What would be the appearanch ofyvb /ww x*c:i:8-te 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 inl-kpr5avz- kae8xt y0q*h: m7 the harbor of Syracuse by focusing the rays of the Sunt*kazv8: l -r k5 hpa7yxqe0m- with a huge spherical mirror. Is this reasonable?

Although a plane mirror appears to revexdc 2c3w;uv6u rse left and right, it doesn’t reverse up u 3 ;2dx6vuwccand down. Explain.

If a concave mirror produces a real image, is the image necessarilyp1op+fd i0twv9vq55, 0uu7 ddawix i9 inverted? Explain.x 9u t ,iw5f7dvui01pdv+9idwoq5ap0

An object is placed along the principal axis of a spherical mirro65 )o 3 al5abri6d93srzqmsdn r. The magnification of the object is -3s)z3rnia65lq35a6ods mdbr 9.0 Is the image real or virtual, inverted 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 discussed with reference to (Fig. Beo om8prha,6 s4w-e qsw167 q,xccuci( low a), draw ray 2 for (Fig. Bel7 swc,i6c6 p -s1r8w4qox (omqaehcu,ow b).
(a)
(b)

What is the focal length of a plane mirrore el aeb1ydvq90 .45le? What is the magnification of a plane leyvl. 954 e1qdb0eaemirror?

When you look at the Moon’s reflection qu,khmsp(( 2 p6j)kmb from a ripply sea, it appears elongated . Explm62h (b,) ujkps( qmkpain.

What is the angle of refrnm05zbuq 0f 6vf* rd)yaction when a light ray meets the boundary between two materfq5y zn* 0du6bf0)rvm ials perpendicularly?

How might you determine the speed of light in a s 1/qsoewh,y x: 4jx v1m3zorsb n. uhj.oi8*+qolid, rectangular, transparent object?qs4:u81v.wihexh/1,3 qomy.ro b*s+j oznj x

When you look down into a swimming5;+u-a 1 hzwtemxi;hl pool or a lake, are you likely to underestimate or overestimate its depth? Explain. How does the apparent depth vary with the viewing angle;w axz+i ml5tu1h; e-h? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks bent whenpwpi /k:cg 5-w part of it is under water (Fig:5 wwi-p/gpck . Below).

Your eye looks into an aquar6oi+v9vja oivz(1x.acjtokn* +66rv/bj3laium and views a fish inside. One ray of light that emerges from the tank is shown in (Fig. Below), as well as the apparent position of the fish. In the drawing, indicate the approximate poscvo txail / jo+an1v 6v*k.3(6brvz6+iajjo9 ition of the actual fish. Briefly justify your answer.

How can you “see” a round xcebrb n.gkpf1r.y:+v0 ws 0, drop of water on a table even though the water is transparent an.nrs0vc0.b g+ypb k 1fw:x,red colorless?

When you look up at gef h+jfp c07,nz7)d/;6p jpc9ckxa wan object in air from beneath the surface in a swimming pool, does the object appear to be the same size as when you see it d0 ez f7wj/;xf6 kpnch),pcg+ 9ajp7dcirectly in air? Explain.

How can a spherical mirror have a negative object distan0c;zew3mukjc a ;/j8ac v7cr/ce?

Light rays from stars (incl n* j h6ygz d3.hsln;d7uu+3ppuding our Sun) always bend toward the vertical direction as they pass through the * ; h+nyj6ug dpl.ndh37u zsp3Earth’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 mu s. u,6rzrz* (8gk) w 5zqsdnhso26bbake a sharp image of an object ve 8*u(6rq.dw5rzhkz6) ,2 s unsg zobsbry far away?

What type of mirror is shown in (Fig. Below)? Expbi ,n u)lt678gfsd92ytj:s ix lain.

A photographer moves clo.j.e lrapm1t 8ser to his subject and then refocuses. Does the camera lens move farther from or closetl.mp a1j. 8rer to the film? Explain.

Can a diverging lens form a real imag0-x4f gcqq*ww- p26 4ya1chgh ns6cwue under any circumstances? Explain.

Use ray diagrams to show that a real image formed by a thin lens r.gzvz nmi-z4qu82 g+ is always inverted, whereas a virtual image is always upright if the object is8zr 4iznm .-g2uqgvz+ real.

Light rays are said to be “reversible.” Is this consistent with the thx i7y5ym19r scin lens equation? Explainx5y9c mr1s 7iy.

Can real images be projected on a screen? Can virtual images? Can either bejlolt,dx 5e 08 photographed? Discuss ca5,djeoxl0 l8 trefully.

A thin converging lenyfgleu ;)w n(l0jkumie/:8: hs is moved closer to a nearby object. Does the real image foj 8:elmhfe; i kgu()y0 /u:wnlrmed 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 In air, it gm+ks p49rnpyx+e 6 *fis a converging lens. Will it still be a converging lens if plmr*k +6e4y n+p9gp sxfaced in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in . i9gblw :9ixrob;6hpthe air stands facing a converging lens. If the nose and the tail are each focused on a screen6ibirh o9: xw;pb9g.l in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facing a converging lt8 7l; mmja1avens. Under what circumstances (if any8vm1 a;lm atj7) 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 focal length thanf wj;,s f( 0*u2z jcxt+15vyos/owxnb the diverg/ x0u(fz,*;2tc s oo5 f+bjjxws1vynw ing lens if the latter’s focal length is to be determined by combining them?

Explain how you could have a virtk -ca9m* bx4wnual object.

  An unsymmetrical lens (say, fl scc.u,2, smn mam)dl)u)t) planoconvex) forms an image of a nearby object. Does the im.)s atfdc),) ) l ,uucnm2mmlsage point change if the lens is turned around? ----待选择----yesno 

The thicker a double conveb v 41)ajux krz6bsb 15-it.6sf8z nrlx lens is in the center as compared to its edges, the shorter its focal length for akr5 1sivub)b-ztnraj6lx s6 bfz 814. given lens diameter. Explain.

Consider two converging le i,3n-zwxwpg8nses separated by some distance. An object is placed so that the image from the first lens liw8,n- p zwxg3ies 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 /f6ralwsp8fab a:4ik7gi zk 3k+ds)5 yourself as you look at your image in a flat mirror 2.5 m away. Fkiik f wbsa/) f3k84r:6l7s5z pd+ag aor what distance should the camera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mazut53zsu (l:2+jze kc j pa:(irror, you see the same amount of your body whether you are close to the mirror o z2 kz:luje a+za c(3uts(:p5jr far away. (Try it and see.) Use ray diagrams to show why this should be true.

  Two mirrors meet at a 135*owrb , xj xfi30b4mu)$^{\circ}\,$ 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 oi wt/3rustv4(ys /e 0m above the floor stands 2.20 m in front of a vertical plane mirror whose bo y(0svt3tw /o/ u4esirttom edge is 43 cm above the floor, (Fig. Below). What is the horizontal distance x to the base of the wall supporting the mirror of the nearest point on the floor that can be seen reflected in the mirror?    cm

  Suppose you are 90 cm from a plan zvb4k.we*fe i7hk7g; e mirror. What area of the mirror is used to reflect the rays entering one eye from a point on the tip of your nose if your pupil diameter is 5.5 mm4i7v w7 k;fg*hzk.bee?   $\times10^{-6}\,m^2$

Show that if two plane mirror nknni4o1zkhybm;(e2c-3qa j 1e02 zy /v cyp-s meet at an angle $\phi$. a single ray reflected successively from both mirrors is deflected through an angle of $2\phi$ independent of the incident angle. Assume $\phi<90^{\circ}$ and that only two reflections, one from each mirror, take place.

  A solar cooker, really a concave mirror pointed at the Sun, focuses thre)8 e6dw(9ch; 0bkqimrd ,qje Sun’s rays 18.0 cm in front of the mirror. What isjr bq6c0), qe9mr8id(hkwe; d 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 i e.erouod.* 1 t xmnh689gclj2ts image is to be r8tn6j oeohed9xgu.*2lmc 1. at infinity?    cm

  If you look at yourself in a shiny Christmas tree ball9yuf1qi rk8f2t. rk)m with a diameter of 9.0 cm when your face is 30.0 cm away from it, where is your image? Is irrf.91 mk 82ukt)qyfi t real or virtual? Is it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shows an upright d1d*dnjk) cu 2*/ftimimage of any person who stands 1.4 m in front of it. If the imagefukitdm n1/*2d d*c)j is three times the person’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror that, when 2.p ctl:y319;mym mgr 1g20 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 smaller tha2pgfe+s.ckdu 3moqb;0ti a)0n they would be ioka3t0+mqus.;e )p2g ib0d cf f the 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 co/5n i0 :ili ijamav0k8bqo/ *snvex mirror of radius of curvature 20.k5b0ma/ as8iij vqi o/*0n :il0 cm.
(a) Show by ray tracing that the image is virtual, and estimate the image distance.    cm
(b) Show that the (negative) image distance can be computed from Eq. 23–2 using a focal length of -10.0cm
(c) Compute the image size, using Eq. 23–3.    mm

  You are standing 3.0 m from a convex security mirror in a store. You estimate thru 1pkias555g e height ogr5 1 i5su5akpf your image to be half of your actual height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object be placed in frhxtnp :vugy(/p;47 +i)gm 6c up.kudmont of a concave mirror so that it produces an imag7+uc;g /yn:g uhvx )4.p6pidt(ukp mme at the 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 virtual3bb6 x8 hl2upj zh1m9m and very small when viewed in a curved mirror. The image appears to be 18.0 cm behind thjupbhlzmbx3h612 8 9m e mirror. What kind of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniqhe,/ld :(it/ cioa kadtru+41ues,
(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 magnifi q5nzkw(py1:p anf.lvl:wa7 3cation 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, 64x ii+lkmxs :foie7-is valid for a convex mirror as long as f is considkx4-of i+m l6si7i x:eered negative.

  The magnification of a convex m8w,xf-6zmlur*d*yrs tw /g5it( c) jkirror 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 froqp ftrdf+wi6kv ,+)f9nt of a spherical mirror. It is desired to producf9 ,p+ tf+frqv wk6di)e 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 your face by a factor of 1.33 wh/on-j m(8vgenkb44 .rf :ghcaen your face is placeg4mh b/f(g: ak4.cno-jen8rv d 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 ligh2dmqz+j p5kdp* je ;itbxs 068t in
(a) crown glass,    $ \times10^{8 }\;m/s$
(b) Lucite,    $ \times10^{8 }\;m/s$
(c) ethyl alcohol?    $ \times10^{8 }\;m/s$

  The speed of light in ic,wcsonj nh: x 6e.y5.be is $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light inwtic- p-l3/znno8 pe 3 a certain substance is 89% of its value in water. What is the index of refne-oln83w/ 3 -ptzp ciraction of this substance? n =   

  A flashlight beam strikes the sur t)l lkqf1r3v.tkst) r/jv.k8face 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 flashlight upward from beneath the water atop(ek okkh)7 * c(tx,y a 42.5$^{\circ}\,$ angle to the vertical. At what angle does the light leave the water? $\theta_2$ =    $^{\circ}\,$

  A light beam coming fjq*pc k77j -jzrom an underwater spotlight exits the water at an angle of pjjz 7kcj *q7-66.0$^{\circ}\,$ to the vertical. At what angle of incidence does it hit the air–water interface from below the surface? $\theta_1$ =    $^{\circ}\,$

  Rays of the Sun are pdmp to3+hc* sge 8g(v+b7u: *w1kp,ovmjls ;seen 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 glass sidjs5; kqe elb6j)iu3 jl yfw035qp ;c5yes 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 thisp5yc b0l65k; 3q)eqy j3w;5sjil eu fj 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 watchma )ny 4, cn3tox22x qnd*ky8uzan shines a narrow beam of light from his flashlight, 1.3 m above the water level, onto the surface of the water at a point 2.7 m from the edgax)xnt22 n ,o8z d*ny4q3cukye of the pool (Fig. Below). Where does the spot of light hit the bottom of the pool, measured from the wall beneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equilateral glas7gwp3da w kv8rupvj +4n (0y5vs 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 strikes a slab of glass (n = 1.52) and is pa yw+0y vve;9w fxs py-l20;vxfrtially reflected and partially r v+-yv yy2 ff0;0ww;9sxxpe vlefracted. 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 layer of transjud6tft8v- s ;qg-5 zjparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the inci;d86tq ju vzgj --ft5sdent beam, independent of the incident angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on a flat pis h3yx( g,bfeben7m .-ece of glass with index of refraction n as in (Fig. Below). Show that if the incident angle(,3.xnbsh yeefm7g -b $\theta$ 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 Lucite? To be5 htm9wwlg5kd;,n z bo gic64- totally internally reflected, the light must start-w9hgt z4w 5k5b6,;cdlmgnoi in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain li+b0 qw-7+0yhb wy/.n9b srp.yymxltpquid–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 debq(d y *y kw0j-4u)pnwf9ns/do9b+gp pth of 62.0 cm. Where must it strike the air–wd 4pun/()*ps-bwbnk jqd+9wfy0 gy9 oater 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 8rojzpye)8 uet1, :i( z.0 cm beneath the surface of a liquid and strikes the surface 7.0 cm from the point dire)zz:p1 yuet (oe, 8ijrctly 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 rws6a.ssd1 )u a;jo+p 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 9g3p(jgxx sag:s;p6q/bg jz6an optic fiber as shown 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 ( ggjp3qap/ zgjg:6b6xs ;sx9other words, regardless of the angle the light beam reflects back into the material at point a.

  (a) What is the minimum index of refraction for g8, f+uozit3 3d k w;mohu1rw 0g/t2gma glass or plastic prism to be used kudwz0; 3 it 2g1gm,h+oot3w8f rgu m/in binoculars (Fig. Below) so that total internal reflection occurs at 45$^{\circ}\,$? $n_1$ $\geq$   
(b) Will binoculars work if its prisms (assume n=1.50) are immersed in water?  ----待选择----totally reflectingtotally transmitting 
(c) What minimum n is needed if the prisms are immersed in water? $n_1$ $\geq$   

  A sharp image is located 78.0 mm behind a 65.0-mm-focal-length convbov6 l2+a jkz5erging lens. Find the2zvj+6l ao 5kb object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.5 cm behind a lens. wuyz5c5p * pr l)s(3fl
(a) What kind of lens is it?  ----待选择----converging lensdiverging lens 
(b) What is its power in diopters? P =    D

  A certain lens focuses light from an object 2.75 m away as an if+makiet 97s)st8t1 s mn,qj:mage 48.3 cm on the other side of the lens. What type of lens is it and what is its focal leaif : sq9em+)t,1ss7tjt8nmkngth? 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-cm(s)xrxmbli*a6tvc 9od86q 07 d9kdfocal-length lens? P =    D  ----待选择----converging diverging 
(b) What is the focal length of a lens? $f$ =    cm  ----待选择----converging diverging 
(c) Are these lenses converging or diverging?

  A stamp collector uses a converging lens wikhsybr *9 ;0agf:p9 z r slq02+on;v2yq4lvagth focal length 24 cm to view a stamp 18 cm in f skap2r9*0ry+qq9abgv 0s;yng;h lz v :l4f2oront 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 object8d v4 pw-f,e zb-+gq2jahg p-d-vvi)u 4.0 mm high. What are the position, type, and heighgq ufbhvw-- vj,iep4ap+ gz8v)2-d-d t of the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is usedgyph jk6+82jv to focus an image on the film of a camera. The maximum distancevg j 8yjk2+hp6 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 reading)cp5q 5d2iamp material by a factor of 2.5× when a book is placiacd)2p 5q5 mped 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 muq- 1b/alyh vd/aa 122pucs6d zch does the image move if the object is moved /yvsud/12 aa1pld2 -habq 6zc
(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 withcf.q1ti,jr b0bi1 c/. kukcc: a focal length of 25 cm should an object be placed to produce a real image which is the same size as theitji. /u b0b c:f11k,q crckc. object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an object be placed t cofe9az 2+2ge)i.jroh o( +qif its image is to be magnified 2.00× and be +zq cr ag oe9oefjt.2)oi2+h (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-lengqcjf vb0z u79l2 s6l2jth lens must an object be placed if its image is2vjz0cu7f9b q2 jsl6l to 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-lh+u z xsbx)/:pength lens. Where is the image, how uhpx +x) /sz:bhigh 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-htj7 6bpi3 ump57mn3llength converging lens if the itl p b6753pn7ij3muh mmage is 2.5× larger than the object and is real?    m

  A bright object and a viewing screen ardpl fpn3rzcxh;8/7s+x 1is0ee separated by a distance of 66.0 cm. At what location(s) between the object and the screen should a lens of focal length 12.5 cm be placed in order to produce3x1pf cze ;0si7 n/8lrdhp +sx 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 pla;v2t7 w(yuxtl2r z ft/ced 16.5 cm apart. An object is placed 36.0 cm in front of onelu ;f7yzrtt2(xt 2wv/ lens. Where will the final image formed by the second lens be located? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens withy8h -fm;(-qlck ,zr qc $f=-31.5\mathrm{~cm}$ 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 cm behind a d/ ezev l,yq27rqg10ugiverging lens. Parallel light strikesgv/,gy7ez ulreq0q12 the diverging lens. After passing through the converging lens, the light is again parallel. What is the focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Example 23–12 are now placed only 20.0 cm apart.pn xy ku htl+tq(/p(ef:.d;vz3 oalze3;e -8x The object is still teu ( t-l dx3np ky;z3+:a;ze/(fhe l8oqxp.v60.0 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 placedco96a4 g pvpgf ;-pwl6 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 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 -c 4wgg6p9o6 pvf;lpathe left of the 15.0-cm-focal-length lens is the original object?    cm

  A diverging lens with a focal length of is pla twpy6za1xc- 0ced 12 cm to the right of a converging lens with a focal length of 18 cm. An object is plc6 0p-xazt1ywaced 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 converg. p7go:nvc/mvcwj6( dfli-h6ing with focal length 20.0 cm and one diverging with focal leng p66hmvc(l7 w g: co-ifvdj/n.th are placed 25.0 cm apart. An object is placed 60.0 cm in front of the converging lens. Determine
(a) the position    cm to the right of the diverging lens
(b) the magnification of the final image formed.   
(c) Sketch a ray diagram for this system.

A diverging lens is placed next to a converging len vc37)un6 8h 2q2lfhxlphexz.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 pr.bik sk)z6sjtl z38u 4z4,s+u z/w kcm and 23.8 cm. What is the focal lksk.z4js br,8/+ku)zl puzz 346iwt sength if n = 1.52?    cm

  Both surfaces of a double copq .m:(3 x 3iv)jttqnunvex lens have radii of 31.0 cm. If the focal length is 28np q(tx) :tv3j.m3iuq.9 cm, what is the index of refraction of the lens material?    cm

  A planoconcave lens (n=1.50):gupifm50 1sgko*u)x/)hp 9 zw e-zbz has a focal length of -23.4cm. What is the radius of the concave surface?/:okwpe gz m-us0i51h)f ) 9bugzp* zx    cm

  A Lucite planoconcave lens (see Fig. Below(jr3p p+ik-tn tid -r7) has one flat surface and the other has R = -18.4 cm. What iskpr(p ttjidi +nr3-7- the focal length?    cm

  A symmetric double convex lens with a focal length of 25.0 cm isz2sjj )sy0 hb5 to be made from glass with an index of refraction of 1.52. W5yj )hbj2s0zs hat should be the radius of curvature for each surface?    cm

  A prescription for a corrective lenscs*r 05ezyg7 x calls for +1.50D. The lensmaker grinds the lens from a “blank” with n=1.56 and a preformed convex front surface of radius of curvature of 40.0 cm. What should be the radius of curvat*ezxg5 0 rcys7ure of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apaf c59gbcu3+gzx 1p4 z1oxix m+rt as in (Fig. Below). You stand 1.5 m away from one of these mirrors and lookbc 1xgg++9p4 cz5 om1i u3xfzx into 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 wabwcu.fawd1b ; 4 n4m7zno yeo.*pp 6+d j:lx1nter. We measure the width (x=5.50m) and then note that the bottom edge of the pool is jzxwn 1 opfj m cn7pe6 b:..4l;41dbu+daw *ynoust 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 oh3.eqkpbf6 e5z*burr,o9z , a certain piece of plastic in air is $\theta_{\mathrm{C}}=37.3^\circ.$ What is the critical angle of the same plastic if it is immersed in water?    $^{\circ}\,$

(a) A plane mirror can be considered a limitxkh+d iy j1bh*+(a*od ing case of a spherical mirror. Specify wy1o(dh k*jah+b*d +ixhat this limit is.
(b) Determine an equation that relates the image and object distances in this limit of a plane mirror.
(c) Determine the magnification of a plane mirror in this same limit.
(d) Are your results in parts (b) and (c) consistent with the discussion of Section 23–2 on plane mirrors?

Stand up two plane mirrors so they form a 901sf)4 hh1p 7kpa fn:uu$^{\circ}\,$ 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 le*4zz2+ v a;8bi*4wn l fopn fqkdez:m4ns can never form a real image of a real object. Can you describe:*amvdinek *zf;z f284p wob+44zqnl a situation in which a diverging lens can form a real image?

  Each student in a physics lab is assigned to find the location where im ta1q.bvkhx 4,eeq(wj* bj 450yn(ia 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 equipbwqh5.*m0ijbq(a41x ,nje et4i( ky vment, 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 pris04gtz f b:,:tgr s8 kmn+abwil*s(*prm 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 cyld2l1 qi t2ppi4e9 ;ppwindrical 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 placenn87hiqq1de 3cgn 7a1 d 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 length f,(p dub.*uehsd; 4fkja (4x-rj and a white screen for viewing the image kb.4us-d 4p((;* jjed rfa uhxis on the opposite side. The distance $d_T=d_i+d_o$ between the object and the screen is kept fixed, but the lens can be moved.
(a) Show that if $d_{\mathrm{T}}>4f,$ there will be two positions where the lens can be placed and a sharp image will be produced on the screen.$d_T$>4$f$
(b) If $d_{\mathrm{T}}>4f,$ show that there will be no lens position where a sharp image is formed.
(c) Determine a formula for the distance between the two lens positions in part (a), and the ratio of the image sizes.

  In a slide or movie projector, the film acts as thd76lpog4 qbk4zjy/(. d+ ui ulbfvstx5m) f/:e 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 thx)mbzu (/o7l4f5fltvd yjkq/gd+ u.4p 6s: bie screen? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (picture size iszw9m j7m-me 9c fpe8ov0,g88yzmn3 if 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 i9 o c zz n,gy88vm83m-pmjefw7me9f0the image is to cover the screen?    cm

Show analytically that the image formed by a converging lens is real and invert:v2 sru . z4;pqjdyn5ced pzs:;cun5d. r4jqy2vif the object is 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 reporter shooting pictures of her at home. She claims th2 hk*p/0. j 4mtncxk-kxf+wkfe reporter was trespassing. To prove her point, she gives as evidence the film she seized. Her 1.75-m height is 8.25 mm high on the film, and the focal length of the camera lens was 210 mm. How far away from the subject wtfwj0kkh. x4*+ xc2n- k/fpk mas the reporter standing?    m

  How large is the imagey;*w(jer qx:v g9ij /j 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 imaged 8.20 cm in k+gxbc.o6) uc front of that lens (on the same side as the object). What type of lens is this, and what is its focal lexogk+ 6 cc.ub)ngth? 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)