What would be the appeara r*su- n f:az+obe4h8fza/sh6nce of the Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fd-hck,mikstp79s 4 dqqw46)pqeo7m1a3 y* grleet in the harbor of Syracuse by 7s79 m k6 y4apqrh3tkmis,oc4ed1d*)pwgq-q focusing the rays of the Sun with a huge spherical mirror. Is this reasonable?

Although a plane mirror appears to revers,x f6r-sz- uide left and right, it doesn’t reverse up and down i-sxzud,f6r -. Explain.

If a concave mirror produces a real image, is the image necessarily inveroow +g:gqvx .4sh72ented? Explainn2qvg: heowo4 g .7x+s.

An object is placed along the principal ax hv/k)y4h25pvv f2s jm q)qa9wl(:pnhis of a spherical mirror. The magnification of the object is -3.0 Is the image real or virtual, inverted or upright? pv(hm/w n):lv qh vpa9hj524y) k s2qfIs the mirror concave or convex? On which side of the mirror is the image located?

Using the rules for the three rays discussed with reference to (Fig. trs; ko b-.u3zBelow a), draw ray 2 forrk z-bt uos.3; (Fig. Below b).
(a)
(b)

What is the focal length of a plaqjysxtbfo 1; uux 3;km8 b)-:cu+m rv.ne mirror? What is the magnification of a planeq+3ftxuv;k om -uux1 y.:s8cb m;b)j r mirror?

When you look at the Mmtahoq :i+y 81iq kfh,o.u5qex 2*x 2coon’s reflection from a ripply sea, it appears elongated . Explai5c q. mu,i oq+2ioa1ty2eq kfh:8x*xhn.

What is the angle of refraction when a light ray meets the boundary b )) rgw2oz:ilh.x0zfv crj6p7etween two materials perpen fv7cr:i) howlg0zr.z26px)jdicularly?

How might you determine the speed of light in a solid, re a e8)p/nm4hgwab.ko 7ctangular, transparent objectwhb8kaga.o/7 np)e 4m ?

When you look down into a swimming pool or z+8*i,xgmyfkwa )n 3ya lake, are you likely to underestimate or overestimate its depth? Explain. How does the apparent depth vary with the viewing angle? ( )xfmy+zka,wyi8n *3gUse ray diagrams.)

Draw a ray diagram to show why a stick loi jc gaj;zk m4h/-v*v9 pl;e(voks bent when part of it is under water ;4g -*kjv/mp; ihcvl(jze9a v(Fig. Below).

Your eye looks into an aquarium and views a fish inside. One 5b*jlq63aife7 h9f rjray of light that emerges from the tank is shown in (Fig. Below), as well as the apparent position of the fish. In the drawing, indicate the approximate position of the actual fish53b*herajf 6jlfq7i 9. Briefly justify your answer.

How can you “see” a round drop of water on a tab)+wtnf; c9/ x1fsq bjdle even though the water is tran9xdb/t1jqfw;c s+n) f sparent and colorless?

When you look up at an object in air fj*ats8 yf)kot5 0cr yog2ed, )rom beneath the surface in a swimming pool, does the oycs2dy,t 0too)j*)5 a8re fkgbject appear to be the same size as when you see it directly in air? Explain.

How can a spherical mirror have a negativc qu*7u,,hztc6o4t3 ; awtmcdrjj;m, e object distance?

Light rays from stars (including our Sun) always bend to l 6woe :et-,k-ke0/s;fxpnczward the vertical directokkp-ele ce/s,fw6n; 0tz-x :ion 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 bee6n/2)alv1 a or y,x7k3qyoo s placed if a camera lens is to make a sharp image of an object very farooy 3x2 v7ra6la,qy1s k/)en o away?

What type of mirror iqai0l0zs )1mdyy8* ums shown in (Fig. Below)? Explain.

A photographer moves closer to his su5ek 3d d7hl/hobject and then refocuses. Does the camera lens move fartheldo7h d/ 5kh3er from or closer to the film? Explain.

Can a diverging lens form a real image under any circumstances? Exx4a+ sx+rpqz*plain.

Use ray diagrams to show that a reakbryhd1hf ) 1/whulnn;y 1,w zs)k/i9l image formed by a thin lens is always inverted, whereas a virtual image is always upright if the obf/ l)zwy1i k h1d )rh1wus9;,kbyn/hnject is real.

Light rays are said to be “reversible.” Is thxm3-ry 3 bdn-pis consistent with the thin lens equation? m-d-ry 3p3nxb Explain.

Can real images be projected on a screen? Can virtual images? Can eh,g)8 lue 0du1:d hqifither be photi g)hf e01 :qd8uhuld,ographed? Discuss carefully.

A thin converging lens is moved closecpu(59l5t xlt r to a nearby object. Does the real image forlx(t l95cut5p med change
(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 x0xz.cs6oe3 33-o)yh zdgojv In air, it is a converging lens. Will g d3o s.-j h3)ozvxz3e0oyx6c it still be a converging lens if placed in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands facing a cot+horo1.rf b iru 910snverging lens. If the nose and the tail arri 0.s 1 ob+oth1r9rfue each focused on a screen in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facing a converging letvs*/b jag h yffq1448ns. Under what circumf8sqfg bj/vt 441h*y astances (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 cat be?

Why, in Example 13, must the converging lens have a shorter focalv.o .dpj( zh3-s4 eurn ydn:8 5cyecq- length than the diverging lens if the latter’s focal length is to be determined by cocy-jrd84 o.y qudeep5nz- : c3s. (nhvmbining them?

Explain how you could have a virtual o4d+4fa rnv .nrsx1v w*wrz3.object.

  An unsymmetrical lens (say, planoconvex) forms an image of a nearby objecfx uhg x7:i ejw),g5,8.gv kqbt. Does the image point change if the lens,xjvbk hig 7f g,u8g:.qe) w5x is turned around? ----待选择----yesno 

The thicker a double convex lens is in the cent c 7l9ulvgv 6(2wg )twby.f1cfer as compared to its edges, the shorter its focal length for a)uvfc g(wcw91v f b6l7y l2g.t given lens diameter. Explain.

Consider two converging lenses separated by some distance. An objectd,jgg wt-x *g, is placed so that the imagex,,tgj g- g*dw from the first lens lies exactly at the focal point of the second lens. Will this combination produce an image? If so, where? If not, why not?

  Suppose that you want to take a photograph of yourself as you look at yo (q5a 1sj8tweour image in a flat mirror 2.5 m away. For what distance should the camera lwjae1sqt(o85 ens be focused?    m

When you look at yourself in a 60-cm-tall plane mirror, you see the samfy qh w 1xw)59*n8njyfjk,1qbe amount of your body whether you are closkwqy njx f81hw yj1fq) b9*5,ne to the mirror or far away. (Try it and see.) Use ray diagrams to show why this should be true.

  Two mirrors meet at ub 9+ i- 2;zdzxwtu:) qxqnb0ta 135$^{\circ}\,$ angle, (Fig. Below). If light rays strike one mirror at 40$^{\circ}\,$ as shown, at what angle $\phi$ do they leave the second mirror?    $^{\circ}\,$

  A person whose eyes are 1.68 m above the floor stands 2.20 m in front of a vertp+h2u.y0nirw q1/ m mjical plane mirror whose bottom edge is 43 cm above the fl02 qumnim/+yjp . 1rwhoor, (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 fromv tefj)w;w/n8wz-r* r 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 yourr-w ;w*f8en) /v zrwtj pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mtkofs1i-n 73 f1xos,hirrors 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 mio gz(gz-pxf;7 rror pointed at the Sun, focuses the Sun’s rays 18.0fgz(7;xo p zg- cm in front of the mirror. What is the radius of the spherical surface from which the mirror was made?    cm

  How far from a concave mirror (radius 23.0 cm) must an object be placed if its i+c::w9jw, becva271lyazx pimage y1za+:ea2vc,ji 7wx9b pcl :wis to be at infinity?    cm

  If you look at yourself in a shiny Christmas tree ball with o9 cp o6+/nkwxq,l2ry9uqq h5a diameter of 9.0 cm when your face is 30.0 cm away from it/ h w5 xo9uqnkorcp ,9lqy+q62, 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 amusemmv /x5;omg1)am9ru peent park shows an upright image of any person who stands 1.4 m in front of it. If the image is three times the personv9g ;)1 xmema omp5ru/’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror that, when 2a4a dk:/ dq u9h(etq)j6-,x cn mrxir3.20 cm from a tooth, will produce a $\text{4.5×upright}$ image. What kind of mirror must be used and what must its radius of curvature be?
 ----待选择----convexconcave 
r =    m

  Some rearview mirrors produce images of cars behind you that are smallsf1p flb tto(4.wt,(2 dsii:rer than they would be if the mirror were ft1:( f4.s(sbwip trlftd, i2olat. Are the mirrors concave or convex? What is a mirror’s radius of curvature if cars 20.0 m away appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is placed 20.0 cm from a convexj mcz/lch,(kb: +0 +5tkayztb mirror of radius of curvature 20.0 cayk l+k zj5 :,b(c0 th/+mbzctm.
(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 v eg4 mv4oyocdgl: t1+0q9n6o security mirror in a store. You estimate the height of your image to be half of your at evg14o + n0ocl496v: oqymgdctual height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object b gzao4/ nrdc*/lk:6t)s q6l ute placed in front of a concave mirror so that it produces an image at the same locatioadcr6 g 4)ztkq *:ot/nlu6/sl n 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 virtu ):0cihvmkdu. al and very small when viewed in a curved mirror. The image appears to be 18.0 cm behind the mirror. What kind of mirror is it c0d)k hu:im.v, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniques, m8p yap 9z sbr*d:0cy1
(a) a ray diagram,
(b) the mirror equation, to show that the magnitude of the magnification of a concave mirror is less than 1 if the object is beyond the center of curvature $C\left(d_0>r\right),$ and is greater than 1 if the object is within $ C (d_0 < r) $.

Show, using a ray diagram, that the magnification m of a convex mhgpt7vd :t4dqdfi) xxt )u 12l1:3lxfirror 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 for apebpm t3gg sexh(, rfm42/. ( ci:(dtqlcz.f8 convex mirrtm(h:x ier4cd pegf/z ((lm3.8 cfbts2.g ,pqor as long as f is considered negative.

  The magnification of a 4i e i9vbxlt3. pp,j ibd8.x4kconvex 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 it* tu1 z+ p)gejck*e,nn front of a spherical mirror. It is desired to produce a virtual image that is upright and)gt ep tjn1 *c+*zek,u 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 y 3o+suez4p s6u-x6 dffour face by a factor of 1.33 when your face is placed 20.0 cm in front of it.-ex6us+so3d zp f 4fu6
(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 inqqez 21j8v, snw whm3 ,j;cgv-
(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 kg68ngr( 1tshice 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. Wk 6lg(6;rcmvb 15+x6byv rr3p: c iqfuhat is the index of refr1rx6 cvkcr6b 3:v+m6q i5 lgyru;bpf(action of this substance? n =   

  A flashlight beam strikes the surface of a pane of glass (n = 1.58) at ah*h7j ocxv0p 7d i9 5 fmbr(ra5gq0ae9 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashlight upwar 7;bd .:dsalrmk7 ncj6d 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 underwc(/k0sj9*y +p yegmn :b ujdas d1x2mkw(w.* jater spotlight exits the water at an angle of 66.bka1xe np9c 0j sdu* jmg.(+(k mws/d*:j2wyy0$^{\circ}\,$ 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 eq ou )m.qebfkep) wqq8;;jc3nl94mu05 x 6avseen to make a 31.0$^{\circ}\,$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?    $^{\circ}\,$

  An aquarium filled with water has flat glassd4 py*20ce) t/ ztt k-uli.qcs sides whose index of refraction is 1.52. A beam of light from outside the a/.ktd s2t-iuz)y plc04t*q ecquarium strikes the glass at a 43.5° angle to the perpendicular (Fig. Below). What is the angle of this light ray when it enters
(a) the glass, $\theta_2$ =    $^{\circ}\,$
(b) the water? $\theta_3$ =    $^{\circ}\,$
(c) What would be the refracted angle if the ray entered the water directly? $\theta_3'$ =    $^{\circ}\,$

  In searching the bottom of, esczfzv2p /5 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 5vp,z c/e2zs fthe 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 equila8-ty/e m5.; thfoe hgtteral glass prism at a 45.0$^{\circ}\,$ angle to one face, (Fig. Below). Calculate the angle at which light emerges from the opposite face. Assume that n = 1.58.    $^{\circ}\,$ from the normal

  A beam of light in air strcwl yb9e2y- m;ikes a slab of glass (n = 1.52) and is partially reflected and partially refracted. Find the angle of incidence if the angle of rel;9y-cem 2wy bflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam incident on a uniform layer of transparekl gvpf*:/*p6ix e d*pnt material, as in (Fig. Beloex*k *gp *pl6d: vi/pfw), the direction of the emerging beam is parallel to the incident beam, independent of the incident angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on a flat piece of glass with index of refrpzce izcr6i;b)/ab4- 3vu rs9 action n as in (Fig. b )i3rci4/pc z; uvb9ares6-zBelow). 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 ff (a,6)*z sbtmzu :qkdor the interface between water and Lucite? To be totally internally reflectedqt b:f,d(zz) 6 *kusam, the light must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certai rgh +h*en5d/82r ekyzn 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 poomnbk0r (gw.. d5 hujf8l 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 mg85 bf.(n0uw kdh.rjthat the light does not exit the water?    cm

  A beam of light is emitted 8.0 cm8o7an;yd6byjccp4wanab/f s *n+/ f) beneath the 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 the index o6cbs ycja )* /ad 4wnoyfa/pn7;f8bn+f refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes thehkjgx9,e xe5 x p ,qn1)*fi:einpa,1n left face 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 optic fiber as shown in (Fig. kvalg0eqm 9 (t6u8 dh w.2su-mBelow). Show that we can guarantee total internal reflection at the side surface of the material (at point a), if thel vesm6dh tq(uw-a.ug0m 9 k28 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 index2)8t ghz.viw /veqf(x of refraction for a glass or plastic prism to be used in binoculars (Fig. Belw8xh/)gv iv 2fqte(.z ow) 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 78.0 mm behind a 65.0-mm-focal-length converging lens. lko )imlk,2h;pth :es8q-iv0Find the ob;oitkm0 l)vp es2,:ihqhk l-8ject distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focusfb+lsd8x xqm 6 1+k2iajrh5uit . 5tg9 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 axf cuyl3y; ) igbr7/m2n object 2.75 m away as an image 48.3 cm on the other side of the lens. 2x g;bm7 u3r/filycy) 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-lep (0noop otux pd;)pv028kyhccbd401 ngth 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 conl7)auus5d 6- qqhrs:b verging lens with focal length 24 cm to view a stamp 18 cm in fudb6u7 aq hqs5l)-s:r ront of the lens.
(a) Where is the image located?    cm behind the lens (virtual)
(b) What is the magnification? m =   

  A -5.5-D lens is held 14.0 cm from an object 4.0 mm high. What are the position,4q e y2:wzx*trn2/ hvv thv:vr*4tx zw 2/ qeyn2ype, and height 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 on the film of a camera+3rs;f/f x )j5l u 9tz0hwz5 dbdchmw-. The maximum distance allowed between the lens anhw xfr-sdc5u 9zfj3w;0+ 5mbh/)tldzd 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 u* j)*cie/i tk2.5× when a book is placed 8.0 cm behindt ke*i*iu)j/ c 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 doe1nyupu sn. rhh9p(p,7s the image move if the object is moved 19hs (ynph,upp7. n ru
(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 57m8 jn9ekrz.puy0 zwwith a focal length of 25 cm should an object be placed to produce a real image which nu w5 z j7erzp0y.m98kis the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens miw j+x8ey-1 j i6hakhoo1l:takdd)(yw d -k03ust an object be placed if its imageyd-d hk ij t)+wkh1d6aya1(0 i-8w:j3o xloke is to be magnified 2.00× and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm

  (a) How far from a 501vw dacf,s:: o 2nv1yo.0-mm-focal-length lens must an object be placed if its image is to be magnified 2.0ydsw:v,ov1n:f 21c oa0× 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/;te uk/ wgn(x 1.20 m from a 135-mm-focal-length lens. Where is the imx /tuneg w(/k;age, how high is it, and what type is it?
$d_i$ =    mm (real,behind the lens) $h_1$ =    cm (inverted)
(b) What if $f=-135\mathrm{~mm}$?
$d_i$ =    mm (virtual,in front of the lens)
$h_1$ =    cm (upright)

  How far apart are an object and an image formed by a 75-cm-focal-length convergi2b 4/zwp:9r0+g kvgo-ohmp n hypt 0p0ng len9 kpoy0 mg0:+n gp-h0rpzv 4hwt2/bpos if the image is 2.5× larger than the object and is real?    m

  A bright object and a viewing screen are separated by a distance of 66.0.ccmus l /i8r.m/)cpx cm. At what location(s) between the oblc/cc)i..xms/ u r m8pject 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 conw01x2p0 2an8jhoj ape verging lenses are placed 16.5 cm apart. An object is placed 36.0 cm in front of one lens. Where will the jp n80a jpwe02oxah2 1final 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 fj zu,yjf: , 2mnk88bq$f=-31.5\mathrm{~cm}$ 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 conver 2s 6xe;plcb7zpba6 hxd,5t.aging lens is 21.0 cm behind a diverging lens. Parallel light strikes the diverging lens. After passing through the converging lens, the lig pa566.;2hpb s dt,lxcb7azxe ht is again parallel. What is the focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Example 23–12 are now placed onhc;pmm d.1ey1.q75ibys- pwm ly 20.0 cm apart. The objec;s ..cp1 y 7 ydm5qm1hbewmip-t is still 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 placxh++ )xi zevy0ed 30.0 cm apart. The focal length of the lens on the right is 20.0 cm, and the focal length of the lens on the left is + )0+zxeyiv hx15.0 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 length of is placed 12 ch: av q3hll;cyg ) aq;pn88g+** ekuvgm to the right of a converging lens with a focal length of 18 cm. An object is placed 33 cm to the left of the laqgc) pk;u;+*8 v*hg: yhnalve83 gqconverging lens.
(a) Where will the final image be located?    cm to the left of the converging lens
(b) Where will the image be if the diverging lens is 38 cm from the converging lens?    cm to the right of the diverging lens

  Two lenses, one converging with focal length 20.0 cm and one diverging with focft e5gq:;o ol1yxj;:pal length are placed 25.0 cm apart. An object yq:f l:; 5pjxo1 ;ogteis placed 60.0 cm in front of the converging lens. Determine
(a) the position    cm to the right of the diverging lens
(b) the magnification of the final image formed.   
(c) Sketch a ray diagram for this system.

A diverging lens is placed next to a converging len jn4fxnn8dib1o +r( c)s 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 a0e dbdfg:de;; nd 23.8 cm. What is the focal length if n g;eb;:d efdd0= 1.52?    cm

  Both surfaces of a double convex lens have radii of 31.0 c,(pu ;a ec a4q0o:ivukm. If the focal length is 28.9 cm, what is the index4eao ivuq,c:k ;a p(0u of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm. -)tciiec5hua wf mrl2x 4y s)b4g8)wi0p:2mxWhat is the radius of the c42-cbt4 y)i8xxce:m w0s)giahp ui 5mf2r )wl oncave surface?    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat surface and the ot5q gd3:uga orc5*6lc6 0 yx8 d;ixhqdfher has R = -18.4 cm. What is the focal hd; cg6:x38drad 55xfuq i6*0y clqoglength?    cm

  A symmetric double convex lens with a focal length of 25.0 cm is to b8gx *jgrnk9( o p3x aszkbe213e made from glass with an index of refg1g9z 8 ksnxjpk(r2xae 33*ob raction 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 lensma :+zy/uo oq*bxker grinds the lens from a “blank” with n=1.56 and a preformed convex front surface of radius *y obo:zq/+ux of curvature of 40.0 cm. What should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each othe5.k dr.f ekkd(r 2.0 m apart as in (Fig. Below). You stand 1.5 m away from one of these mirrors and look into it. You.e.kr5k (fkdd will see multiple images of yourself.
(a) How far away from you are the first three images in the mirror in front of you?
$d_1$ =    m
$d_2$ =    m
$d_3$ =    m
(b) Are these first three images facing toward you or away from you?
the first image is facing  ----待选择----toward youaway from you ;
the second image is facing  ----待选择----toward youaway from you ;
the third image is facing  ----待选择----toward youaway from you .

  We wish to determine the depth of a swimming pool filled with wahhrj xy 7 0zb1/7pia*vter. We measure the width (x=5.50m) and then note that the bottom edge of the pool is just visible at an angle o iy1ap jb/hr707* vxhzf 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 plastic,d)ybppmp+v25z9kgtccdc ( / in air is $\theta_{\mathrm{C}}=37.3^\circ.$ What is the critical angle of the same plastic if it is immersed in water?    $^{\circ}\,$

(a) A plane mirror can be considered a limiting case of a sphericaln), unu-cfdl 4 mirror. Specify what this limit is. - ),n fdcn4uul
(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 mirrom9y)).fgp1v)o er 7x *g 5apd4syk jqvrs 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 can never form a real image of a rav5m 6irn( wq:1bt ex8eal object. Can you describe a situation in in q(b8w x15r6mate:v which a diverging lens can form a real image?

  Each student in a physics7wa;f*tie9vy lab 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 ;ea fw* t9i7yvthree 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 repeat the lab, and justify your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of as h1n(3n 2lstkv db*y: prism is $\phi=72^\circ$ see (Fig. Below), what is the minimum incident angle for a ray if it is to emerge from the opposite side (i.e., not be totally internally reflected), given $\mathrm{n=1.50~?}$ $\theta_1$$\geq$    $^{\circ}\,$

The end faces of a cylig:+l3 j:mqc wxndrical 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 y:sb *muu5oq1 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 one side of a converging lens of focal lengthu(* ;igv1x asl f, and a white screen for viewa (;i*s1l xvguing 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 aco eo c92di; d x/c7j6(cuadr6r wp6x:s)gbz;uts as the object whose image is projected on a screen (Fig. Below). If a 105-mm-focal-length lens is to project an image on a screen 8.00 m away, how far from the lens should the slide be? If the slide is 36 mm cpb d:g/rrjux7; x usc)9oz;c6ad2dei6wo( 6 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 to be projectedwxs *d;)ez mm+ on a screen 1.80 m by 2.70 m placed 7.50 m from theswzx )m* ;+dme 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 converg ).n6d,imjrccjs95mm tqum 25 ing lens is real and inverted if the object is beyond the focal poij ju dm 29).i5mcrm6ncqts,m5 nt $(d_0>f),$ 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 j . pjfa6gk* p*voav/pl)(9cpclaims the reporter was trespassing. To j.* ojvv)g*/p(6akpp ap9fclprove her point, she gives as evidence the film she seized. Her 1.75-m height is 8.25 mm high on the film, and the focal 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 idcd*lg2(b8ha 7ed, csn 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 fron1.i skv*+zle dkmy -i)t of that lens (on the sazs1di+ilekk )m- * v.yme side 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 certap-whx- .qp7i kin converging lens, it forms a real image. When the object is moved to 40.0 cm from the lens, the imppx.-w7 - hiqkage moves 10.0 cm farther from the lens. Find the focal length of this lens.    cm