What would be the appearance of r2pgj el+6nv6 the Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said tof3/ooq/x ae6 ts vdy4: have burned the whole Roman fleet in the harbor of Syracuse by focusing the rays of the Sun with a huge spherical mirr/v4d3 x q a6:tyfoeso/or. Is this reasonable?

Although a plane mirror appears to reverse left and right, it doesn’t reversezp j1rx08ku/ r up a10xp k 8rurj/znd down. Explain.

If a concave mirror produces a real image, is the image necessarily xcddn- )s-y;y by8df .inverted? Ex-y 8.byn ddc)xdy;s- fplain.

An object is placed along the principal axis of a spherd uyljm1 5wgqpp*4yl p g8w3,ad,w)q4ical 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 of the mirror is the image lo8l1a m*wp4qq)ddgg ,5y p3ylp4,wju wcated?

Using the rules for theyhnjtp1, /mf wgpmq3-y f 4t7zi4f 3v* three rays discussed with reference to (Fig. Below a), draw ray 2 for (Fig. Belogmitpjz4v1fpy3 n q ,/w*h3f-fm4y 7tw b).
(a)
(b)

What is the focal length of a plane 9 m7; mrac e0 zp)k/e txye399c74ow-tbd vkmtmirror? What is the magnification of a plane mirrork7o 7mpc4yt 0;9retcz-/ m9m ea)xbet3wdkv9?

When you look at the Moon’s rxb2*zg2fk btx 9n:cd6eflection from a ripply sea, it appears elongated . Explain.n6fkcgxxb:9t2 b 2dz*

What is the angle of refraction when a light ray meets the boundary bet h.:7cp lxi0ffween two materials perpendicuc7lff.x0h :pilarly?

How might you determine the speed of light in a solid, rectangular, transpa hj: fgd(5if+srent obh5:g (sj i+dffject?

When you look down into a swimming pool or a l utx+16yuz q)cake, are you likely to underestimate or overestimate its depth? Explain. How does the apparent depth vary wit)1ytzxu+uc 6q h the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks bent h.*s4iun vq +.qaxed) when part of it is under water (Fig. Be)*qu+hxn.ei. s4qv a dlow).

Your eye looks into an aquarium and views a fish inside. One b:l-:zdipae52p /7rtkqf ; dyray of light that emerges from the tank is show5ep;fqb: z- :p 2yi l/dk7tadrn in (Fig. Below), as well as the apparent position of the fish. In the drawing, indicate the approximate position of the actual fish. Briefly justify your answer.

How can you “see” a rounufzg 4tn1g 53ev2/fg qm .id;ed drop of water on a table even though the water is transparent af3; ift egd mg5g uqv4ze/12.nnd colorless?

When you look up at an object in ,*xl 5m wabs-xj6(aej air from beneath the surface in a swimming pool, does the object appear to be the same size as when ea - xj*ax,ws6blm5j( you see it directly in air? Explain.

How can a spherical mirror have a negative ou g0)uhy+fys,bject distance?

Light rays from stars (including our Sun) always bend toward thefcx1hg 7vw/ ibil4s pq 06n m4h gid9f:x-m;n- vertical direction as they pass through the Earn0-hnm 6:x4lig q7v sw9pid4mff 1 xibhgc -;/th’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 ,6;su1zqqgbx to make a sharp image of an object ver;,uzb 6q 1gqsxy far away?

What type of mirror isiqhv,ua g0q12 z,it2v shown in (Fig. Below)? Explain.

A photographer moves closer to his subject and then refocuses. Does i, zhc0euzlxcl3b+ag0gz y(t81 5f8c the camera lens move farther from or closer to t10ace 38z cuh5tx0c8bgzf (lzy ig,+lhe film? Explain.

Can a diverging lens formu;*hyb p4g7jm qs; pe. a real image under any circumstances? Explain.

Use ray diagrams to show that a real image formed by aysm igciv 2)j2t5:bjjcfr 1o,78bsy+ thin lens is always inverted, whereas a virtual image is always upright if the 2cgjbmv18o7fj+:bs)2y c irtysi5j, object is real.

Light rays are said to be “reversible.” Is this consistent with the thin lentt+ ct)gi4z +ps equation? Explz g+tip c4t+t)ain.

Can real images be projecg:gut-6dftj.( 0 z dcm( iv1wcted on a screen? Can virtual images? Can either be photographed? Discuss carefu(0 gz1 dg:.-u6 (wtctdicmfvj lly.

A thin converging lens is moved closer tok ;tcietb k.ps,eot ,:74ah2 w cr0:rq a nearby object. Does the real image formed change rkq4ei2k :ceca0,tr;sow ,thb. :p t 7
(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 a,g yrcvtz8db:j /dp,,ir, it is a converging lens. Will it still berbdc,t v/ yzdg:,8 pj, 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 converging lens. If the nose w1w7omm1 svl52qm .o9 8qnzz xand the tail are each focused on a screen in turn, which will haveon17w9.szmlmxvq z158qmw o2 the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facing a converging an vq(eq10n0,vpa*u e lens. Under what circumstances (if any) would the image of the nose be virtual and the image of the tail be real? Where wouluqaep*v01,qe a0 nv(n d the image of the rest of the cat be?

Why, in Example 13, must the converging lens have a shorter focal length thanotv 9/)xrx3ba the diverging lens if the latter’srxoa tx /)v3b9 focal length is to be determined by combining them?

Explain how you could h*u-nr s 3sc r7jqad23-y+ewvx ave a virtual object.

  An unsymmetrical lens (say, planoconvex) forms an image of a nearby r.igp5k9oht, object. Does the image point change if the lens is tu.gi9pk, 5o trhrned around? ----待选择----yesno 

The thicker a double convex lens is in the center as5dbw x9tx d +q ;xzznz;;0too9 compared to its edges, the shorter itx;zd 5 b9o9oznq xzx0; t;+wtds focal length for a given lens diameter. Explain.

Consider two converging lenses separated by some distance. An object isgpy 1z ,s anq/qh 8c;mz,18kfe placed so that the image from the first lens lies exactly at the focal point of the second lens. Will this cqz k ganyfmeszhc;p,/ 1,q188ombination produce an image? If so, where? If not, why not?

  Suppose that you want to take a photograph of yourzaujuatm04w tvv68lq om9s.2 7t32lfself as you look at your image in a flat mirror 2.5 m away. For what distanc.za6a mtuv sjwolt78ult22qf 04 v 3m9e should the camera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mirror, you see the same 8mw1dyim.2iua:6kck amount of your body whether you are close to the mirror or far away. (Try it and see.) Use ray diagrams to show why thismymck 1iw. d2ui68:ka should be true.

  Two mirrors meet at awvng7l;q;2ajl e gyh9i f51o;y5) tzm 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 abbb 1x59dh)grb ove the floor stands 2.20 m in front of a vertical plane mirror whose bottom 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 mirrh 9x1 bb5grd)bor?    cm

  Suppose you are 90 cm from a plane mirror. What area of i n8xf(twg0ce)5, vqro- -c s39uk,sc g+butcthe mirror is used to reflect the rays entering one eye from a point on the tip of yourc- og9wufguks0)3rvctncs 5,xi+ c( t-ebq,8 nose if your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors meet g 3j lvc:y,2jwat 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 the Sun’s ro7z+uqa84p*kl7 1/0tyw)im q ihlgioays 18.0 cm in front of the mirror. What is the radius of the spherical surface from which the mirror was m+7glwph * o04i7/lqtyu 1izo)kq aim8ade?    cm

  How far from a concave mirror (rad 8u2c2jfz/+gp (ykjf :j*0vyzz l-wyqius 23.0 cm) must an object be placed if its image is toqcz v*l/2f2 zpkyjfg0-(j+wy z:8jy u be at infinity?    cm

  If you look at yourself in a shiny Christmas tree ball with a diameter of 9.0 q f/dr74k4gq p7gqzke3q.2k ecm when your face is 30.0 cm away from zgqeq4 g rfq 2e .3k/kk7q4p7dit, where is your image? Is it real or virtual? Is it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement par(qr/+ fm8sdxbzla +x8 mvnu*- k shows an upright image of any person who stands 1.4 m invlsd/88 q+z xn+*ba( ru-mfxm front of it. If the image is three times the person’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror a**7 f0ksn:z tokqs1f that, when 2.20 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 produc /y7x12xtigw: .y mvs0g ltwr:e images of cars behind you that are smaller than they would be if the mirror were flat. Are the mirrors concave or convex? What is a mirror’s radius of curvature if cars 20.0 vgymt s:y l2i1t/ gx:w0x7w .rm away appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high 1nesd6j ha /s8xbi2w85dx1rnq uus 04is placed 20.0 cm from a convex mirror of radius of curvature 20.0 cm. q018/rwj dnsbe8d 4 u52niuas xxh61s
(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. Yoyt.;v57nspf bh0n(f dr- j7 fsu estimate the height of your image to be half of yo0fs7n- bvnyf. jf ; p7r(h5dtsur actual height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object be placed 5l*37x pnqqwvkbd+ t1 in front of a concave mirror so that it produces37+dl*kq1vn t5xbpqw an image 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 distanteod r-s/5i vyyg+g+. yoaj.8v tree is virtual and very small when viewed in a curved mirror. The ima g+sj+r y.vi.ooyva5-ed/ yg8ge appears 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 techniques, hjr f4l5auq e.)+t-admcy9 k9
(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 tht6b,6p+qvhv ke magnification m of a convex mirror is $m=-d_\mathrm{i}/d_\mathrm{o},$ just as for a concave mirror. [Hint: consider a ray from the top of the object that reflects at the center of the mirror.]

Use ray diagrams to show that the mirrortbvnfex1 , d62 equation, Eq. 23–2, is valid for a convex mirror as long as f is considered negat2dxenfbv 16t ,ive.

  The magnification of a convex miw y7jyso+3 ;uxrror 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 front of a sphenuh p;u 6npxwr/ja/ +eon9o*9 rical mirror. It is desired to prodonux9/w; jh*pa ore9pu /6nn+uce 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 magni;ayj 4;( fjhfafy your face by a factor of 1.33 when your face is placed 2ahffa4; yj(; j0.0 cm in front of it.
(a) What type of mirror is it?  ----待选择----convex mirrorconcave mirror 
(b) Describe the type of image that it makes of your face.
(c) Calculate the required radius of curvature for the mirror. r =    cm

  What is the speed of light int /6s5m)ornn b
(a) crown glass,    $ \times10^{8 }\;m/s$
(b) Lucite,    $ \times10^{8 }\;m/s$
(c) ethyl alcohol?    $ \times10^{8 }\;m/s$

  The speed of light in ice i0 sz j;cwu-5qns $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain substann 9)k92cbb3 8f-pn,ec lhw wbrce is 89% of its value in water. What is the index of ref2 b rhcp3wnbb ke9c8fw,) n9l-raction of this substance? n =   

  A flashlight beam strikes the surface of a pane of gla,w w1sa8 chjjk222pj wss (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 at a 42 p6ep4f1.nskt iagv4 p+t.d o5.5$^{\circ}\,$ angle to the vertical. At what angle does the light leave the water? $\theta_2$ =    $^{\circ}\,$

  A light beam coming from an underwater spo+2u g8qg wt8ostlight exits the water at an angle of 66.8go s8wg utq2+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 seov +g5.k dd.ween 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 sides whe k;s7 e/(lcohose 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)ke( e; l/7shco. 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 a pool at night, a watchman shines a 10 qv52h. +t xf;d5:rokbnzfy9ephd f 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 theqd51offf ;dvxh: 0tk2.rbn9hp5 z+e y edge of the pool (Fig. Below). Where does the spot of light hit the bottom of the pool, measured from the wall beneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equilateral glass prism at a 45.8 ;ou5e6wg ykx. 4ddnd0$^{\circ}\,$ 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 8:.0ik tk peutc7y :7p w-yvovslab of glass (n = 1.52) and is partially reflected and partially refracted. Find the angle of incidence if the angle of reflection is twice the angle y:wt:-kki veyc .p0 uo87pvt 7of refraction.    $^{\circ}\,$

Prove in general that for a aikvubgxc n /.5;u,3llight beam incident on a uniform layer of transparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the incident unxvaib5/ 3.lug,;kc 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 ;ar,y fob -n;sglass with index of refraction n as in (Fig. Below). Show that if the incident angle as-;,; ynbfor$\theta$ 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? Too :njf088c a jk9r9)jwe r)uqw be totally internally reflected, the light must start in wh:fecwojqun 9j wr)a08 jrk)89 ich material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle fo.r /)z(98 vyxy,gxwhjjks)-ep2j p e hr a certain liquid–air surface is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in a pool of wa+wgfhsish: ,3ter from a depth of 62.0 cm. Where must it strike the air–water interface, relative to h3,:h+igfss wthe spot directly above it, in order that the light does not exit the water?    cm

  A beam of light is emitted 8.0 cm beneath the surface of a liquid and s ulq(of tj) ip3l7b3-ak7hm9 ftrikes the surface 7.0 cm from the point directly above the source. If totbfm3 (9 tao l7kpj-lifhq)3u 7al 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 pris c0r up+ompf g .f9(*9npo.yckm 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 opti31ivrbc -o 9osm6 g0klc 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 ofvg63oo1 im0 9 ckb-slr 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 in vpipe(:v-t v ki(u1,ldex of refraction for a glass or plastic prism to be used in binoculars (Fig. Below-,pvev(1 (ikvt l piu:) 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-forapwy x)9q83r:eojt2d)s*du3;lguo gc,j g ;cal-length converging lens. Find the 2pe)3)j3qwc;rxads* 9lodu 8y,roug; j g tg: object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to fxpe* /hkit 3k9e8sb19/q g6c bb )bqlvocus 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 lg: q)s75(slt hxoxcv)9yz/nt ight from an object 2.75 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 focat sq h) syzx(o7t5 lcg)/n:v9xl 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-lengt7q9up cux52mb h lens? P =    D  ----待选择----converging diverging 
(b) What is the focal length of a lens? $f$ =    cm  ----待选择----converging diverging 
(c) Are these lenses converging or diverging?

  A stamp collector uses a converging lens with focal length 22001+fx) e0sj sh ujrurysw1 l4 cm to view a stamp 18 cm in front of j1 2e r+yxsfl1s0jh uru00s)wthe 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 ar5-bvz6uc j o7ge the position, type, and heigu 6jc 75gzbov-ht of the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-lengthu4nos 4rm8pqn0tl k 25 lens is used to focus an image on the film of a camera. The maximums8 qktnn544l 20promu distance allowed between the lens and the film plane is 120 mm.
(a) How far ahead of the film should the lens be if the object to be photographed is 10.0 m away?    mm
(b) 3.0 m away?    mm
(c) 1.0 m away?    mm
(d) What is the closest object this lens could photograph sharply?    mm

  It is desired to magnify readixvni( s2:dsv/ fp27u zoi/7tjds d(u/ng material by a factor of 2.5× when a book is placed 8.0 cm behi:vs/2 p tn/ d/s(7zd oxu(fjsd2vu7iind 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. 3n- q8mks/,kkcpre2 nBy how much does the image move if the objmq 28n-/k cr,k3knspeect 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 wi7++ o/qjgtpn x8;dvwpth a focal length of 25 cm should an object be placed to produce a real image which is the same size as the object?; pog/j8 +7qvndx+pwt    cm

  (a) How far from a 50.0-mm-focal-length lens must an object be placedo-2,*h ux. +yhuyg fvp if its imagegh v-y,f hy2u*+u. pox 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 50.0-mm-focal-length lens must an objeco3 y9:iq 4r(vzhdnq0nt be placed if its image is to be magnified 2.00× and n39ydqhq(:4no 0irvzbe 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 4;s(c wg fhbtq2 u8a):t,akao 1.20 m from a 135-mm-focal-length lens. Where is the image,2qb ha(a c:; ktta8fw4 u)osg, 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 -aa3tf n2umge o-yr0- and an image formed by a 75-cm-focal-length converging lens if t0fyn meo3arga-u2- -the image is 2.5× larger than the object and is real?    m

  A bright object and a viewing scy1 .h qkz4zh b2pu,f(wxg246sds8xbu reen are 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 produce a crisp image on the screen? [Hint: first draw au6xq(f.pu81 h4zy2wg4 bzk 2bds ,h xs diagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length converging lenses are 7 o:jem0c -c y8ady7ckirm 4e9placed 16.5 cm apart. An object is placed 36.0 cm in front of one lens. Where will the final image formed by the second lens be located? Wh0 c7e-ikm yoyr 9:e8m7c 4dacjat is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens with ( mq7y cdbls2p ol4*pc;na/*j.j+rdn $f=-31.5\mathrm{~cm}$ 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 diverging 1,cwmw yp kf)wiv3 t62lens. Parallel light strikes the diverging lens. After passing through the converging lewtp)cv12w,w 36mkifyns, 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 o4 hapj*gem f9m(. eoe;f Example 23–12 are now placed only 20.0 cm apart. The oee m*g h(4mof.;eap9jbject 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 placed 30.0 cm apart. The focal length of the lens on au7g yo9s)m(gdc4h *ithe 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 finhy gg(ica4s 9*m du)7oal 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 f; 9r2hrqpj7xv :ch(k gocal length of is placed 12 cm to the right of a converging lens with a focal length ohqkx;:9h j rrpvcg7(2f 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 lp* 8tomrqz/ *wength 20.0 cm and one diverging with focal length are placed 25.pom**/ rwq8zt 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 lens of focal length 1g56xigq6 hfs $f_C$ 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 a).qs.6ver8e9 kp+ -cxg o fawond 23.8 cm. What is the focal length wao e+spxc.r8 .vego6 -9 k)qfif n = 1.52?    cm

  Both surfaces of a double convex lens have raee(( .zn2fb-cv lxw/ o7 /vkgpdii of 31.0 cm. If the focal length is 28.9 cm, what is the index of refraction of the lens materlkn(vfvg.2zb weox( c e//7p-ial?    cm

  A planoconcave lens (n=1.50) has a focal length of f+q9jiahhn bc 5yz:3(-23.4cm. What is the radius of t qy a:z +(nbih9jhcf53he concave surface?    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat surface and the other pfk( oix756qkpk)fmz9d1ii/ has R = -18.4 cm.dk6i)pqzk 5x7o1f/(ip9 i f mk What is the focal length?    cm

  A symmetric double convex lens with a focal length of 25.0 cm is to be made gme3pp-mb4sni-r,. n from glass with an index of refraction of 1.52. What should be the rab gm-s3.p,4rnmip e-ndius of curvature for each surface?    cm

  A prescription for a corrective lens calls for +1.50D. The lensmaker g i)a*xnjwnnrn5 8b 3c0rinds the n8bacr3 )0jxin *w n5nlens 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 curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fig. Below). You s zq*6yn.+fg b0jwwu/ k jk7(betand 1.5 m away frojjg/ 6q.ubfy0wkkeb7*nz(w +m one of these mirrors and look 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 water. We meas; w )il. ;e3e:wsdlfzwure the i d)wz3:s ;ww.lfee; lwidth (x=5.50m) and then note that the bottom edge of the pool is just visible at an angle of 14.0$^{\circ}\,$ above the horizontal as shown in (Fig. Below). Calculate the depth of the pool.    m

  The critical angle of a certain piece ;2c v0 zvvemay 9jqn k649m9frof 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 limiting case ofvpx5lr.mc (tk 8f, .gqw4ug: t a spherical mirror. Specify what thi, 5l4vgwu(.rf g.x8kpqcm:tts 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 formm +5hu6r(hft6zi mg6l 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 divergiqi39oxh yc 3ow86po0 n1ul.; pmq0sjdng lens can never form a real image of a real object. Can you describe a si;c h1 pq.s8 w l0iuo6np9qo30x mo3jydtuation in which a diverging lens can form a real image?

  Each student in a physics lab is( owl./ gzs1pf assigned to find the location where a bright object may be placed in order that a concave mirror with radipl(/.fo1 gz swus of curvature r = 40 cm will produce an image three times the size of the object. Two students complete the assignment at different times using identical equipment, but when they compare notes later, they discover that their answers for the object distance are not the same. Explain why 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 prism is.hux5f/ h3pj zs 86ppb $\phi=72^\circ$ see (Fig. Below), what is the minimum incident angle for a ray if it is to emerge from the opposite side (i.e., not be totally internally reflected), given $\mathrm{n=1.50~?}$ $\theta_1$$\geq$    $^{\circ}\,$

The end faces of a cylindrical glassqvf0 /ge(s9dt 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 cmmu-f:bscxywf/ wun 3m8pcbv*wb1 .5) 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 convergy utoox/(ck( 4ing lens of focal length f, and a white screen for viewing the image ity(/4c oxkou (s 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, t **h0vgr0,)qck jiwx ix1 wzrnz .e ay9ld271bhe film acts 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 wide, how wide will ci)*,za2x91w.l y0hxr nz*0r 1egj 7wdbkqivthe 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 besu *( 3tu urrcrrc7b0; projected on a screen 1.80 m by 2.70 m placed 7.50 m from the projector. What focal-length lens* r;cuub 37s0u crrrt( should be used if the image is to cover the screen?    cm

Show analytically thap do38r da vsp/r;f4t-vud(+38plf dmt the image formed by a converging lens is real and inverted if the obje p-(p/vosl8 df38pa 4+dmr3;turvd f dct 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 re bf;o5ei+wqhs90r t*rporter shooting pictures of her at home. She claims the reporter was trespassing. To prove her point, she gives as evidence the film she seized. Her 1.75-m height is 8.25 mm high on the film, and thrfw;ros * bh9 i+05qete focal length of the camera lens was 210 mm. How far away from the subject was the reporter standing?    m

  How large is the image of the Sun on film used in a camera withjtlo-yxv9 eb hh5a;nl3um - )+
(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 ot-j, qzly:p2dx hv3) ud dmrc s3r/,2is imaged 8.20 cm in front of thatu/vd 2c3dlrdtryo :j2 -mh) pqx,sz,3 lens (on the same 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 certain conver e*zc9i2t o+ (al9zshzging lens, it forms a real image. When the object is moved to 40.0 cm from the lens, the image moves 10.0 cm fzei92+9 (ola t*z hczsarther from the lens. Find the focal length of this lens.    cm