What would be the appearance of thtnctc6/q9+ wzzt g)+re Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the h4v, esvp zpcp++(/m kwhole Roman fleet in the harbor of Syracuse by focusing the rays of the Sun with a huge spherical ek4vpsp,(+ pm/zv+ch mirror. Is this reasonable?

Although a plane mirror appears to reverse left and right, it doesn’t reverse uper1wadjk4q 7, and down. kdeq1 ,47war jExplain.

If a concave mirror produces sfjc qx:b-)u4a 9/dtta real image, is the image necessarily inverted? Explai-s9: jd4f xutt) aqc/bn.

An object is placed along the 5r:x zgz 9f8u-yho0dq 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 concave or convex? On whic xo8:9fh0u5 -z qdryzgh side of the mirror is the image located?

Using the rules for the three rays discussed with reference to (Fi:a+qi-yxh6e7c)wpl e a y*e ;bg. Below a), draw ray 2 f 7exli: w)6+y*;qaa ebyh- cepor (Fig. Below b).
(a)
(b)

What is the focal length of a plane mirror? What is thc)k bhe:5d cjd(k42n me magnification of a plane mn dkj (:c45e2k bhmd)cirror?

When you look at the Moon’s reflection from a ripply sea, it appears elongated*g:00fbcdpuflv0 + j36ox stp 1/ wwlb . Explain.j+l wdp0v 3 :p wsl0bx6cutof0f/b *g1

What is the angle of refraction when a light ray meets the b+0+p mguwl/7 57 wmdhkqk(cg u afr+j9oundary between two materials perpendich+ wg ug fmqukk77p0+lar9+j(/cmdw 5ularly?

How might you determine the speed of light in a solid, rectangular5w5 tq9 mqf(zl, transparent ob9mz5(qt f wql5ject?

When you look down into a swimming pool or a lake, are you likb j0mqroiwgv*d2 g9z v5r) -2oely to underestimate or overestimate its dep22g 0mw-v 5j qo*9bizv)rdogrth? 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 parthr zc5x*og ) k8o;y9v /kq ,ptwj-g+qd of it is under water (Fig. Belowz5j;+gqwk ptq g/9vkc,o8h* rodxy-)).

Your eye looks into an aquarium a/0 pw+dxvs2fq gj7e4 wnd views a fish inside. One ray of light that emerges from the tank is shown in (Fig. Below), as well as the apparent position of the fish. In the drpj7/xs q+ w g4fw0ev2dawing, 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 the water 0nmns po4e d 6n:m3o hf99ufe9is tranoumh f9eom6n9n 0df:9 spen34sparent and colorless?

When you look up at an object in air from beneath the surfa0y(sg lj 6a(ifce in a swimming pool, does the object appear to be the same size as when you see it directly in air? Explai(sfljg(0 y6ian.

How can a spherical mirror have a negative /qix:2fb i*f. tafxncs4/e/ yobject distance?

Light rays from stars (including our Sun) always bend t5n;e lzf a04xcoward the vertical direction as they pass through th5x4 eclzn0f;ae Earth’s atmosphere.
(a) Why does this make sense?
(b) What can you conclude about the apparent positions of stars as viewed from Earth?

Where must the film be placed if a camera lens is to make a slnfr. nzs7a)x +chc +yr2q3r05 2jtpqharp image of an object 3sya.n)7f+c2 q 2rhtzq0+rx 5 ljrcn pvery far away?

What type of mirror is shown j3y zi2wu, 0mlin (Fig. Below)? Explain.

A photographer moves closer to his subject and then refocu; gyqn60 m*kyty/ twp2ses. Does the camera lens move farther from or closer to yp2w0gmn t6yk ;qy/t*the film? Explain.

Can a diverging lens form hp:oiu c9v(oy 95 m-qia real image under any circumstances? Explain.

Use ray diagrams to show that a real image formed by a thin lens is always inv+ / kb-jrzc 93adsm8w h)btv/gerted, whereas a virtual image is always upright if the object is re)zdbs +b v8j/r9-wt/gh3mk c aal.

Light rays are said to96p4 hp) -krykb1vudu be “reversible.” Is this consistent with the thin lens equa) pkyv-uh ud69k14brp tion? Explain.

Can real images be projected on a screen? Can virtual images?9zevh5zh0ju5g 1 0sig Can either be photographed? 1vg5 h059usigzh z0je Discuss carefully.

A thin converging lens pzbb t*d2 .p5sc(n,hh;:wn scis moved closer to a nearby object. Does the real image formed c d(n pb2*ch b:tw.snchp5z ,;shange
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of refraction n = 1.2l 7v6s( i5zs:+ecagr oyc6mas+:gv l 30 In air, it is a converging lens. Will it still be a c s7 +l 6iscmyv5zavc6s 2(:+lr gg:aeoonverging 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.ks-x* md7/ l n.-lyxgq If the nose and the tail are each focused on a screen in turn, which will have the - dll qygks7nm -/x*x.greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facing a converging lens./i ye en73fv,s Under what circumstances (if any) would the image of the nose be virtual and the image of the tail be f7v,y3s / ienereal? Where would the image of the rest of the cat be?

Why, in Example 13, must the converging lens have+ e8o iuc(:vc8;-a +navxbnq e a shorter focal length than the dxneac8(:uvn+eao -v; b8+qi c iverging lens if the latter’s focal length is to be determined by combining them?

Explain how you could have a virtual obr nre23xa9i8l ject.

  An unsymmetrical lens (say, planoconvex) forms an image of a nearby object. Do zj 851qiusik,s; y8lies the i; izy u 1s,klj5iqi88smage point change if the lens is turned around? ----待选择----yesno 

The thicker a double convex lens is in the center as compared t c ek;r86nd:wy5ywx s3o its edges, the shorter its focal length for a givrx8k:n5w wys6ce ;d3 yen lens diameter. Explain.

Consider two converging lenses separated by some distance. An*5-ho 9m a( xxvona(aglbhh; - object is placed so that the image from the first lens lies exactlya--; 9hnb5glxxo(om(h* hvaa 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 ipjht x,a/; v9tmage in a flat mirror 2.5 m away. For what distance should the camera lens t,j ;9h/taxv pbe focused?    m

When you look at yourself in a 60-cm-tall plane mirror, you see the same amou5 5gg. ee;em epd(dnn4e;)aonnt of your body whether you are close to the mirror or far(5e ;p dnan5gg.;eedo mne)e4 away. (Try it and see.) Use ray diagrams to show why this should be true.

  Two mirrors meet at a 13eyo/a e9 +jsf-fn*we6pewv k ;k6p3c95$^{\circ}\,$ 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 oi3n r xxm(l)4 g7di 9ic5qnmxu83(ttaqy m:l .f a vertical plane mirror whose bottom edge is 43yq59.)nt mx3d lxmqiun 8mx(gta i(l 34 :ri7c 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 pnhky)0 .a79pij xj9q from a plane mirror. What area of the mirror is used to reflect the rays entering one eye from a point on the tip of your nose if your pupil diay)i 0j9jh9a.qk7 pnx pmeter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mimmrdtf)3bh: /rrors 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 x-f p s- 7.+;5 xsxnaspb+xk pqh8mx7nSun, focuses the Sun’s rays 18.0 cm in front of the mirror. What is the radius of the spherical su-sx p;8 phxkn.m7-+fq +x7xpn5x a ssbrface from which the mirror was made?    cm

  How far from a concave mirror (radius 23bchn.3n p vm4mvga+ /6.0 cm) must an object be placed if its image is.4gp 3/nmc+ hn6vb vam to be at infinity?    cm

  If you look at yourself in a shiny Christmas tree ball with a diameter jza4hlh / )7j4ws0r)9u,y*vgnzv fw s (0civoof 9.0 cm when your face is 30.0 cm away from it, where is,soy40u0/izwl f4vr z()hj)cv7j 9hsg na v*w 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 j,;0 huf (3o zca7ovvhupright image of any person who stands 1.4 m in fro zoo7fa0jhv ( ;3v,hcunt 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 cm from a tooth, wilfoe 3: +gp(nhs1u.dspl 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 mirror,sm3fw+*j yj9el q811rtmux tsz+ ;uss produce images of cars behind you that are smaller than they would be if the mirror were flat. Are the mirrors concave or convex? What is a mirror’s radius of curvature if cars 20.0 m awjqs uj91;m l8 t+1rz*+sxtm ,3uwfeysay appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 g-db1v exmqv5(k b4e/ mm high is placed 20.0 cm from a convex mirror of radius of curvature 20.4 bme-e(5kgvv1qbd/ x0 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. You jv(/es -ssj(q estimate the height of your image to be half of your actual(s-(/jjesq sv height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an obj pi5:n +6i8xvcomzw+ahe737 vy iv 0ylect be placed in front of a concave mirror so that it produces an image at the same location as tho+xi vy7eii zh:nv +cpa067m wlyv8 53e 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 whem3fhi z nci* a49skn35n viewed in a curved mirror. The image appears to be 18.0 cm behind 3n 95*maizhks n c34ifthe mirror. What kind of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniques, g2s09 hlp;yvl
(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 diagrff kq43gv rh :yt-cnap; +vx-8am, that the magnification 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 eq(uomyp yd95/ yoe b u4q2;onwda,3os.uation, Eq. 23–2, is valid for a convex mirror as long am,4.s ; /yoo(uoy9ded5qa 3b2wyponus f is considered negative.

  The magnification of a convex mirror f*t2c*uh dy2ruu 1dtz78+vllis $+0.65\times$ 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 f6b08pjdw(nx d ront of a spherical mirror. It is desired to produce a virtual imaj n06d(dw8 bpxge 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 gnx-2n5fzzc v3 tgdpl 8i2b8(y,6hbq your face by a factor of 1.33 when your face is pf8(82nx5yz gpb b,3tv-z2 qgc6h ilnd laced 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 lightggf9q y-wd.;g 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 ice is :0n;: wlk7pj e0bzurgdq :m 1z$2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain substal ef7qxh9i )9gnce is 89% of its value in water. What is the index of refracthxel9)q9f 7i gion of this substance? n =   

  A flashlight beam strikes the surface of a pane of glagsa 9kng* jf7bgq73)p ss (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 beneat/ hy xo;6bu5ean0m/9j xp.zfxh the water at a 42.5$^{\circ}\,$ angle to the vertical. At what angle does the light leave the water? $\theta_2$ =    $^{\circ}\,$

  A light beam coming from an underwater spotlight exits the water at aur yrlme *+l+sv8)m)wn angle of 6 ryme swu)++ 8*llrv)m6.0$^{\circ}\,$ 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 setmb).a9kn3 k cen 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 fla:j1/vje0 oat pt 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 (Fip/:vo0ea1tj jg. 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 ofml zk f(+,aa+c a pool at night, a watchman shines a narrow beam of light from his flashlight, 1.3 m above the water level, onto the szf kcla(a,++m urface 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 atw7sb(x-clm +jona h,: kkh :kb.2dn 2t 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 q3o7h4pz) s ;fnsdzs /strikes a slab of glass (n = 1.52) and is partially reflected and partially refracted. Find fo;zsd/p)nz 7s3 4qshthe angle of incidence if the angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam incident on a unifaxe)t;r9ku )kc5 4awqv p2 /alorm layer of transparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the incident beam, independent of the incident angle wr)tqluaa 5vx ap c ;4/2kke)9$\theta$. Assume air on both sides of the glass.

A light ray is incident on a flat piece of glass with index of refrac4tp *1m8cd:4 8nx ja9xbmo lfhtion n as in (Fig. Below). Show thata :x19nm4md bx4lhfotj*c88 p 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 for the interface4rcfw ,-1d pbk between water and Lucite? To be totally internally reflected, the light must start infkbr1 w ,cp4d- which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–air surface 1znl16 (rnwno is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emit o2n6ucnv9ik:8p 09: bj9k9xi dwmvl vted in a pool of water from a depth of 62.0 cm. Where must it strike the air–water interface, relative to the spot directly above it, in order that the light does not exit the water? luvmxc p9d9i8 w06v2k:9nvn 9bo:ikj    cm

  A beam of light is emitted 8.0 cm beneath thx( z,a*5efq kce surface of a liquid and strikes the surface 7.0 cm from the point directly above the source. If total internal reflection occurs, what can you say about tk zx5 a,qcf*e(he index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left fwp p+0pj 36elqace of the prism in (Fig. Below) at 45.0$^{\circ}\,$ as shown, but is totally internally reflected at the opposite side. If the prism apex angle (at the top) is $\phi=75.0^\circ,$ what can you say about the index of refraction of the prism? $n \geq$    (retain three decimal places)

A beam of light enters the end of an opti (*)znhi7d weec fiber as shown in (Fig. Below). Show that zw*h ni)(e7d ewe 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 beam reflects back into the material at point a.

  (a) What is the minimum index of refraction for a glass or /eecdw0w9a5gw43 *lby+ + sqgp0 ionjplastic prism to be used in binoc+e qcdpa3 wwo gi 9lb0sej5g04*y+/ nwulars (Fig. Below) so that total internal reflection occurs at 45$^{\circ}\,$? $n_1$ $\geq$   
(b) Will binoculars work if its prisms (assume n=1.50) are immersed in water?  ----待选择----totally reflectingtotally transmitting 
(c) What minimum n is needed if the prisms are immersed in water? $n_1$ $\geq$   

  A sharp image is located 78.0tz(v2in./e e m /qk)hza srf;; mm behind a 65.0-mm-focal-length converging lens. Find the object d/h/km)aifvrnet.zs;q ;2 ez(istance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.5 ,b,bdq;w5.q *3w xp tvijz jt-cm 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 m aw wm-xyq;nq;e- ay as an image 48.3 cm on the other side of the lens. What type of lens is it and what is its focal length? Isq- nqmy-xe;w; 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--,j/,og ya kx)gumui ,focal-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 converging lens with focal length 24 n7yl6(x;r v6x.m12c g3sh+xs qtq ojqcm to view a stamp .3srgm2sn(q jqox 76+6xqxtc yh;lv1 18 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 hid(7mbb+dnu f5gh. What are the position, type, and height m 75nu(dfd+bbof 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 ;ip1xj. y/syy. The maximum distance allowed between the lens and the fil isx1 yyp;.j/ym 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 matkf*:u0p ta4 t xr.runw1f 9fw7erial by a factor of 2.5× when a book is placed 8.0 cm behinr kxttw9 7r 0*fa.pfw1u :u4nfd 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. Bk4gpb *vjpt95 y how much does the image move if the o *gtp 95vjb4pkbject is moved
(a) 1.0 m closer to the lens,    cm away from the lens
(b) 1.0 m farther from the lens?    cm cm toward the lens

  How far from a converging lens with a focal length of 25 cm should an o /c c0uk+ue;qwbject be placed to produce a real u+;qcu/ce wk0 image which is the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an object be placed ifho t gxk *yhp5d/*(e1q its image is to be magnified otk5eyq/*( h1xhg dp*2.00× and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm

  (a) How far from a 50.0-mm-focal-length lens must an object be placed v u+c,4/p ue +rmzb;bf:hrw 6bif its image is to be magnified 2cfr+ zuvbr;hp4,m +:u bew6/b.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 135y8q cfu:glz:l c: wqv r-, g8)(ppal;g-mm-focal-length lens. Where is the image, how high is it, and what cp:l8f -gu8)l:qlp ( g a qgrzc,:;vywtype 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 obje :q +d pz3t2msjjkm ka)09k6mkct and an image formed by a 75-cm-focal-length converging lens if the image is 2.5× larger than the object and is rsk3 2k)qj amd0: 9k+z mtk6jpmeal?    m

  A bright object and a viewing screen are separated by a dist,ilnkixy7l3enl45 3 5tjq hz9ance of 66.0 cm. At what location(s) between the object and tn37li nl 5jxkqelz3 5y9,t h4ihe screen should a lens of focal length 12.5 cm be placed in order to produce a crisp image on the screen? [Hint: first draw a diagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length conv;6*yr. zp3ctza s+ms*8 wliyderging lenses are placed 16.5 cm apart. An object is placed 36.0 cm in front of one lens. Where will the final image formed by the second*cimadl w8ytz6;sz3+ *yrp s . lens be located? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens wits 6 u)2)cvnzbo4rj q3hh $f=-31.5\mathrm{~cm}$ 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 isl2jdd0 -mup4h 21.0 cm behind a diverging lens. Parallel light strikes the diverging lens. After2d dpj4- mu0hl 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 Exf-/)pmrsv:r tample 23–12 are now placed only 20.0 cm apart. The object is still 60.0 cm in front of the first lens as in (Fig. Below). In this case, determf : -pr/t)vrsmine
(a) the position of the final image,    cm
(b) the overall magnification.    cm
(c) Sketch the ray diagram for this system.

  Two converging lenses are placed 30.0 cm apart. The focal length of the 7cg .ube zq5z+,iq ;fmudzf((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 andzez, f .ud m(;q(ci75 u+qfgzb 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 yasoz 3+ry)b42+u-3fpoij a h of is placed 12 cm to the right of a converging lens with a focal length o2 b3aop 3)s+4of+z yhuryaji-f 18 cm. An object is placed 33 cm to the left of the converging lens.
(a) Where will the final image be located?    cm to the left of the converging lens
(b) Where will the image be if the diverging lens is 38 cm from the converging lens?    cm to the right of the diverging lens

  Two lenses, one converging with focal length 20.0 cm and one div,o a1yct *gfy6erging with focal length are placed 25.0 cm apart. An object is placed,*ycf 61yg tao 60.0 cm in front of the converging lens. Determine
(a) the position    cm to the right of the diverging lens
(b) the magnification of the final image formed.   
(c) Sketch a ray diagram for this system.

A diverging lens is placed next to a conhg ujpm4g/ .7,nm,eo6+mt kcvverging 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 34.2dsxk/izzq5z 9f 5k q0) w8)i h7e7oebx cm and 23.8 cm. What is the focal leb 7qkx59i0k zws/8x)q7o5 e)hfzdzeingth if n = 1.52?    cm

  Both surfaces of a double convex lens have radii o +hcr(b17fd5o e8gcy 0l0yzx xf 31.0 cm. If the focal length is 28.9 cm, what iso dyr(10fxge0+ chlbc7yx z58 the index of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal lengkf+* w b /-nips8n0lfmth of -23.4cm. What is the radius of the concave surface?m0fib/ wflns+*kn -8p    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat surface a+enk36kv7tj p iuvs43nd the other has R pvjtksu i74 nv+k33e6 = -18.4 cm. What is the focal length?    cm

  A symmetric double convex lens with 58pisi ad42v6 ktv+f w dh9h9d+jf;cz a focal length of 25.0 cm is to be made from gla2 zfcj t 9vhdh4+6w8+i fski;9 advp5dss with an index of refraction of 1.52. What should be the radius of curvature for each surface?    cm

  A prescription for a correck(s 1l 5y4)bbvhppv zpijz9* )tive lens calls for +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 51yip sb)b k(lpv)4jzv *zhp9cm. What should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fig. Below). You stand 1.0v-z. kdrb 7vq+g br84kg, edo5 m away from one of these mirrors and look into it. You will see mulb4v0r zq-rog.,78bvdkk dge +tiple images of yourself.
(a) How far away from you are the first three images in the mirror in front of you?
$d_1$ =    m
$d_2$ =    m
$d_3$ =    m
(b) Are these first three images facing toward you or away from you?
the first image is facing  ----待选择----toward youaway from you ;
the second image is facing  ----待选择----toward youaway from you ;
the third image is facing  ----待选择----toward youaway from you .

  We wish to determine the depth of a sqx10w6 jb ip+xwimming pool filled with water. We measure the width (x=5.50m) anw 0qixp+b x61jd 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 o1 o o:rp;s(a.c 7w5 aftcwnz3ob;xer6f 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 limitingqzi.0: . e6o7 ircrnhb case of a spherical mirror. Specify what this limit is..: 6rqirboi7z. en 0ch
(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 mirrorsrayxqz*3d cns,2lm)1 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 divergin :4 pky 7u2fh,)uhdfmmg lens can never form a real image of a real object. Can you describe a situation in which a diverging lens can forhfh4 m:pdkmf 2y),uu 7m a real image?

  Each student in a physics lab is assigned to find the location wherca foh*b 0y86 f5kx-mxxr8jm2e 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 compareafx8o2yx6 k 8- f*xmb5jrchm0 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 jd(e *.m:l ficprism 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 c88jt eni nr*7xylindrical 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 place6 e;vnx,6 gfmld 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 on *; z31lk4shu a/j2kcuz bbk;de side of a converging lens of focal length f, and a white screen for viewing the imagel*;z;3b4k/sa k jc bu uk1hdz2 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 film acts agtrm ,5pe-55 hnaj3lz s 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 picturag5le- 5jh,zn ptm 35re be on the screen? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (picture size is actually 24 by 36 mm) is to be projected on a sc w21.;s5irq3sd p;hevox o-fx7(k1dymd;by ereen 1.80 m by 2.70 m -;fhdvk2d(x7;oqweyr.pobi1e5sx3; 1 ys d mplaced 7.50 m from the projector. What focal-length lens should be used if the image is to cover the screen?    cm

Show analytically that the image formedc3 q-zd:g5zala3 uj0 m by a converging lens is real and inverted if the object is beyond the focal point 3um3c-j:agzl0 qdz 5a$(d_0>f),$ and is virtual and upright if the object is within the focal point $(d_0>f),$ Describe the image if the object is itself an image, formed by another lens, so its position is beyond the lens, for which $-d_0>f$, and for which $0$<$-d_0$<$f$.

  A movie star catches a reporter shooting pictures of her at home. She claims tvjr8pg- t ;g/jhe 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 focalg;/ptjjvr 8g - 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 tg1 ai5qadh ;k3he 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 a certain lens is imaged 8.20 cm in front oou6i d 90wbt)of that lens (on the same side as the object). What type of lens is this, and what is its focal length? Is the image real0uo9td6o) biw 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)