What would be the appearance of the Mot2o ,eh8c, nc;yutn)eon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fleet in the harbor of syj un88(d 2l*kq(p3fprl.b rSyracuse by focusing the rays of the Sun with a huge spherical mirror. Is this reasonable . ( ylbr *sppd3lurfq(8j2kn8?

Although a plane mirror appears to revers,fgtcx++ gkd/e left and right, it doesn’t reverse up and do,/+dxgc+f tk gwn. Explain.

If a concave mirror produces a real image, is the image necessarily inverted? E2y jjrfm+hh (rrc)-9+: qzv yv: rz1kdxplaincy rvrf)-+h2k+qdz :: mh9rjyr(1jvz.

An object is placed along the principal axis of28 mg 7dueb 6g /-bgly4yb1x9:skjigf 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 which side ofybs lb/ix8m gg 2 ed:g-jkyb4169f7gu the mirror is the image located?

Using the rules for the three 8 j9,oll nmrc)rays discussed with reference to (Fig. Below a), draw ray 2 for,rol9j n8 m)lc (Fig. Below b).
(a)
(b)

What is the focal length of a plane mirror? v o;):x6 tiqnoWhat is the magnification of a plane ox:t;nov)q6 i mirror?

When you look at the Moon’s reflection from a ripply sea, it appear vu,1f4l 2g3iefssu3 rs elongated . Expl2i 1egsfur3usl v34f, ain.

What is the angle of refraction when a light ray meets the boui(gps2m.v cu 0:p+/h vipomu,ndary between two materials perpeup+c/pug2i(i 0. v,ovmp hsm: ndicularly?

How might you determine the speed of light in a solid, rectangular, transparent ae8/ rta6ex*j(j xa;a aa6 r8(jex e*t a/;jaxobject?

When you look down into a swimming pool or a lake, are you likely to zbv4b 0nj /h.dunderestimate or overestimdbb/h4zv 0. jnate its depth? Explain. How does the apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks bent when part )(3w(kde qjn:1/hq,,akkp lt/qo pph of it is under water (Fw k,lkt:/ k3q1h q(qeph( ap)do,p /jnig. Below).

Your eye looks into an aquarium and views a 64hn- /l jdqupfish 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 drawing, indicate the approximate position of the u nd46/qphlj- actual fish. Briefly justify your answer.

How can you “see” a r4 i1 8sht*zjhround drop of water on a table even though the water is transparent and colorlt18zrj hsh* 4iess?

When you look up at an object in air from beneath thl)tgoscg;v/9rrk3z.. +z v q ua* ietn1*g.cke surface in a swimming pool, does the object appear to be the same size as when you see it directly in air? Expla)t.gv.esc.qli1tr3v u no c +kr * gz/zg9;ka*in.

How can a spherical mirror have a negative object distancramif: tr, + 88zfd7mn;n ;trre?

Light rays from stars (including our Sun) always bend toward the vertih-f +t5tixpc; cal direction as they pass through the Earth’s fttc 5p;i+hx- 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 sharp 3. cik, xcbhx3*2dmck bmj/rcv4r,8z image of an object very far awb., dx3i2rmzhk*/ 4jrcc v ccx8,mkb3ay?

What type of mirror is shown in (Fig.gzk rp5y65 l,l Below)? Explain.

A photographer moves closer to his subject and then refocuses. Does the camerabi46.gx be-n lqh7v .l lens movg.h 6vb7 4 ilqbnl-x.ee farther from or closer to the film? Explain.

Can a diverging lens form a real imaget.r)ajmbp : .r under any circumstances? Explain.

Use ray diagrams to show that a real image formed by a thin lens is a,k1:ppr(eqq b lways inverted, w,qk:qrbp ( 1ephereas a virtual image is always upright if the object is real.

Light rays are said to be “reversible.” Is this consistucb5giay-g ,/h66m i ient with the thin lens equation? Expl m6ii-5hgg6cu/ia,b yain.

Can real images be projected v5fev29fcs:y on a screen? Can virtual images? Can either be photographed? Disc:vv5sce2yf9f uss carefully.

A thin converging lens is moved closer to a nearby object. Does the ruk;ew;l0 o cr:nfl*dpk:qa/ .eal image formed c;q/l f c .p :0wnu;kkaod*elr:hange
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of refraction n ( o,u*t*p-w0s)hgfv vfeje , m= 1.30 In air, it is a converging lens. Will it still be a converging*)(jw*s v eufhptvm,-geof ,0 lens if placed in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air standhe5efx p0,z6 ys facing a converging lens. If the nose and the tail are each focused on a screen in turn, which will have the greater 0,eye5h z6 xfpmagnification? ----待选择----nosetail 

A cat with its tail in the air stands facing a converging lens. Undhk;ghv :8nbz3er what circumstances (if any) would the image o:;hhnb8 kg3vzf 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 havhs4 t::il ndythy, g 9ue;*a0oe a shorter focal length than the diverging lens if the latter’s focal length is to be determinygauy 4tdh9ne0 ::;o*s, itlhed by combining them?

Explain how you could have a virtual objec 26*tqqq; )dgah jg2vst.

  An unsymmetrical lens (say, planoconvex) forms an image of a nearby object.a y.ozq:b9w)ivg 2 ju5 Does the image point change if the ib2oyq)zav9 5:u gjw.lens is turned around? ----待选择----yesno 

The thicker a double convex lens is in the center as compar-s1+xq i 2chakf2qwo qw 22.kxed to its edges, the shorter its focal length for a given lens d22 qswk aki 2.q1ofxxc2wq- h+iameter. Explain.

Consider two converging lenses separated by some distancvk (rzye;6 2gfe. An object is placed so that the image from the first lens lies exactly at the focal point of the second lensr2evf g(;6k yz. 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 imaggb 6/ izl mgge ;lni (1dxalh10j-5s8ze in a flat mirro( lln sgi- ;g5zz1dbae1i hx m08gl6/jr 2.5 m away. For what distance should the camera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mirror, you see the same amouid/qwqck-/ y-)wm 1j snt of your body whether you are close to the mirror or far away. (Try it and see.) Use ray diagrams to show why this shouliq/mwj c qw-/)k1s-ydd be true.

  Two mirrors meet at a) gy;olb .m1 nbx 2tz3b v2iu5;n5qvfl 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 s 6o5b6ob0 pdnhtands 2.20 m in front of a vertical plane mirror whose bottom edge is 43 cm above the floor, (Fig. Below). np66hd 0bb oo5What is the horizontal distance x to the base of the wall supporting the mirror of the nearest point on the floor that can be seen reflected in the mirror?    cm

  Suppose you are 90 cm from a plane mirror. What area o cm+ qpd,.fe)of the mirror is used to reflect the rays entering one eye from a point on the tip of your nose if your fdo .,eqmcp) +pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane 9vjmrd :opmk,fg89 .e mirrors 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 poineu2t jv4 zf g)aq--9iqted at the Sun, focuses the Sun’s rays 18.0 cm in front of the mirror. What is ji94z2e-ag- q)vtfu q the radius of the spherical surface from which the mirror was made?    cm

  How far from a concave mirror (radius 23.0 cm) mvbo*n, fpl zqg-el) 80wm1y6 wx4mry fpn:;+eust an object be placed if its image is to bmf foe p8;y4 *zv06lnpne+-gm)1,q xy l:rww be at infinity?    cm

  If you look at yourself in a shiny Christmas tree ball with a diamgv hxic6u/d::eter of 9.0 cm when your face is 30.0 cm away from it, where ig: u6/:cvihx ds 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 upri5azk9/p kisd,qd:w6iq vp5 i xh;(r 4gght 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 of c 4z5sdpi9 kpri;g/q,6vdhi:5wkax(qurvature?    cm

  A dentist wants a small mirror that, when 2.20 cm from a tooth, will produce 1w44pxcmfz 089pm/ltuvn 7nla $\text{4.5×upright}$ 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 imayfr jq s99z4t(-x-vz yi.+0dbynj5 qeges of cars behind you that are smaller than they would be if txy4n(y -rzfd9 ey0+bzqtqjs 9 v-i5j .he mirror were flat. Are the mirrors concave or convex? What is a mirror’s radius of curvature if cars 20.0 m away appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is placed 20.0 cm from a convex mirror of7bulhxqp38 0wxj i 2v/ radius of curvature 20.0h3qlx xu 8wbi7 /0j2pv 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 6d) vz)pu*/r d5dwil tm from a convex security mirror in a store. You estimate the height of your image to be half of your actual height. 5vdi/ )6w*uzdlptrd )Estimate the radius of curvature of the mirror.    m

  (a) Where should an object be placed in front of-6gwvfc/ p)zuu6 ix 5o a concave mirror so that it produces an image at thefi 6ouw-)v/x g 6zu5pc same location as the object?
(b) Is the image real or virtual?  ----待选择----realvirtual 
(c) Is the image inverted or upright?  ----待选择----invertedupright 
(d) What is the magnification of the image?   

  The image of a distant tree is vir x)6pwdjtc3 vu2d* o5vtual and very small when viewed in a curved mirror. The image ap5vo *)xtc6wj dvp23ud pears to be 18.0 cm behind the mirror. What kind of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different te6dvb.dgtm/r-52d;,*l7w uko vt snapchniques,
(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 convz )7o 9 wdlur(1.ajisdn (cy6sex 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 mpv-,zp i9 t o:ej.q6hgxb ix:)irror equation, Eq. 23–2, is valid for a convex mirro bxhv6jz,egi9) : .op:i-xqptr as long as f is considered negative.

  The magnification of a convex mi mbmr:qten2u, 1 o 3yly404n13xifujerror 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 2rqeo op*0.-pp8 cm in front of a spherical mirror. It is desired to prpqp.po*eo0-r oduce a virtual image that is upright and 3.5 cm tall.
(a) What type of mirror should be used?  ----待选择----convex mirrorconcave mirror 
(b) Where is the image located?    cm behind the surface
(c) What is the focal length of the mirror? $f$ =    cm
(d) What is the radius of curvature of the mirror? r =    cm

  A shaving/makeup mirror is designed to magnify youn :zevdzo(v w,g:i-e-r face by a factor of 1.33 when your face is placed 20.0 cm in front of it. (zov-,e dng:eziwv -:
(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 io cvyx 9vvy*jz pi :74j(7wq+0l+e eopn
(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 )j33qjccy,c,m;hn srice 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. --p44 +4vd/gv fn)tnzppnoh aWhat is the index of refratnhp)44af-novzpv g+ /- pdn4ction of this substance? n =   

  A flashlight beam strikes the surface of a pane of glass (n7t;pc ;:iukm8cb jms9 = 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 beneath the water at a 42.5.2zxxoa)nv; reqhdd85 4i :bqizy0+ c$^{\circ}\,$ angle to the vertical. At what angle does the light leave the water? $\theta_2$ =    $^{\circ}\,$

  A light beam coming from an underwater spotlight ergzj t7:r12l bxits the water at an angle of 66.rb1 2t7: glrzj0$^{\circ}\,$ 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 kql-8hgrd4 u9 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 glassw n1i*l3ax7 sf 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 lnsil 1x*7fa w3ight 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 a narrn,b,rr x 2 kuh49-iye,.il/vehb8zxvow 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 .vvilb ,r-hk 8,eehz/ 2x9 nbiur x4,ythe bottom of the pool, measured from the wall beneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equilateral glass prism at a:f:4aowqf d, +tyz,a1wrt: em 45.0$^{\circ}\,$ angle to one face, (Fig. Below). Calculate the angle at which light emerges from the opposite face. Assume that n = 1.58.    $^{\circ}\,$ from the normal

  A beam of light in air strikes a slab of glass (n = 1.52) and is partially ql )2hikttyf6(w m.q-c2q/ uqreflected and partially 6c 2q/twqth)mlqu2iqyk. -(f refracted. 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 253ma ;pl pkypa uniform layer of transparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the incident be52ylap3ppm;k am, independent of the incident angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on a flatp: b(hc ,*7qagzmp1g g piece of glass with index of refraction n as in (Fig. Below). Show that if the incident anglgq*b (z g,:c 7hpap1mge $\theta$ 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 n hckc-,i09 61ktt :lsduq;sx between water and Lucite? To be totally internally reflected, the light must start in which material?:uxn k0s -i9st16 lqdhc,k ;ct
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–air surface is goat:ok;- 0it kr+p2t 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in a poolv8cvg nrm9z2dn*o +s; 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 no;d2+rvm89 zsnvgco *nt exit the water?    cm

  A beam of light is emitted 8.0 cm beneath the surface of a liquid and strikes th-pzm)md*iv *ukunnb +9 gt3e4 e surface 7.0 cm frv9mi*4u* n3mbednk )-utp zg+om 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 of the prism in (Fig. Below) at 45.0bqp2m7wrzxzyew+e8(lb1 i ,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 showngt 881j(c+ sc+v prejn in (Fig. Below). Show that we can guarantee tv rjje1(8ps8ngt +c c+otal 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 na m ts 2p 2l0yh8.pcsde+,2ice:g5e wrefraction for a glass or plastic prism to be used in binoculars (Fig. Below) so that total internal refwesntc0 2he8lei2cy, s2ad. mp:+ gp5 lection 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 convergitmj95 7 d,w;;lrr)gwls 8 xepsng lens. Find the ssr 7 8x)jdgww, 5p ;9l;ertmlobject distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to foqqp ht8j9 5qv2- *d: xccj4natcus 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 an object i4v 8gk*tm9mw2.75 m away 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? Is the 8ik4wmm vtg9* image real or virtual?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the power of a 20.5-cm-focal-length lens? P = jsg5+ujvf/6 d ( -nspi   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 cm to view i(q-n1iqehpu r c.5b 8a stamp 18 cm in fron uhni.q1cqrpb8 ei5(-t 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 positionw0v,9ap1yt xj5krvnzj1 sm+ +, type, and height of the image?pza0m1 v9+s, 5yvkj1 nxwjr+t
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to fwrjt70y.ijrnh hl7+ : ocus an image on the film of a camera. The maximum distance allowed between the lens in 7 r+0twl hjhrj:.y7and 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 magni)8kaf:r p.4gpz db 2ryf( bcnwg7m8l:fy reading material by a factor of 2.5× when a book is placed 8.0 cm behigbfm7:42dy z.)( npr8c8aw f r kp:glbnd 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 the image movgbbrt 2 4kl;+:a:zpbpe if the ot b;grl :ak p+p2bzb:4bject 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 lengter*r2kg 18b qfh of 25 cm should an object be placed to produce a real image which is theekfb81rr2*g q same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length f, dzm3 e4qb vp2q*o)zlens must an object be placed if its image is to be ),omz *qfq4 z2 bedpv3magnified 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 objecq; 9w1i un-u* tmqjg5lfg99+ +en kgjdt be placed if its image is to be magnified 2.00× andqtgn9qi9+*5ul gd 9 1kmwj fg+u;e n-j 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 z r3:x/e3f,a0fa+a os: sfjv xis 1.20 m from a 135-mm-focal-length lens. Where is the image, how high is it, a,jvzfxa :f+ax:of0 r3/e s3sand 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 convergijoyuhl-a f5 1r5 tisxy. z*r18ng lens if the ir*ujzylyt 5a.1s8io5 hx -r f1mage is 2.5× larger than the object and is real?    m

  A bright object and a viewing scr5tc2ryz - py71eey n-neen are separated by a distance of 66.0 cm. At what locationny e n-ry2 t-51cyezp7(s) between the object and the screen should a lens of focal length 12.5 cm be placed in order to produce a crisp image on the screen? [Hint: first draw a diagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length converging lenses are placed 16.5 cm apart. An 1 :9/wgszvc/b f8d1h3v cp pjgobject is placed 36.0 cm in front of one lens. Where will the final image formed by the second lens be located? What is the 1/9csbwpg1gv:dfz c/3jv ph8total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens with hqyasq, :gaymw1x,+8 $f=-31.5\mathrm{~cm}$ is placed 14.0 cm behind a converging lens with $f=20.0\mathrm{~cm.}$ Where will an object at infinity be focused?  ----待选择----realvirtual ,    cm beyond second lens.

  A 31.0-cm-focal-length converging lens is 21.0 cmlh376 psf esv+4nws5/jv v gp: behind a diverging lens. Parallel light strikes the diverging lens. After passing through the converging lens, t57jsf+ : 6gvn pwl3pse/vs4hvhe 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 Example 23–12 are now placed o+w mcgl1s5ymjm n,f7;nly 20.0 cm apart. The object is still 60.0 cm in wmf gc+,17l5yn m;sm jfront 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. The z76ttg g +f-xefocal length of the lens on the right is 20.0 cm, and the focal length of the lens on the left is 15.0 cm. An object is placed to the left of the 15.0-cm-focal-lentzef gx6 -7+tggth 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 cm to the right gg:w 47+3sc qw0zk;is:zc 3mswumr* nof a converging 0wq cwim :m3r4s: *;gz+u 3scwz7ksgnlens with a focal length of 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 ,pj b,io5qa95e ta v8blength 20.0 cm and one diverging with focal length are placed 25.0 cm at55 ja,,9 bpaveqbi8opart. An object is placed 60.0 cm in front of the converging lens. Determine
(a) the position    cm to the right of the diverging lens
(b) the magnification of the final image formed.   
(c) Sketch a ray diagram for this system.

A diverging lens is placed next to a converging lens o6f e4 2dvg( uh5tz0q*;tj;q wn;hvuy sf focal length $f_C$ as in (Fig. Below). If $f_T$ represents the focal length of the combination, show that the focal length of the diverging lens, $f_D$, is given by
$\frac{1}{f_\mathrm{D}}=\frac{1}{f_\mathrm{T}}-\frac{1}{f_\mathrm{C}}.$

  A double concave lens has surface radii of 34.2 cm and 23wgjy7v /i:q4 f.8 cm. What is the focay4wv:fiq g7j/ l length if n = 1.52?    cm

  Both surfaces of a double conveja w( c) 6wxjp:ltn7hl)ry 3x2x lens have radii of 31.0 cm. If the focal length is 28.9 cm, what is the index of refraction of the lens matehw)3a2 nx l6j:y)7lcxj(twp rrial?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm. What is the radius omq cc6q 0gfvb65*b vzl26 us/xf the concave surfacv sq60cq6m vuf2bc/6bg5l xz*e?    cm

  A Lucite planoconcave lens (see Fig. Below) hviwl(p v4;r h;as one flat surface and the other has R = -18.4 4hvp;i; w(rlv cm. What is the focal length?    cm

  A symmetric double convex lens with a focal length of 25.0 cm is to bi h w*9 e0if.o;z4aol.en6 urqe made from glash ezoa iil0r6w4;.nuqf.e* o9s 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. Th o3tegl+f 7vmy9f -u5zr p9:l.xn7a hle lensmaker grinds the lens from a “blank” with n=1.56 and a preformed convex front surface of radius of curvature -fgp l39 5.m79o uet+hzl v:yrxnla7fof 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). You 40wo eek )*hs.g fozk7rpa8c5stand 1.5 m away from one of these mirrors and look intaprs5ee.fo8w0okc z)* h47g k o it. You will see multiple images of yourself.
(a) How far away from you are the first three images in the mirror in front of you?
$d_1$ =    m
$d_2$ =    m
$d_3$ =    m
(b) Are these first three images facing toward you or away from you?
the first image is facing  ----待选择----toward youaway from you ;
the second image is facing  ----待选择----toward youaway from you ;
the third image is facing  ----待选择----toward youaway from you .

  We wish to determine the depth of a swimming pool filled with n8sj,v0 n:spmpl,2:)q m rardwater. We measure the width (x=5.50m) and then note that the bottom edge of the pool is just visidpp vs)mqjrns m0:: l,a,r82n ble 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 plastic in ai +z5n7gtat3 bid u4kx5r 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 iakyquy 5 h3 /7+o.ujaconsidered a limiting case of a spherical mirror. Specify what this limit h qo3u kuiy+7/.5ayajis.
(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 fs) co*y64 ghweidxol+* 29i aaorm 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 im9mlqm9y y/esri5 6hmh,j )tcrc8: h2b4l q6fbage of a real object. Can you describe a si6l: 9 /mrlhbj8 mt hqmqfbc9ehir ),y 6sc25y4tuation in which a diverging lens can form a real image?

  Each student in a physick 8nc r cw07vwyw/,*1ex x/fgrs 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 three times the size of the object. Two sy8xcnw f,kw*1 /c /wg0rxv7ertudents 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 a pv p,y+btgu15z5al: fj, ;va+ ty uue-arism 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 cylins3 vo x +3no::k ri)uv 9+-ehxmicyzh9drical 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 convergiogxc b sdr)t5q9 3-2lbng 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 length f, ak ,(:. ggktn7qhf/.qsso/89cdr qrmlnd a white screen for viewing the image is . ogl7. n9qqfg (k/m8h/crrs ks,:tdqon 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 asr. slezh nn3kraar)-,* y . 3bvb/jps; 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 picture be on the scrp rksz-b ,;jr. hnv rs*/3n3.e )yaalbeen? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (picture siusu o8se2d-s)ze is 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 screen8e2s u-d) ssuo?    cm

Show analytically that the image forpe nzo. 9su;/3 cbb2txmed by a converging lens is real and inverted if the object is beyond the fo .;/z exbcnos29bt3 upcal point $(d_0>f),$ and is virtual and upright if the object is within the focal point $(d_0>f),$ Describe the image if the object is itself an image, formed by another lens, so its position is beyond the lens, for which $-d_0>f$, and for which $0$<$-d_0$<$f$.

  A movie star catches a reporter shoo8+v7 +d4r6oiz h vqbywting pictures of her at home. She claims the reporter was trespassing. To prove her point, she gives as evi4w ibvyzh+8qro7+d v6dence 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 image0 ,cne e+w4yxf;oa6td of the Sun on film used in a camera with
(a) a 28-mm-focal-length lens,    mm
(b) a 50-mm-focal-length lens,    mm
(c) a 135-mm-focal-length lens?    mm
(d) If the 50-mm lens is considered normal for this camera, what relative magnification does each of the other two lenses provide? The Sun has diameter $1.4\times10^6\mathrm{~km},$ and it is $1.5\times10^8\mathrm{~km}$ away.    for the 28 mm lens    for the 135 mm lens.

  (a) An object 34.5 cm in front of a certain lens is imagednlp s4xo khm60xd*pj n3()l,bn8yp,y 8.20 cm in front of that lens (on the same side as the object). What type of lens l04yy lb n s,8)ppm6*kd3on,(nx jphx 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)