What would be the appearance of the Mooz kq/ss tf44jxfe0f /s61d yu2n if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Rouwsp og.s61 3gal lz7agra7,1man fleet in the harbor of Syracuse1.zl6 3rsa77agl,wgsu o1ga p by focusing the rays of the Sun with a huge spherical mirror. Is this reasonable?

Although a plane mirror appears to reverse left and r f4 knfs,3cxd5f ,45end lgbgrl:1u1 oight, it doesn’t reverse up and down. Explcg5 xe:k 3s f ub1lond4d5nl 1,4gff,rain.

If a concave mirror produces a re4hzkudk*ge .:c4kk4 eal image, is the image necessarily inverted? Explahc4 d*kgk:eu4ke4. kz in.

An object is placed id3cvh-q d ;j.along the principal axis of a spherical mirror. The magnification of the object is -3.0 Is the image real or virtual, inverted or upright? Is the mirror concavdq v- jdic3.;he or convex? On which side of the mirror is the image located?

Using the rules for the three rays discussed with reference to (Fig0a5fn ddo ux.g0m3: ll. Below a), draw ray 2 for (Fig. Below b). 0 fxo:mngdl. 3lua05d
(a)
(b)

What is the focal length of a plane ma*)opwk yg(yud1/:k3wk0 mre irror? What is the magnification of a plane miruy: /gwoa3(1k pkry)ekwm0* d ror?

When you look at the Moon’s reflection from a ripply sea, -4 +-enu ,ch az 7a;vgzntu*agp:zu-xit appears elongated . Exueanp a:-,vu+g; - gz*x zuc4tzh-an7plain.

What is the angle of refraction when a light ray meetsmcxqn,pu k-ovzol*a (+6: ; xe the boundary between two materials perpendicularl,eozq *a;:xuovlmk6+ p -( ncxy?

How might you determine the speed 03qj ycb99;xveyraszm .ei 1( of light in a solid, rectangular, transparent object xr9j9(.yba ic3zs;0 ve qym1e?

When you look down into a swimming pool or a lake, are you likely to unqsg0. nnpe4f 1,w7ydzderestimate or overestimate its depth1q ,zp.0nw n7se4gd fy? Explain. How does the apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why affa6 ;nvmux,x 71v)hh stick looks bent when part of it is under water (Fig. h ; v61)hx, xnmff7auvBelow).

Your eye looks into an aq*ftfs w; mdpf) bdl.(44u)1.jnn 0wp kqjg0wtuarium and views a fish inside. One ray of light that emerges from the tank is shown in (Fig. Below), as well as the s1) pfbt)4k nlj0p;. tw*gdf 0j.m fuq( nwwd4apparent position of the fish. In the drawing, indicate the approximate position of the actual fish. Briefly justify your answer.

How can you “see” a round drop/xp3nn 69jyiv of water on a table even though the water is transparenyix6 9/3npj vnt and colorless?

When you look up at an object in air from beneath o 05.urhlyj 3zt9k-h8f -8xiqdgy6hrthe surface in a swimming pool, does the object appear to be the same size as when you see it directly in air? Expla0yhrrlg -xhk 8ufdj z8 t36q5oi-.9y hin.

How can a spherical mirror have a negative object distanco geks3 oful v1*l7h 23lxf3f9e?

Light rays from stars (including our Sun) always bend toward the vertical dire f g+5lldzkl(0ction as thel(zlgd5fkl0+ y pass through the Earth’s atmosphere.
(a) Why does this make sense?
(b) What can you conclude about the apparent positions of stars as viewed from Earth?

Where must the film be placed if a camera lens is to make a sh vr):3:os izeharp image of an object very farovzh::) rsie 3 away?

What type of mirror is shown in (Fig. Below)? Explai d 5 33wxrgf:(rowa0 5xytspf1n.

A photographer moves c+y dl(v9h z0mvloser to his subject and then refocuses. Does the camera lens move farther from or closer to the film? Explaind y(+vmvzh 9l0.

Can a diverging lens form a real image under any circumstan08j1mkr3 e s lhip1lj/b3 i.5d.myvvhces? Explain.

Use ray diagrams to show that a real image formed by a thin lens i r:*jctma7e/jo8 s*ytb79r ot n ;pp;ks always inverted, whereas a vir o:78myjntcp7; r9;k/ *t *paroejbts tual image is always upright if the object is real.

Light rays are said to be “reversible.” Is this consistent with the thin lens 5:df+z2 )3emluvsecy eqd )v:s+z y52eecf3u mluation? Explain.

Can real images be projected on a screen? Can virtual imagesk*- 1jpfopq4i? Can either be photogr oi *4-fkjqp1paphed? Discuss carefully.

A thin converging lens is moved closer to a neat*(1s0*ujzm .daxk ;yaex ay:rby object. Does the real image formed change *1m0yjkysaxa za (x d*;ue.: t
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an m),/kvq + xuguindex of refraction n = 1.30 In air, it is a converging lens. Will it still be a converging lens if placed in water? uum+xkg/q, v) ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands facing hjqm 838 mwl3n3(grvda converging lens. If the nose and the tail are each focur3m nl 8gm3 w3d(8hqjvsed on a screen in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air*37z22u/wgnsyfdfh ; mybcg( stands facing a converging lens. Under what circumstances (if any) would the image of the nose be virtual and the image of the tail be real? Where would the image of the rest of the cat be/3 s*fcgugd hyw( 2 fm27y;zbn?

Why, in Example 13, must them39pk)s h fh w3+shv pj+7;ist converging lens have a shorter focal length than the diverging lens if the latter’s focal +swj 7pmts) 3spi h3v;9 kfh+hlength is to be determined by combining them?

Explain how you could have a v bdk,x7w* e-duhq5 3xlirtual object.

  An unsymmetrical lens (say, planoconvex) fo*xhzji q:,1lq02mx 1nsk i gdc3uq5)orms an image of a nearby object. Does the iqj,: gq3 qz0* ioxi1kmcudhns5)2l 1xmage point change if the lens is turned around? ----待选择----yesno 

The thicker a double convex lens is in the center y 1:7dpms0r;nrd - gl4dbl7qras compared to its edges, the shorter its focal length for a given lens diamdy:m r7;d1rdlrgq7l0np bs4-eter. Explain.

Consider two converging lenses separn;bdyjqg9yvhdm+ n,u01 s. g ;ated by some distance. An object is placed so that the image from the first lens lies exactly at the focal point of the second lens. Will this combination produce an image? If so,g1 gqn;;,yn. bds0my+h 9v ujd where? If not, why not?

  Suppose that you want to take a photograph of yourself as you look any pe 9zkyne+v: +)m0jt your image in a flat mirror 2.5 m away. For what distance should the camera lens be f9y ykv)ze n0j:ep+nm+ ocused?    m

When you look at yourself in omi 5q(g.t +fba 60-cm-tall plane mirror, you see the same amount of your body whether you are close to 5 g.qtb(m+oifthe mirror or far away. (Try it and see.) Use ray diagrams to show why this should be true.

  Two mirrors meet at a au;3h( tgvnz+ ;fsz5moq4 cjvo -xp3+ 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 abo ec17fnqrq(f; *:l k4ysh5ch qve the floor stands 2.20 m in front of a vertical plane mirror whose bottom fc r7k qh y*;(q4e:nschfl5 q1edge 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 plane mirror. What area ofa;sy )1uawi0,b eyt uh (ha,4m the mirror is used to reflect the rays entering one eye from a point on the tip of your nose if your pupilahuy(4ts1i,y m)uh0aa w,e b; diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mixnuc q)3ed6b pd 3g.le9/4tiarrors 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, fou2*je xf0de ojl8-- gtcuses the Sun’s rays 18.0 cm in front of the mirror. What is the radius of the spherical surface from whf-* 08g jtouxedl-e2 jich the mirror was made?    cm

  How far from a concave mirror (radiu./l;-k3 a e9tzmcj;ta f8afr rs 23.0 cm) must an object be placed if its image is to be at infinilte 8akt-;z.fc r9fara /m3j;ty?    cm

  If you look at yoursv ualfsyq90f3wuwdy4,) ky 1(elf in a shiny Christmas tree ball with a diameter of 9.0 cm when your face is 30.0 cm away from it, where is your image? Is it real wv(0u)f ,y93w l ys f4yqkad1uor virtual? Is it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement park shows an uprig -ah6) vzco9lkm a2;wght image of any person who stands 1.4 m in front of ithl v-k g)z2 ;owmc96aa. If the image is three times the person’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror that, when 2.20 cm from a tooth, will producz,)2/gt1zsl 4 sma 39kpo wdaie 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 car3e:(j yg 8 thu)5kdzgms behind you that are smaller than they would be if the mirror were flat. Are theu(j:t8 hyemdk z5g3 g) 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 20.7nj vl( f4 cy-n b+dtemyc 42n+y(umi),y0 sdr0 cm from a convex mirror of radius of 4-n i2m+ ude(y+crvtbc yy fys ,ml)4nnj(70dcurvature 20.0 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 )dp waxs i3/z4estimate the height ofw /x)z3d4psia 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 front oxlu w+*y( dqe6f a concave mirror so that it produces an image awex* lyu6(d +qt 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 w iv*c2)do)gg8. e yhvqn8y z5is virtual and very small when viewed in a curved mirror. The image appears to be 18.0 cm behind the mirror. What kind of mirror is it, and whoh)28nzw cyiqg5v y)de8*v g. at is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techniques,-zb8 x.g 1zptfnp- n(j
(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 magnificativzn3s:v j3p6 yyy9dl8z/ vi m(bj46juon 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 equatiqq16x+q 0b2bi qc jx; n;zf;dyon, Eq. 23–2, is valid for a conveq nib6q1q0 xq;2;x bfydc; j+zx mirror as long as f is considered negative.

  The magnification of a convex58npk-9th;ap c8eg/hpqhlu , mirror is $+0.65\times$ for objects 2.2 m from the mirror. What is the focal length of this mirror? $\theta_2$ =    $^{\circ}\,$

  A 4.5-cm-tall object is plbyyanhz 6vn 07i6 41ze 61gg)rjtlrh5aced 28 cm in front of a spherical mirror. It is desired to produce a v vnig0y4yrl1)h 7 er6b n 1gh6zz6j5atirtual 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/u r3aq2m8-36ql.sueyi ewna to magnify your face by a factor of 1.33 when your face is placed 20.0 cm 836w2/sqm y ialaureneq3-u.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 ligh i;jn/q6hgv o4t 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 ice is5.i6j3x4qfywn qec 1u $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a cers9 :re5/tba,fqq.wb vakyb7cs/h )g* tain substance is 89% of its value in water. What is the if.bs5b kvraab:,*s )97eq tgq/y /c hwndex of refraction of this substance? n =   

  A flashlight beam strikes the surface of a pane of glass (n = 1.58) at aqk2/p0h-t :vmnm2:wumz aq8ubpfpas t(://q 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashlight upward from beneath the wa+h* oai. io,rm8uc8s0eo sd0mxh . a,hter at a 42.5$^{\circ}\,$ angle to the vertical. At what angle does the light leave the water? $\theta_2$ =    $^{\circ}\,$

  A light beam coming from an underwater spoiu8+z7v g 2zptp b7yx tve)w,*rl1+ optlight exits the water at an angle of 66. yitp* vv+7,tulpop1b+zx27e)r gz8 w0$^{\circ}\,$ to the vertical. At what angle of incidence does it hit the air–water interface from below the surface? $\theta_1$ =    $^{\circ}\,$

  Rays of the Sun are seen to make btydkq;7+* lm nrux62 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 wbg6 g x39ox9h8aycp9 xater has flat glass sides whose index of refraction is 1.52. A beam of light from outside the aquarium strikes the glass at a 43.5° angle to the perpendicular (Fig. Below). What is the angle of thisg9p xa9xx89ocgy6 3hb 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 nigh*a k 90) ml43d4bgmqhaszgq4h t, a watchman shines a narrow beam of light from his flashlight, 1.3 m above the water level, onto the surface of the water at a point 2.7 m from the edge of the pool (Fig. Below). Where does the spot of light hit the4m3 )a sdm9qkqg4* hl0zghab4 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 equilateral7 x9kli/1wem l glass prism at a 45.0$^{\circ}\,$ angle to one face, (Fig. Below). Calculate the angle at which light emerges from the opposite face. Assume that n = 1.58.    $^{\circ}\,$ from the normal

  A beam of light in air strikesqc ,-2(mblu ks a slab of glass (n = 1.52) and is partially reflected and partially refracted. Find the angle of incidence if the angle -mcbu2sqk l (,of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam incident /ii h -9m rfi wzucckfa1;8r+ez-j .(lon a uniform layer of transparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the incidem /fkzz(hu 9ci1il8wfe -r-j;irc.a+nt beam, independent of the incident angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on a flat piece of glass with index of rk 1dv 0sjoy)(9exo9 w7jswe )3zvcux7 efraction n as in (Fig. Below). Show that ifvd)oks vy9()739xcx suej01o ejwz w7 the incident angle $\theta$ is small, the emerging ray is displaced a distance $d=t\theta(n-1)/n$ from the incident ray, where t is the thickness of the glass and $\theta$ is in radians. [Hint: for small $\theta,\sin\theta\approx\tan\theta\approx\theta$ in radians.]

  What is the critical anglvi*76 ma 7ew-stxmbi0 e for the interface between water and Lucite? To be tota -6siiv7mx7te* 0a wbmlly internally reflected, the light must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–air gas(4xehf 2r2h 0go,u surface is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted c-lms uj+6nqut rkubx1y.-bs438 ,oyin a pool 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 not exit the w, xqnly rso63utm-.1ksby u+8j4 u- bcater?    cm

  A beam of light is emitted 8.cxqo: v4v)d ur a19j1k0 cm beneath the surface of a liquid and strikes the surface 7.0 cm from the point directly above the source. If total internal reflection a19d1vqxuv )rjo k:c4 occurs, what can you say about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face of thb l2*fkj( se8nwo 2+p+gucc6n e prism in (Fig. Below) at 45.0$^{\circ}\,$ as shown, but is totally internally reflected at the opposite side. If the prism apex angle (at the top) is $\phi=75.0^\circ,$ what can you say about the index of refraction of the prism? $n \geq$    (retain three decimal places)

A beam of light enters the end of an optic fiber as sho*,dyy4 i-i 4nzbpgn d.3tajc-wn in (Fig. Below). Show that we can guarantee total internal reflection at the side surface of the material (at point a), if the index of refraction is greater than about 1.42. In other words, regardless of the angle the light beam rengc *inza4-. b4-yd,jyt3pdi flects back into the material at point a.

  (a) What is the minimum index of refraction for a glass or plastic prism to bi.dha ws9s)i9 e used in binoculars (Fig. Below) soasi)s9hd wi.9 that total internal reflection occurs at 45$^{\circ}\,$? $n_1$ $\geq$   
(b) Will binoculars work if its prisms (assume n=1.50) are immersed in water?  ----待选择----totally reflectingtotally transmitting 
(c) What minimum n is needed if the prisms are immersed in water? $n_1$ $\geq$   

  A sharp image is located 78.0 mm behind a 65.0-mm-focal-length converging l wyw+x 87r6 fjltci2;yens. Find the objecwyc ;jwy7 62 fx+8ltirt distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a p4vv * q:syv/apoint 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 muf h+c.ucvej,bxvn7v762 g .object 2.75 m away as an image 48.3 cm on t2vb7ghx,u .fec7j.muvc+n v 6he other side of the lens. What type of lens is it and what is its focal length? Is the image real or virtual?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the power of a 20.5-cm-focal-length lens? P = ccz34,.w7iq5 h-hl 8qnveqab    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 with22 7try.cslshk)pi /smx0zfju s+s q t 48v2o6 focal length 24 cm to view a stamp 18 cm in front of thzh sktv ur sol2jyqcf7 /+s2s4.)m80x26spite 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 hi1b:yb/lh:i o 5i6sv qsgh. What are the position, type, and heso :bi5:/yqi61 sv lhbight of the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to focus an image 8m-jhm+gz v.yon the film of a camera. Thehzv y-+gjm.m8 maximum 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 reading mactcs* xbbm469c3 ssfdv(/ nl8 terial by a factor of 2.5× when a book is placed 8.0 cm behind a lends v s*tc /bfc sb3(69c4nm8lxs.
(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 r1mq*)8 tv2p: xmtwwb m from an 8.0-D lens. By how much does the image move if pr1m tq*xw m8)vt:wb 2the object 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 length of 2i - ju/q0fu hpzn48 )pszs+.w +1qlxii5 cm should an object be placed to produce a real image which is the f+84z)zu pii-i u . qxpws1n/s+lq0jh same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an object be placed if )/ppb t/bq52odj lk;f its image is to )fb5/k d2jp/lqo;p btbe 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 object be placed if ijv 6*bm:h x/i)yvuez:ts image is to be magxbeim )hv/jy:: 6uz *vnified 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-l*dezhi.i0fuy y133eyength lens. Where is the im03edfyh 3e1iyu .z iy*age, how high is it, and what type is it?
$d_i$ =    mm (real,behind the lens) $h_1$ =    cm (inverted)
(b) What if $f=-135\mathrm{~mm}$?
$d_i$ =    mm (virtual,in front of the lens)
$h_1$ =    cm (upright)

  How far apart are an object and an image formed by a 75-cm-focal-lengt* h;6 hxxl6uaih converging lens if the image is 2.5× larger than the object and is 6uixa6 h*l ;hxreal?    m

  A bright object and a vai lj)a28f5)m1bg gqzemc *j+iewing screen 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 *8 f)jme+5ama1)i jlq2gg z cbdraw a diagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length converging d b u6kuxa4lldml 5x;7to;f 4+lenses are placed 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 lenstom5f+uu7ad4kx; 4ldlx b6 ; l be located? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens with k -er+(kx16to lq- :frr:ar dg$f=-31.5\mathrm{~cm}$ 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-lengz;rmpimkw g )xk0(;g um6-a*o th converging lens is 21.0 cm behind a diverging lens. Parallel light stri-pxz0o(;r agkuwmg*)mi; 6k mkes 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 of4q) ni4jb1t; *ado pzl Example 23–12 are now placed only 20.0 cm apart. The object is still 60.0 cm in front of the first lens as in (Fig. Below). In this case, determine 44iol bnjz d;q a1)*pt
(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 fo4ujj ohy: pi:)cal 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 the left of the 15.0-cm-focal-length lens is the origyp oh4 )jj:ui:inal object?    cm

  A diverging lens with a focal length of is placed 12 cm to thew s)k(ts e4- mao g9djo46hj4d right of a converging lens with a focal length of 18 cm. An object is placed 33 cm to te4) 6jaw h94 (ostkd-odmjgs 4he 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 wob w(v2: ../nx5v*aytwi zssgith focal length 20.0 cm and one diverging with focal lengs 2a*bz:ns./w x ti.o5vv (ywgth 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 converg2nqgcom8 /u 5ivvq+l;ing lens 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 31ye4 zy.;fhoszy a- 8q4.2 cm and 23.8 cm. What is the focal ;-yoyy zf q8.hsaez14length if n = 1.52?    cm

  Both surfaces of a double convex lpv,co0 o:n y05nzefco )b) gq3ens have radii of 31.0 cm. If the focal length is 28.9 cm, what is the i ,y) q00zbv c )g3nnfoo5po:cendex of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a fo0eudg( )i- uhecal length of -23.4cm. What is the radius of t) gh(eud-eu 0ihe concave surface?    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat surfaceu9b xl 2jih57l+ ev ygscv*/e: and the other has R = -18.4 cm. What is the focal lengslu l/ey civ*5vg+ x9hb27:je th?    cm

  A symmetric double convex lens wi1j5cn7k qfs g+ q.9eukth a focal length of 25.0 cm is to be made from glas7qsfu1+ck.ng9 j 5keqs 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 cale oib71al p*z4ls 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 curvature b41 p*ea7zoil of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fig. lw9 /9lk, mm*avpc,wt Below). You stand 1.5 m away from one of these mirrors and look into it. You will see multiple images o9plwt9,*al ,vwm/mk c f 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. Wed; bij4;jn3e7:xjq g t measure the width (x=5.50m) and then note that the bottom edge of the pool is just visible at an angle of;e3 qjdn t7j4:gjix;b 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 air is r9w3hj zlrpa5e9k6 g/$\theta_{\mathrm{C}}=37.3^\circ.$ What is the critical angle of the same plastic if it is immersed in water?    $^{\circ}\,$

(a) A plane mirror can be considered 65 z5dxan6pufv/cgf *or d) 4va limiting case of a spherical mirror. Specify what this l4a5u6cvr/f )zx* dd6vo gp5fnimit 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 mirrors36qi- cy sbxs2um.h :x so they form a 90$^{\circ}\,$ angle as in (Fig. Below). When you look into this double mirror, you see yourself as others see you, instead of reversed as in a single mirror. Make a careful ray diagram to show how this occurs.

Show analytically that a diverging lens can never* -l1 ;qu a6dqpep-djj form a real image of a real object. Can you describe a situation in which a ddpaql dju6;- peq 1j*-iverging lens can form a real image?

  Each student in a physics lab is assigned to find the location t/gowk; el 4 )zxkk(ec.3.gbclry)4i where a bright object may be placed in order that a concave mirror with radius of curvature r = 40 cm will produce an image three times the size of the object. Two students complete the assignment at different times using identical erg)/(4e k.)t3xey;cb ci lg lz4ok w.kquipment, 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 pris al owost+t*jbk9m1/p 7m* yb5m 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 cylindrical glass rod 8ij1mia8 5mms $(n=1.54)$ 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 converging lens of fgmqvxj 9:ic54 ocal 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, a4apl(axl m i)4 l/az9gnd a white screen for viewing the image is on am all a()49pz li/gx4the 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 projei*-rv6a3x yh zctor, the film acts as the object whose image is projected on a screen (Fig. Below). If a hx-z vi r3ya*6105-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 screen? $d_0$ =    m $|h_1|$ =    m

  A 35-mm slide (picture size is u) t5g*q17jns) k cpecuvk;k7pe,g0pactually 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 s7e7tp kke1qun csu0 p*,g)jcp 5v)k;g hould be used if the image is to cover the screen?    cm

Show analytically that the image formed by a converging lens is x7tta,:wi 3+5 b we pgu+dvd*wcio8q, real and inverted if the 8tiwdtw ,q +:u* aeioc57gvw x+3pbd, 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 tp7 ,3+cy3nv3w+sjwg h po wqa15p8uv of her at home. She claims the reporter was trespassing. To prove her point, she gives as evidence the film she seiz8,aj pg31+37 t wn whpvq5pswcy3v+oued. Her 1.75-m height is 8.25 mm high on the film, and the focal length of the camera lens was 210 mm. How far away from the subject was the reporter standing?    m

  How large is the image of the Sund9,)fr ek ed(pu,hny7 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 front of p/h5pgtad/cqr-uu(s/s7* mzdl6 o w3that lens (on the same side as the object). What type of lens is this, and what is itsa r/5-hdsgutpzc sm*d3w6 ( o/7pluq / 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)