What would be the appeasw :;h:i h-dgerance of the Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fleet inydorjmjox sl-r (e;r ;.x2*h3 the harbor of Syracuse by focusing the rays of the Sun with a huge spherical mirror. Isj2rr;dmx;j- *hsy.x3l( oroe this reasonable?

Although a plane mirror appears to reverse left and right,.j9y g/oen4y;g jrm,x it doesn’t reverse up and down. Exp/xoj g9 ,.yeyr;jnmg 4lain.

If a concave mirror pr4 ngr ad(1 7bvv)kfy-roduces a real image, is the image necessarily inverted? Explai1dfrk yvnvbr)7g( a -4n.

An object is placed along the principal axis of a spherical mirror. Thl3r o-ah;hnc+tvbn .m)rmm 13vm -ux(j vqb84e magnification of the object is -3.0 Is the image real or virtual, i 3mh8.j--( cbmx;ntmvln+ ou4q1arrmvh3 ) bvnverted or upright? Is the mirror concave or convex? On which side of the mirror is the image located?

Using the rules for the three rays dihz z boj0memn,wpd.f:f+.i . 6scussed with reference to (Fig. Below a), draw ray 2 for (Fig. Be bn0if wo,.+.pfm h.zmj:e 6zdlow b).
(a)
(b)

What is the focal ley0h;-; r swmjdngth of a plane mirror? What is the magnification of a plane mir;y shdw- jmr;0ror?

When you look at the Moon’s reflection from a ripply sea, i8d hv18*. v( broi*za) vimxkmt appears elongated . Explain(8mi*vmx .iokva1 z bv hd8)r*.

What is the angle of refraction when a light ray meets the b0d+ o9ri:ld 3eukom3boundary between two materials perpendicularly?3romd:do3e+lbi9uk0

How might you determine the speed of light in a solid, rectangular, tran4i knjzqkkf4k 6o8x1l ; w emg:w7nr2/sparent o8jkrn ;m6 zn:ik/gk2w1f744el qko xwbject?

When you look down into a swimming pool or a lake, are you likely to atq,w3zheal -jyg.5 2underestimate or overestimate its depth? Explain. How does the apparent depth vary with the viewing anglet jz w,g- .35yaal2qhe? (Use ray diagrams.)

Draw a ray diagram to show why a stick loo /;a8uduswx ca5 :;ydfks bent when part of it is under water : uda;/a;scuf5 y8x wd(Fig. Below).

Your eye looks into an aquarium and views a fish inside.rf8s h4 0vdzfc 4bhqqfb.e+i46 5pyj 4 One ray of light that emerges from the tank is shown in (Fig. Below), as wfq48 qz bv 4i.+6chfh 4yesb5drjpf 40ell as the apparent position of the fish. In the drawing, indicate the approximate position of the actual fish. Briefly justify your answer.

How can you “see” a round drop of waudli 1j07 8 j*aw*bzg2 +j:teq56 qqgz uu1fqrter on a table even though the water is transuzbd zj27e6l1:08jwqu 5qq1a*i * gjutfg+q rparent and colorless?

When you look up at an object in air from beneath the surface ie.rz0yeiq4p)9 zx gjq 1r*ha/q qt1 4an a swimming pool, does the 4e1 zytrjhqz4.0gq q1ra 9)a q/px* ieobject appear to be the same size as when you see it directly in air? Explain.

How can a spherical mirror have a negative object distancvvq8s oyuz+d.7e4 u6 he?

Light rays from stars (including our Sun) always ben/uy d3jf- d2yy3: gpwmd toward the vertical direction as they pasjdwug /- y:df23py ym3s through the Earth’s atmosphere.
(a) Why does this make sense?
(b) What can you conclude about the apparent positions of stars as viewed from Earth?

Where must the film be placed if a camera lens is to make af*lp yoeh*e-(x z v(l66zha;c sharp image of an object very far away?6choz plf l6vy(-x*a(e h z*e;

What type of mirror is shown in (Fig. Below)g) hp 03syxs8+vwwg xr-h +xlq-94dgq ? Explain.

A photographer moves closer to hiiu 51:0vedtm cs subject and then refocuses. Does the camera len u0 51ivdec:tms move farther from or closer to the film? Explain.

Can a diverging lens fth 4l85 .qym m bko+1ucfa7m8uorm a real image under any circumstances? Explain.

Use ray diagrams to show that a real image formed b:mtaclv5(u:+ ( mtaa 3cg uxq;y a thin lens is always inverted, whereas a virtual image is always upright if the o ucc( gv uta:m(q +;35mtaa:lxbject is real.

Light rays are said to be “hd0 );o(rcx/-so ;lrfzo(nwp o iv9m,reversible.” Is this consistent with the thin lens eqn(p /ozio ;dw;s,fr0-xlh9omvo r( c) uation? Explain.

Can real images be projected on a screen? Can virtual imag cjus:ylychs y/9..o 1ehx 66fes? Can either be photographed? l.ecc6s:x6 sy foh1. hujy9y/Discuss carefully.

A thin converging lens is lt5x-z gxx:7a9qo5 iq moved closer to a nearby object. Does the real image formed z iqqlx9x5ag75:ot -xchange
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an 1vo vbt6tku 34iz01mtindex of refraction n = 1.30 In air, it is a converging lens. Will it still be a converging lens if placedbtvvkmu zt6031i4 1 ot in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands fzk).t h/ s3 mea8nv/wfy 7x0j rxs8kn/acing a converging lens. If the nose and the tail are each focused on a screen ikh//30zk88 st v rnfxsmn j e7x)w/a.yn turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facing a npj8v0 qru :5kconverging 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 re0pq8r j:knvu 5st of the cat be?

Why, in Example 13, must the converging lens have a shorty;g g2dum/z 5ydhd k;7er focal length than the diverging lens if the latter’s focagdm /udd7 zkyy;h5g;2l length is to be determined by combining them?

Explain how you could have a0w 0 sj8tbugbzhb+;+u virtual object.

  An unsymmetrical lens (say, planoconvex) forms an image of a,2szt zs *;crcm*d*e i nearby object. Does thes2m c r;d*ezt,*zisc* image point change if the lens is turned around? ----待选择----yesno 

The thicker a double convex lens is in the center as compared to oi.p-vcs co4 q7 v2zfuf952hxits edges, the shorter quop h52fxfv-2czos9i v. 47cits focal length for a given lens diameter. Explain.

Consider two converging lenses separated by some distance. An object isi4t97hnp,1 * gadgvwj placed so that the image from the first lens lies exactly at the focal point of the second lens. Will this combination produce9g,a tn 7d1*iw gvp4jh an image? If so, where? If not, why not?

  Suppose that you want to takkb,/ ry43i 3x0wgdrzz1 pi n2ee a photograph of yourself as you look at your image in a flat mirror 2.5 m away. 3i,/nr1pgrz2 w0x 4i3 edbkzyFor what distance should the camera lens be focused?    m

When you look at yourself ik/ww -tdj9)r yn a 60-cm-tall plane mirror, you see the same amount of your body whether you are close to the mirror or far away. (Try it and see.) Use ray diagrams to show why this should be true./-jk) try d9ww

  Two mirrors meet at a; g,f: ; ,g-eeql0ow aprfw/2qas4ona 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.s)5sm + z3,:tuvcx ot an)+bed68 m above the floor stands 2.20 m in front of a vertical plane mirror whose bottom edge is 43 cm abovm)ot ta5s:3+e nv ,b d+u)czsxe 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. Whaq 2tk:2ry*pjwua0/b/ bm n(u qt area of the mirror is used to reflect the rays entering one eye from a point on the tip o2pnu :bau/(2*kyqjmtqr0 wb /f your nose if your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors meet at am( sax;7japyty)u- qaf/ q6h /n angle $\phi$. a single ray reflected successively from both mirrors is deflected through an angle of $2\phi$ independent of the incident angle. Assume $\phi<90^{\circ}$ and that only two reflections, one from each mirror, take place.

  A solar cooker, really a concave mirror pointed at the Sun, focuses thekn 08hv p-qqz4.tu0gk Sun’s rays 18.0 cm in front of the mirror. What is the radius of the spherical surfa0n k.4k v0uzp 8t-hqgqce from which the mirror was made?    cm

  How far from a concave mirror (radius 23.0 cm) must an ob,crk49:c hnj gject be placed if its image is to 4,c:9j hn rkgcbe at infinity?    cm

  If you look at yourself in a shiny Christmas tree baloc w- /rvsjs1e7ck3otnm2 0w/l with a diameter of 9.0 cm when your face is 30.0 cm away from 0 c/j erc ts vkon1/mw7so3-2wit, where 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 showsry3+v o1lb)e56ynus b an upright image of any person who stands 1.4 m in front of it. If the image is three times the person’s height, what is the radius u1 b+oebyls)n35rv6 y of curvature?    cm

  A dentist wants a small mirror that, when 2.20 cm from a tooth, wilxbvh h-- 1oha0tg86)egt ly.ml 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 tha/h2j lls e;kj+t are smaller than they would be if the mirror were flat. Are the mirrors concave or convex? What is a mirror’s radius of curva+;e2j lhj/l ksture if cars 20.0 m away appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.04xp ;5c-qg)acxp5l wi mm high is placed 20.0 cm from a convex mirror of radius of curvature 20.0 q5p la) 4wcxxcgip;-5cm.
(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 l:k29nj8d3 iqsc :e nva store. You estimate the height of your image to be half of your actual height. Estimate the radius of curvatur3d :s n28ikejq9lcn:ve of the mirror.    m

  (a) Where should an object be placed inzm/;g x y4)p z-n*ednz front of a concave mirror so that it produces an image at the same lo zend)m/y* pzxz;n g-4cation 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 very small when viewed in a curved tzr+w24r 9mh3j(xof 8-lk+zrd fo t-ymirror. The image appears to be 18.0 cm behind the mirror. What kind ork t 9+wzf4rj-o+m3ofh2r y-l8t(dx zf mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniques,ub,pdou :53mo d n( h*c4bvg3qoy-se*
(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 th0ztpjn 4z608q0*4fu sigxv 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 equation, Eq. 23–2, is valid 0g:pp0n .21lk9upjxjz cfl.1syr f. qfor a convex mirrouf 0 xl2 gf1k z9 pjqc1:lp.p0j.sny.rr as long as f is considered negative.

  The magnification of a convex mirrtr x1ur taw e/-.z8h qv+o.9p/;dipaaor 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 f p+gt6b2cz- f 1x3grteront of a spherical mirror. It is desired to produce a virgt1g -et 23cr 6b+xfzptual image that is upright and 3.5 cm tall.
(a) What type of mirror should be used?  ----待选择----convex mirrorconcave mirror 
(b) Where is the image located?    cm behind the surface
(c) What is the focal length of the mirror? $f$ =    cm
(d) What is the radius of curvature of the mirror? r =    cm

  A shaving/makeup mirror is designed to magnify your face by a factor of 1.33 3ld9;gb3ql wowhen your face is placeb3 ;9dg3wqlo ld 20.0 cm in front of it.
(a) What type of mirror is it?  ----待选择----convex mirrorconcave mirror 
(b) Describe the type of image that it makes of your face.
(c) Calculate the required radius of curvature for the mirror. r =    cm

  What is the speed of light in r0 p3.(,r psx h0ga) rwgess2r
(a) crown glass,    $ \times10^{8 }\;m/s$
(b) Lucite,    $ \times10^{8 }\;m/s$
(c) ethyl alcohol?    $ \times10^{8 }\;m/s$

  The speed of light i0rc/ co m*vg-jd) fm/vn ice 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 watea)xq2w8l xs -qn :vqm(r. What is the index of refraction of this substance?sn-2 (wv:q)a 8 xxmqlq n =   

  A flashlight beam strikes the su)bart ph9jf53pg :5w hrface 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 flashli 3col5+dyl nz;ght upward from beneath the water at a 42.5$^{\circ}\,$ angle to the vertical. At what angle does the light leave the water? $\theta_2$ =    $^{\circ}\,$

  A light beam coming from an underwater spotkd(o4qp vc- 1:rph v km6phj-(light exits the water at an angle of 66.0drphhm6pj k( 1v: v (ck-4-qop$^{\circ}\,$ to the vertical. At what angle of incidence does it hit the air–water interface from below the surface? $\theta_1$ =    $^{\circ}\,$

  Rays of the Sun are seen to makek5/nm azv z(w6 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 o(xt;3 scoyhq * ww7+3ar7kqdt* ey v,has flat glass sides whose index of refraction is 1.52. A beam of light from outside the aquarium strikes the glass at a 43.5° angle to the perpendicular (Fig. Below). What is the angle of this *q+* x3teo yoc7 wa3,rdqws7 kvty;h(light ray when it enters
(a) the glass, $\theta_2$ =    $^{\circ}\,$
(b) the water? $\theta_3$ =    $^{\circ}\,$
(c) What would be the refracted angle if the ray entered the water directly? $\theta_3'$ =    $^{\circ}\,$

  In searching the bottom of a pool at night, a watchman shines ab-6m*hj 2h m(2kn mdew.oab0l 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 beneab*mwebla mj2nk odm6-h .2(0hth his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equilateral glass2sk0, cg -sgu0 1ejd;m/su pbp prism at a 45.0$^{\circ}\,$ angle to one face, (Fig. Below). Calculate the angle at which light emerges from the opposite face. Assume that n = 1.58.    $^{\circ}\,$ from the normal

  A beam of light in air sdoug 460l jsk(trikes a slab of glass (n = 1.52) and is partially reflected and partially refra4(gdl ks oj0u6cted. Find the 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 uniform 5; cp*fn74 foc*fk6zlxu 8foplayer of transparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the incidoc ku f* 87c*;pfop4x5n zf6lfent beam, independent of the incident angle $\theta$. Assume air on both sides of the glass.

A light ray is incident n f/p)naw b 28uv;fj8ejtsy18on a flat piece of glass with index of refraction n as in (Fig. Bela1vn e ;bfj wu8p y)nt8j/8s2fow). 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 for the interface between water and Lz. /57bhkhdlcl-:jnuucite? To be totally internally reflecnl k:.h/dc7lzub -5jhted, the light must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a cafcqo s kr7g0* (+zi;gertain liquid–air surface is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in a pool of water from a depth of 62.0 cm. Whep 8 pac+vhz oo ;pf3h*;ihq5o5re must it strike the air–wateqf po+p*3i5;v ochphzo5ha;8r interface, relative 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 benea2q/gwcl-htb :j (41 og+djr hjth the surface of a liquid and strikes the surface 7.0 cm fromlhc d gtjr-41b jq(hj/+2wog: the point directly above the source. If total internal reflection occurs, what can you say about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face 77nt4n27x-e e:0 me)b: olmaqlaxnezof 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 optic fiber as a9:jlvn m sw e7,kq48w6r8vx jshown 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 beam reflects back int7 xm9jqvs 8w6rvwe48, kal :njo the material at point a.

  (a) What is the minimum index of refraction for a gljkd sqf/,s0p+ : knj9lass or plastic prism to be used in binoculars (Fig.jsd90/q:sk+j nk f,pl 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 locater8v-)v :wri yud 78.0 mm behind a 65.0-mm-focal-length converging lens. Find the object distance:v)r -wyur8 vi
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus,mq0a4l. upel at a point 18.5 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 anz,gmg j3s.s,0li s) vz object 2.75 m away as an image 48.3 cm on the other side of the lens. What type mz,l.)s vz jsg3g0, isof 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 lenn4qxdgb/b67 jdt;s bj / pgd,+7 tfuv2s? 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 usinnh/ 7uso-u 3es a converging lens with focal length 24 cm to view a stampnn7 s/3-h ouui 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 3d1fqjg:7t8byk m.j. qkze7o object 4.0 mm high. What are the position, type, and my e. 7q1jdj7.8to:kkzfb 3qg height of the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used tongim/m:8 h7 xb focus an image on the film of a camera. The mxmimb/ngh87: aximum distance allowed between the lens and the film plane is 120 mm.
(a) How far ahead of the film should the lens be if the object to be photographed is 10.0 m away?    mm
(b) 3.0 m away?    mm
(c) 1.0 m away?    mm
(d) What is the closest object this lens could photograph sharply?    mm

  It is desired to magnify readpg9e1 n,l:r q.meb+fw ing material by a factor of 2.5× when a book is placedee,9rg wn+p1bm .l fq: 8.0 cm behind 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 how much does thecmwdur tc4 (vg /2z6g+ image move if the object irvzcu /g2(wctd+ g64m s 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 witp)g4za-yx nr/xh54 kllv19pph a focal length of 25 cm should an object be placed to produce a real i 14kx a/4lp)xhnp-r5vpl y9zgmage 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 if itsmb4w4(il pff- image is to be-bf4iwf 4 l(mp magnified 2.00× and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm

  (a) How far from a 50.0-mm-focal-length len4g)oiyg7li7 .eika1 g s must an object be placed if its image is toii.gk)o g1l7 ag e47yi 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 135-mm-focal-length lens. ss h;xgwtm,m(y 513 q -tvk+wwd+.5u(en vepdWhere is the image, how high is it, and what type is itd(e m(x; vte5w+s.v1+,3ystd-hq w wkgup5n m?
$d_i$ =    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 lte iu-w d4d/3cmn r q))te)i;formed by a 75-cm-focal-length converging len 3)d/ ndu)tecw)ir q4tm- i;les if the image is 2.5× larger than the object and is real?    m

  A bright object and a viewing screen are separated b4xn 5w*cjb3 szy a distance of 66.0 cm. At what location(s) betw*b5s3wznj4 cx een the object and the screen should a lens of focal length 12.5 cm be placed in order to produce a crisp image on the screen? [Hint: first draw a diagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length converging lenses are plaprt1w;31j 3;x; kmipyzqsgd6 ced 16.5 cm apart. An object is placed 36.0 cm in front of one lens. Where will gq3j1d6p;zir;; 3m tspwkxy 1the 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 witqy w )l:x; 2uod+nvs95ku*pfth $f=-31.5\mathrm{~cm}$ 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 le+f6ut0eb*fr; vekblo4lh 7 g f0 b8j.n-dzd;lns is 21.0 cm behind a diverging lens. Parallel light strikes the diverging lens. After passing through the converging lens, the light iozl;dt;k* v fgb8efd b 0nul0 . h4+frjlbe6-7s again parallel. What is the focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Example 23–12 are now placed only 20.0 cm apart.s6- pm01erx vy The object is mxs16-0 pyverstill 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 are placed 30.0 cm apart.:xc **k5olps pg) elm,jnkq917wyqm, The focal length of the lens on the right is 20.0 cm, and the focal length of the leny)95p* cowqs ,j,m*mx 17 lq:nlgekkps 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 focal wgder)kgd3z4f 7, w a4length of is placed 12 cm to the right of a converging lens with a focal length of 744edw za)3kgwr dg 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 diverg;3rq8 ax*n0iwodyn y79g jzj7 ing with focal length are placed 25.0 cm apart. An object is placed 60.0 cm in front of the converging lens.iyjq 7 na038z *r9xg;nw7yj do Determine
(a) the position    cm to the right of the diverging lens
(b) the magnification of the final image formed.   
(c) Sketch a ray diagram for this system.

A diverging lens is placed next to a converging lens-tcb7bs z/w1o 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 h3bjgu cmv -.(1)c /jdcn (skzhas surface radii of 34.2 cm and 23.8 cm. What is the focal length if n = 1.52zg/vc(ckun .3jd jchm() 1- bs?    cm

  Both surfaces of a double convex lens have radii of 31.0 cm. If the focal lehxpy26gd66 gp 2rxsa0 ngth is 22ydxr6 60gh p ps26axg8.9 cm, what is the index of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm. What is thodw+z yyo 0y+8e radius of the concave soy d+08oyy +zwurface?    cm

  A Lucite planoconcave lens (see Fig. Below)r((j99o lx(qr1jqlae z9gj .tiu kk:l w*++e z has one flat surface and the other has R = -l*jrg:+u.a9z+99ozr ( j ll(ix1qwkeqe t (kj18.4 cm. What is the focal length?    cm

  A symmetric double convex lens w: /sjubka4h :hith a focal length of 25.0 cm is to be made from glassab :/hjksu :4h with an index of refraction of 1.52. What should be the radius of curvature for each surface?    cm

  A prescription for a corrective lens calls for +1.50D. The lensmaker grip6sh:2z cpg(tnds the lens from a “blank” with n=1.56 and a preformed zc pp:2gh(s6t convex front surface of radius of curvature of 40.0 cm. What should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fig. Below). You1qdv0 zd+u 6 vua4s9ll stand 1.5 m away from one of these mirrors and look into it. You will selz vlvaud1q06+ud4s 9 e multiple images of yourself.
(a) How far away from you are the first three images in the mirror in front of you?
$d_1$ =    m
$d_2$ =    m
$d_3$ =    m
(b) Are these first three images facing toward you or away from you?
the first image is facing  ----待选择----toward youaway from you ;
the second image is facing  ----待选择----toward youaway from you ;
the third image is facing  ----待选择----toward youaway from you .

  We wish to determine the depth of a swimming pool filled with np iii5qxxj4v(6 jx6g*lpl 41water. We measure the width (x6qx* v ilnj1li( 64x4jpgx5ip=5.50m) and then note that the bottom edge of the pool is just visible at an angle of 14.0$^{\circ}\,$ above the horizontal as shown in (Fig. Below). Calculate the depth of the pool.    m

  The critical angle of a certain piece of jo97 ayht2q p475bzop 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 cuw p09/ese(pyar4npp/z,hc +onsidered a limiting case of a spherical mirror. Specify what this rzc(/p9h04 /,w yepep+ uapnslimit is.
(b) Determine an equation that relates the image and object distances in this limit of a plane mirror.
(c) Determine the magnification of a plane mirror in this same limit.
(d) Are your results in parts (b) and (c) consistent with the discussion of Section 23–2 on plane mirrors?

Stand up two plane mirrors so they for )ydb d/.w2u79ufsdjzm 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 can never form a real image of a r3exnt0dc8*fy eal object. Can you describe a situation in which a diverging lens can form a re3 08 yntxcf*deal image?

  Each student in a physics lad2fl/6iab e x)b is assigned 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 for the object distance are not the same. Explain why thf )laib/xd2e6ey 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 prism isac9 :d54vgqe w $\phi=72^\circ$ 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/pjfgkfheo bzg c3 ms2 h4*467 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 cm in front of a conver.ivj(bc. (pupf fu c;ga6;e i(ging 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 placc vpn1h0m*xes *b4z7q ed on one side of a converging lens of focal length f, and a white snez 0 *c*mx q1v4psbh7creen for viewing the image is on the opposite side. The distance $d_T=d_i+d_o$ between the object and the screen is kept fixed, but the lens can be moved.
(a) Show that if $d_{\mathrm{T}}>4f,$ there will be two positions where the lens can be placed and a sharp image will be produced on the screen.$d_T$>4$f$
(b) If $d_{\mathrm{T}}>4f,$ show that there will be no lens position where a sharp image is formed.
(c) Determine a formula for the distance between the two lens positions in part (a), and the ratio of the image sizes.

  In a slide or movie projector, the film 8 ,3mu96 /nbi zdhcsakc-tsm8acts as the object whose image is projected on a screen (Fig. Below). If a 105-mm-focal-length lens is to project an image on a screen 8.00 m away, how far from the lens should the slide be? If h3zt88iscmn-s9,k/m u da6bcthe 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 i m b+27,coamozk :c.ehwe 3ib5s actually 24 by 36 mm) is to be projected on a screen 1.80 m by 2.70 m placed 7.50 m from the projector. What focal-length lens should be used if the image is to cover the scri.b ezo 3kcbwa m:2mh,o75ce+een?    cm

Show analytically that the in/s i,:1bk+io,- br duu-zmf80xgoej mage formed by a converging lens is real and inverted if the object ii:-gbx+ smikr0e uo -zj,bf,1d/o n8u s beyond the focal point $(d_0>f),$ and is virtual and upright if the object is within the focal point $(d_0>f),$ Describe the image if the object is itself an image, formed by another lens, so its position is beyond the lens, for which $-d_0>f$, and for which $0$<$-d_0$<$f$.

  A movie star catches a nh1nr w8 qa15ureporter shooting pictures of her at home. She claims the reporter was trespassing. To prove her point, she gives as evidence the film she seized. Her 1h 1wranu 18nq5.75-m height is 8.25 mm high on the film, and the focal length of the camera lens was 210 mm. How far away from the subject was the reporter standing?    m

  How large is the image of the Sun on film used in a cofe* t*p2z, 2c5uyr b.qks e+damera 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 ouhex95s+d8khp5u5 ;y 5np6r dq8pu s sf that lens (on the same side as the object). What type of lens is thu9yd5sxp r6 uh5+8h8 q5ep; ssdkpnu5is, 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 z(,- 94t pu5htmrryrqcertain converging lens, it forms a real image. When the object is moved to 40.0 cm from the lens, the image moves 10.0 cm farther( rzrr95yt u,4pqhmt- from the lens. Find the focal length of this lens.    cm