafofj zd,d-.-z;w-9oh 8sfxxption? Explain.

Can real images be projected on a y 4jtt)b6osj *screen? Can virtual images? Can either be photograp*ybj)t4 st6j ohed? Discuss carefully.

A thin converging lens is moved closer to adx4 e6us +zq6tmsi(m/1sk 1up nearby object. Does the real image formed change +p6 i4ksmsu(u/1 6e ds 1zqxmt
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of refraction n = 1.30 In kdnxeiw.-) g3air, it is a converging lens. Willd.) g-xki enw3 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 r38zn yf9mm3r stands facing a converging lens. If the nose and th9y8m3fn r 3rzme tail are each focused on a screen in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail ini k ;* dbs)8ktr-mw/p4cu oh7x the air stands facing a converging lens. Under what circumstances (if any) would the image of the nose be virtual and the image of the tail be real? Where would the image of the rest of the cbp)u;*wtk78ohdx 4msc/ -ki r at be?

Why, in Example 13, must the converging lens ha 1wuv w/ 5(zpj2puph6gve a shorter focal length than the diverging lens if the latter’s focal length is to be determined by combini1j2/pgp( zuhw56 wvp ung them?

Explain how you could have a v(e;oq d7 o-vsyirtual object.

  An unsymmetrical lens (say, planoconvex) forfqfrtc17r,c /ms an image of a nearby object. Does the image po1cfr,c q7 rf/tint change if the lens is turned around? ----待选择----yesno 

The thicker a double convex lens is in the center as compared to its edges, ipkpd+b)b( cc 3l/h5bthe shorter its focal length for a given lens diam/bb+cp5 b(clk pd)ih3 eter. Explain.

Consider two converging lenses separatedf8*mnn iov3 m)uq; a.u,clk2x by some distance. An object is placed so that the image from 2xa i)mnqukm*c ;u l.8vn3 ,ofthe 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 yo:5i ;j fogc*xnq, 2jfyu look at your image in a flat mirror 2.5 m away. For xq*;og5 cffyjji,2 :nwhat distance should the camera lens be focused?    m

When you look at yourself in a 60-cm-tall pl1t3 u-s nffsc yzb9sl+ p:vv5,ane mirror, you see the same amount of your body wheth9by-nf:z sfpvsc3,s 5v tlu+ 1er 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 135zk kl7etda:2 ky69m4 l ,x(edq$^{\circ}\,$ 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 verti1 zda: /rcxeb e.j*9w(cp(mrdx)2koj cal plane mirror whose bottom edge is 43 cm above the floor, (Fig. Below). What is the horizontal distance x to the base of the wall supporting the mirror of the nearest point on the floor that can b *1ex rjc)mb :.a e/jow(xkzp(d92rd ce seen reflected in the mirror?    cm

  Suppose you are 90 cm from a plane mirror. What area of the mirror is uhomo5l- jvh7i z+3 7ydsed to reflect the rays entering3- vho l j5y+77ziohmd one 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 at an e3/ / etfpi;:9cg*)dijv ggxwangle $\phi$. 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 mirs *+nx7 (-8q 7fwenr6yks yi()k(bv agbzd:raror 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 was made? -+nyv r(s*ea 7z(db() k6gri y:fawsk x87 nqb   cm

  How far from a concave mirror (radius 23.0 cm) must an object be7tqnj4nr7i ; +hu /.bt )fhgxe placed if its image is to be at in4 u)7x.r nnq7egbfih j th+/;tfinity?    cm

  If you look at yourself in a shinc hbxvk893 2cj+n/,fdguv ms5y Christmas tree ball with a diameter of 9.0 cm when your face is 30.0 cm away from it, where is yourmb9gf vx/ vdcnj+h8s 2k,5uc3 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 s*brau o /+rsr/)q2gg1 rw:ghui -;qug tands 1.4 m in front of it. If the image is three times the person’s height, wh;hs-gguuqg+ru1/2b *:r)ag o rrwi/qat is the radius of curvature?    cm

  A dentist wants a small mirror that, when 2.20 cmn;0wzgfil 5f*h2lb 0i 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 bre: zts(6 gq7iehind you that are smaller than they would be if the mirror wges t i7:z(rq6ere 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 3.05bj n.y0yvyo 9f5 id;t mm high is placed 20.0 cm from a convex mirror of radius ofy5njt b0f.5dvo;yi y9 curvature 20.0 cm.
(a) Show by ray tracing that the image is virtual, and estimate the image distance.    cm
(b) Show that the (negative) image distance can be computed from Eq. 23–2 using a focal length of -10.0cm
(c) Compute the image size, using Eq. 23–3.    mm

  You are standing 3.0 m from a convex security mirror in a store. Yqkk+ )r ni1)g :km9da83l xovjou estimate the height of your image to be half of your actual height. Estimate the radius ofqdilkgka+o: )vjx r83 k 1n)9m curvature of the mirror.    m

  (a) Where should an object be placed in front of a concave mirror so tha oyq :e7uqk+xg3d5)1b2asnmat it produces an image at the same location as the object? :e1mobq53+ua gs 2xqydna) 7k
(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 ve36lcne m 0/y ugxzi-1ury small when viewed in a curved mirror. The image appears to be 1gyle 3c mu1i-6xuz0/n8.0 cm behind the mirror. What kind of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniqueooegv;ow8-u)56 s jlts,
(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 magnifgbv (o: ygew43e.p-weiw- 4 ikication m of a convex mirror is $m=-d_\mathrm{i}/d_\mathrm{o},$ just as for a concave mirror. [Hint: consider a ray from the top of the object that reflects at the center of the mirror.]

Use ray diagrams to show that the mirror equ1 kf tem.c((av/0yfuu+1 qfmwation, Eq. 23–2, is valid for a convex mirror as long as ft+fau cmyev.0/fuk1mf(1w q( is considered negative.

  The magnification of ak*/h,.pkaq k(kbjyb 0icptd9)p 0bh 1 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 in front of a spherical mirror.:eym wa sm2m5 :)ai3he It is desired to produce a vir3we 2y)ms:hma 5mai: etual 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 mlx1qd x+ /. e4vdmplt7agnify your face by a factor of 1.33 when your facx/4epmqtxdd. v 71l+le 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. qs 79lfl3rxy in
(a) crown glass,    $ \times10^{8 }\;m/s$
(b) Lucite,    $ \times10^{8 }\;m/s$
(c) ethyl alcohol?    $ \times10^{8 }\;m/s$

  The speed of light in g76 v3lculma+qz+jywb7 z5j d9zj*;rice 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 value in water. What is 3.th o a (v 6x(aq-zj+-iyzmkdthe index of refrac t6.xzhzvd jy-3kq(ia a+(mo-tion of this substance? n =   

  A flashlight beam strikes the surface of a pane d.iz ;uyore m/krl7 ))p4ny8n 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 fromlyw0xo2x0xf bf9-+ cg 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 spm bq ,hj17i*6dcf96wnkp t d-dotlight exits the water at an angle of 7 fqi* d1 6-hdpjc,bdtn69kwm 66.0$^{\circ}\,$ 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 toq:z(g99a opaznjxf + r7x+mw1 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/fs be 6;uyyss4+2tp b whose index of refraction is 1.52. A beam of light from outside the aquarium strikes t6s+buys fp 4s;2tb/ eyhe 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 bottgsip :o8/:z xq w68ymeom of a pool at night, a watchman shines a narrow beam of light from his flashlight, 1.3 m above the water level, onto the surface of the water at a point 2.7 m from the edge of the pool (Fig. Below). Where does the spot of light hit the bottom of the pool, measured from the wall beneath his foot, if thewoxgem:6y s 8/:z8q pi pool is 2.1 m deep?    m

  Light is incident on an equilateral glass prism at(lg8 2rjbrrbn j1jz 9nnd42v 2 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 l)g bro/+o28h+ l t6ccqj)hptslab of glass (n = 1.52) and is partially reflected and partially refracted. Find thc2+tc)+)gjq lolp8t6h br ho/ e angle of incidence if the angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beamidv 6( (ts-gmu+-n qqom)s y4p incident on a uniform layer of transparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the incident beamp(oid gt4un(+q -s6m ) s-qvmy, 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 *skau 1eveam30n 7nv +refraction n as in (*avv7nua n + 0sm1ek3eFig. 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 critical angle k0xnb (doaad 3aj663zfor the interface between water and Lucite? To be totally internally reflected, the light must start in which aj(6 0kxzo abd a6d3n3material?
$\theta$ =    $^{\circ}\,$
 ----待选择----waterLucite 

  The critical angle for a certain liquid–xs/sx6b xen8 k)jdhplsk 2sj m(r,d+j/h*x 0(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 /lk cpxj7 ud*je 20h/qpool of water from a depth of 62.0 cm. Where must it strike the air–water interface, rekj/u7d*jp /eq0x2cl h lative to the spot directly above it, in order that the light does not exit the water?    cm

  A beam of light is emitted 8.0 cm beneath tofb/v4hqy+fud2et ,g9vlr6 pj ;g/+qx84q obhe surface of a liquid and strikes the surface 7.0 cm from the point directly above the source. x ,y4b/v 6oo9beqpht gjrqf+ f v gl+qu/4d8;2If 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. Belowqkli5q8fmx *b u*+jg3( 5c pac) 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 shownea+d/ny j+ .gl 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 the light beamyed+l .nga/ j+ reflects back into the material at point a.

  (a) What is the minimum in.4el9 7+9fprz pazjgndex of refraction for a glass or plastic prism to be used in binoculars (Fig. Below) so that total internal reflection occurs at n p7jp49f ezl.z gr9a+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 converging lt 2c 8bvz+*fjiens. Find t+2v f 8jtcb*izhe object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.5 cm bdtz m92zv *cu3ehind 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 o1 o,rfo:ergy9 fl8r2ljqyqr z 3y( 6i+bject 2.75 m away as an image 48.3 cm on the o i,3 g1ryl 26qo8fr9r oq+ yrezljy(f:ther 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-focal-length lens? P pajhql* d1, 8bulafl 7i7in7: =    D  ----待选择----converging diverging 
(b) What is the focal length of a lens? $f$ =    cm  ----待选择----converging diverging 
(c) Are these lenses converging or diverging?

  A stamp collector uses a converging lens with focal lengthgd b9jqmz i1d16 4l2zy*d.jdlaeh g95 24 cm to view a stamp 18 cm in front ogdm1ja6jhb.edqi54 l* gd1z 9zdl 29yf 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 hels00x5z0 t*zcx ot2nv hd 14.0 cm from an object 4.0 mm high. What are the position, type, and heightxczh 0ntov5 stx 00z*2 of the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to focus an image ong1b,d og)sfo*rx f39s0k+jj z the film of a camera. The maximum distance allowed between t ogxdrsj)9z,o sj b03f1*fk +ghe 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× when a book is emnkva63 2kcnid4;xwx v:4j 0rtq/whu+d44xplaced 8.0 cm behind a lens. 44;vq/:ekxi4dxwx4vk c 6r mhnt+2dw3 j0una
(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.i8qx q sg+ oce7p/p7xy3wo- e45 m from an 8.0-D lens. By how much does the image move if the object is +q-87ox347si gxpew opcye/qmoved
(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 4c9qppw/qa8hobject be placed to produce a real image which is the same size as the ob4c q8pa/pw qh9ject?    cm

  (a) How far from a 50.0-mm-focal-length lens mlkl ;n2wf //aeuia v6;ust an object be placed if its image is to be magnified ;/k v/e all6f uia;nw22.00× 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 mumx tvr+4gb00,84h 6b zjc8i 5briwmm;-rjbsv st an object be placed if its image is to be magnified 2-b v b;5,irt mxi wg hcjmrmz4 6bvrs480+0jb8.00× 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 135-mm-focal-length l yk1vx9g- 5eop1e dt*xens. Where is the image, how high is it, and what type is it? gk *xo xeyv1p1 5-t9ed
$d_i$ =    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-foc d0htbp *(5nijal-length converging lens if the image is 2.5× larger than the object p 5htjbi(*0n dand is real?    m

  A bright object and a viewing screen are separated by a distance of 66.0 cm. Atwg- tz 69 2deyv2iv)rm 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 screetv9d22)6vz-wyg ire mn? [Hint: first draw a diagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-lenrtr,5jr4eqw 6 gth converging lenses are placed 16.5 cm apart. An object is placed 64q wrjr 5re,t36.0 cm in front of one lens. Where will the 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 with f ry3 ,7xo t,g7v;xeqhlbp4b2 $f=-31.5\mathrm{~cm}$ 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 2y)ir3dc hqa/u7d2; x of h*od91.0 cm behind a diverging lens. Parallel light strikes the dii/)c9yhx fo;7d urdaohd *32qverging lens. After 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 le 0*:j 7osp-xx)lkvzgo.d t4 gh;meqoj(mi04onses of Example 23–12 are now placed only 20.0 cm apart. The object is still 60.0 cm in front of the first lens aogz 4mxk;: ot0d74 .q)iogjxlo *v (-0hmspjes in (Fig. Below). In this case, determine
(a) the position of the final image,    cm
(b) the overall magnification.    cm
(c) Sketch the ray diagram for this system.

  Two converging lenses are placed 30.0 cm apa ajgx+g a6 2km/2kmvc-rt. The focal length of the lens on the right is 20.0 cm, and the focal length of the leagk2/xk gv mamj+ c2-6ns 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 left of the 15.0-cm-focal-length lens is the original object?    cm

  A diverging lens with a foc/ef4 w9o7q, dyy .crsbal 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 the left ,4qs. yywof9 crbed /7of 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 q/yf 41gbt3 sz,vw, dsone diverging with focal length/gsf,v,dsyt b4wz31 q are placed 25.0 cm 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 placju 253kbym 1wt zl.:oued 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 d55g8xh ew z:z 7v/w*zf9oqtq focal length if n = 1.52? 7 tw 5wog/zd *q9fzx8z5:qh ve    cm

  Both surfaces of a double convex lens xko he26zeskyt4*w9 - have radii of 31.0 cm. If the focal length is 28.9 cm, what iz -et*o s62khkw9x y4es the index of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm. What is the rad s0p knwy88qwr/ np/ 39kq8cckr+pk8y ius opk8y/w/kr r88 +nc9ppyk8k wqcq0 n3sf the concave surface?    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat surface and t8 g8yqkc,q4zuzpu 713 uul0cehe other has R = -18.4 cm. What is the focal lengt u 3z470zeuc l8,y1cqqukg8uph?    cm

  A symmetric double convex lens with a forjfv3 dql3.gw,* b(hzcal length of 25.0 cm is to be made from glass with an index of refraction of 1.52.d* fq(wrv3hjglz b3,. What should be the radius of curvature for each surface?    cm

  A prescription for a corrective lens calls for 2jxm/ks4auo onn7/m. +1.50D. The lensmaker grinds the lens from a “blank” with n=1.56 and a preformed convex front surface of radius of curvature of 40.0 cm. What should be the radius of curvature of the other suro4 ua/s.kmm2no/ n xj7face?    m (convex)

  Two plane mirrors face e 4n qg.9auwm0z7jh*, vlgctm2ach other 2.0 m apart as in (Fig. Below). You stand 1.5 m away from one of these mirrors and look into it. You will see multiple 9c 4 al2vt.uj0m,g z w7*qhmgnimages 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 (o jwks39 wnvv,gh59yfilled with water. We measure the width (x=5.50m) and then note that the bottom edge of the pool is just visible at an a, 3 gkhw(yj ws9onv9v5ngle 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 o/:f4tw hip*pif: 5dvwyj, r7l f 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 limitipt6e* bzflwxn2/c 9k-6 nh3.geri i 8fng case of a spherical mirror. Specify wcw82rb 3-n. n9ehge ip/6l* fit6xfkzhat this limit is.
(b) Determine an equation that relates the image and object distances in this limit of a plane mirror.
(c) Determine the magnification of a plane mirror in this same limit.
(d) Are your results in parts (b) and (c) consistent with the discussion of Section 23–2 on plane mirrors?

Stand up two plane mirs7qb /u zggw15:w ian-z4n6yxrors 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 diverging lens cwjdl/gp8pk)7yuh8 9u)k y eg,an never form a real image of a real object. Can you describe a situation in which apk/y8p8 7,gul) uk hgj w9de)y diverging lens can form a real image?

  Each student in a physics lab is assigned to find the location where a brigv*npj+nb-lmj; 8z x/aw;4 ljcht 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 need to repea v-zjn w c+m8 l/nxa*;bj;lpj4t the lab, and justify your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of a prism y z(v1w0elr28m0t (vuysj, zmis $\phi=72^\circ$ 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 glass rodkta547* ahpli $(n=1.54)$ 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 placf++k bv*: mmrj - 5dhrui-;blted 33 cm 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 j8k;iysz- fvy6.and52c0 mjk one side of a converging lens of focal length f, and a white screen for viewing the image is on the opposite side. The ds6cma0z52j jv kn iyf.-d;8ykistance $d_T=d_i+d_o$ between the object and the screen is kept fixed, but the lens can be moved.
(a) Show that if $d_{\mathrm{T}}>4f,$ there will be two positions where the lens can be placed and a sharp image will be produced on the screen.$d_T$>4$f$
(b) If $d_{\mathrm{T}}>4f,$ show that there will be no lens position where a sharp image is formed.
(c) Determine a formula for the distance between the two lens positions in part (a), and the ratio of the image sizes.

  In a slide or movie projector, the film acts as the object who:-d 5a ya)wb(la4wy8 s;tbi pnse 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 biswadl- ;5pay y)4w(8n:btathe 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 s4y;h-;*s3tv i+l wxnipmus; to be projected on a screen 1.80 m by 2.70 m placed 7.50 mt x*;sm3 vh;w; +up4iinslys- from the projector. What focal-length lens should be used if the image is to cover the screen?    cm

Show analytically that the image formed by a cr)orjny l6ho181 f pl5+kre 5je34d mdonverging lens is real and inverted if the object is beyondl4+l j rmo8k136 hj) edef51ydrp5orn 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 1mszuhvpy2 /(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 fil1 yshpmvz/ (2um, 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 imagw*mq)e9 ztay )j n9fjooy,-8ge of the Sun on film used in a camera with
(a) a 28-mm-focal-length lens,    mm
(b) a 50-mm-focal-length lens,    mm
(c) a 135-mm-focal-length lens?    mm
(d) If the 50-mm lens is considered normal for this camera, what relative magnification does each of the other two lenses provide? The Sun has diameter $1.4\times10^6\mathrm{~km},$ and it is $1.5\times10^8\mathrm{~km}$ away.    for the 28 mm lens    for the 135 mm lens.

  (a) An object 34.5 cm in front of dfg o +s3-rmlb0 inb+5a certain lens is imaged 8.20 cm in front of that lens (on the same l 5 bd0r-+g+b oismfn3side as the object). 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 converging lens, i pgdvz996dywf; 1k (ugt forms a real image. When the object is moved to 40.0 cm from the len z9yv1 p6g(f 9w;dugkds, the image moves 10.0 cm farther from the lens. Find the focal length of this lens.    cm