What would be the appp ,j5q+wlgsw( earance of the Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have bu-:uf8. go yzgdw*x 4nzrned the whole Roman fleet in the harbor of Syracuse by focusing the rays of the Sun with a huge sphericalw8*u dxyf g:o-n z.gz4 mirror. Is this reasonable?

Although a plane mirror appears to reverse left and rh; fubu- s )nl5.oe4xz0hw-el n;h,e bight, it doesn’t reverse up l,sne-h be;fl.45 0n ;whbzh)u ux -oeand down. Explain.

If a concave mirror produces a real image, is the image necessacp 0ry pcf1f:*rily inverted? Explar c01cp:p*ff yin.

An object is placed along the principal axis of a spherical mirror. The m5oafzz5,s:suy jj-m 0agnification of the object is -3.0 Is the image real or virtual, inverted or upright? Is the mirror concave or convex? On which side m5 ju:z,5yzo sj-fa0sof the mirror is the image located?

Using the rules for the three rays discussewo3-s*68wp yc h ;choqd with reference to (Fig. Below a), dc sw8;po hyqw3hc-* 6oraw ray 2 for (Fig. Below b).
(a)
(b)

What is the focal length of a plane mirror? What is the magnifi 1j koo1km* uwwjd*a60cation of a plane mirror? *doj1u6 koja1wwm*k0

When you look at the Moon’s reflection from a ripply sra(f3k6 jtay 5v+,zrpea, it appears elongated . Explainrp,fa y6zrj+t3v 5k( a.

What is the angle of refraction when a,y /yjdssdy(wggf.1h*3 thv7 light ray meets the boundary between two materialsy ,/g1sdvwf.3hyy 7j*htds( g perpendicularly?

How might you determine the speed of light in a solid, rectangular,ytn+tb,3ym 3d dk9wm - transparent dmwnd- ktym3t9b+ y,3object?

When you look down into a swimming pool or a lake, are you likely to underestimajx)i1dk8; o iad+f(t gte or overestimate its depth? Explain. How doiax1d8djf);+ogi (tkes the apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks bent whenmi 6jkbxc,/ 2c part of it is under waterbijx6m,k /c2c (Fig. Below).

Your eye looks into an aquarium and ,w, s.ug41pd dyfyhm2views 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 position of the actual 4d1 ,uwfsy.md2h ,ypg fish. Briefly justify your answer.

How can you “see” a round drop of water on kl v4imgfve c 7,.0:mea table even though the water is transparent and7vv eg.m 0,l4 im:cfke colorless?

When you look up at an,c2d+ faksp-ho9(9noysv +nm object in air from beneath the surface in a swimming pool, does the object appear to be the same size as when youk9mndp9oa,vfh +2os- yn +s( c see it directly in air? Explain.

How can a spherical mirror have a negative object distancsf /;aax32p xde?

Light rays from stars (including out2:q w q41ibv3 *whecsr Sun) always bend toward the vertical direction as theyst2 *bwqvciqw:h4e3 1 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 tamm ktdpu3uwp/pbt3 ,8f yf)5-9d k :a camera lens is to make a sharp image of an objepapkmfm3bf- ytddt9p tu uw )k/,35:8 ct very far away?

What type of mirror is shown in (Fig. Below)? xm86q3z r6 pp/wtf:h tmkf08qbp+td0Explain.

A photographer moves closer to his subject and then refocuses. ww6n40pd9 bq bDoes the camera lens move farther from o4 6w 9bbnpdwq0r closer to the film? Explain.

Can a diverging lens form a rey6y3yfmh jsdk7 om++2h;fn*b q4 cii, al image under any circumstances? Explain.

Use ray diagrams to showr1 ifzps9+v lm y21ve2 that a real image formed by a thin lens is always inverted, whereas a virtual image is always upright if the e ipm9vyf12l +12rzsv object is real.

Light rays are said to be “reversiuzmcel5 5vlx qy* 3i35ble.” Is this consistent with the thin lens equatev3c5y * 3mxul55qilzion? Explain.

Can real images be projected on a screen? Can virtuaued) ay1m :+ 7tcgxmj2l images? Can either be photographed? Discuss careeu7d a:tj 1+g)x2myc mfully.

A thin converging lens is mtfl zki)d69f5 oved closer to a nearby object. Does the real image formeddflk5z t)9f6i change
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material widjl gi) ,+s lvw2)/e5ryzm,na th an index of refraction n = 1.30 In air, it is a converging lens. Will it still be a converging lens if 2m +dlnisv5,,w ))l/ajzgeyr 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 anzjswm*(e1( 55z *h26fuzq gch o v(fyad the tail are each focused on a screen in turn, whi es*fcgh1*(q55(f6uv2o z (wzhm yjzach will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands 0r -d+bbahzxhr r4* a6facing a converging lens. Under what circumstances (if any) would tra4x6*rh0b b+r -zdha he 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 hajbhod,jo)2k uuztw( ll, q,50ve a shorter focal length than the diverging lens if the latter)j tbw2,odl zhl,kj (o5u0,uq’s focal length is to be determined by combining them?

Explain how you could have a virlq*xbor0a ),-fpj hef vxs4 u1vv360 ptual object.

  An unsymmetrical lens (say, pur id;iegy9wm ,2k( *klanoconvex) forms an image of a nearby object. Does the image point change if thge*iwi,k ;mk2yu 9( rde lens is turned around? ----待选择----yesno 

The thicker a double convex lens is in the center as comparaxi .zgj( ym-7(bbdg 0f pc3c4ed to its edges, the shorter its focal length for a given lens dia(mcg7yic40 ( xfaj-b3gd. b pzmeter. Explain.

Consider two converging lenses separey 9t/ggr3fx/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 combination9e// txggfyr 3 produce an image? If so, where? If not, why not?

  Suppose that you want to take a photograph of yourself as you look at you rdcb5v/gc;d97i;x 9g pg(v tgr image in a flat mirror 2.5 m away. For what distance should the;rp/t7d c(cggxig9dv ;v95 bg camera lens be focused?    m

When you look at yourself in a 60-*z.kp,iqp0hqwx; dps2nn-3g r0ueyy0 /*f gtcm-tall plane mirror, you see the same amount of your body whether you are close to the mirror or far away. (Try it and si xz0dfgh*3- krgpq; .pn0e2p ys*w, /tynu q0ee.) Use ray diagrams to show why this should be true.

  Two mirrors meet at a :)fqd-.x vq io135$^{\circ}\,$ angle, (Fig. Below). If light rays strike one mirror at 40$^{\circ}\,$ as shown, at what angle $\phi$ do they leave the second mirror?    $^{\circ}\,$

  A person whose eyes are 1.68 m above the floor stands 2.20 m in front of a v(iy;fh q/:0j e+c/qp av z3/0pqeuu nrertical 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 seyq/ jf/n 0qi/u3ea(q; ehppur0:z v+c en reflected in the mirror?    cm

  Suppose you are 90 cm from a plane mirror. What area of the mirrwio*acs 4ju)z8cyr/;or is used to reflect 4ijuwc*;r8za/y cs o)the rays entering one eye from a point on the tip of your nose if your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirro1haig ;fkyz i;f8(xw58;cibd rs 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 Ste3 ojka-+4vnt4u) xuun, focuses the Sun’s rays 18.0 cm in front of the mirror. What is the radius of v43ko unt4au-x )ej+tthe spherical surface from which the mirror was made?    cm

  How far from a concave mirror (radius 23.0 cm) must an object be pla f/f:i 4i+g;r*jdt rewced if its image is to be at infing 4;e*dfit+/ j:wr ifrity?    cm

  If you look at yourself iz: tavn+8sx p5n a shiny Christmas tree ball with a diameter of 9.0 cm when your face is 30.n+:v astp5z 8x0 cm away from it, 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 park shows an upright image of aqaoi3rvax;g8g 1g1q 6ny person who stands 1.4 m in front of oiqa;ax g v 11rgq36g8it. 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 2.27 )cv1--tmspv at,q0fsur la-0 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 to,va)wj5y,halz/ 2t chan they would be if the mirror were flat. Are the mirrors concave or convex? What is a mirror’s radius of cacl /,,aoj w2yth)v z5urvature if cars 20.0 m away appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is placed 20.0 cm from a convex miwdh:fj7i:3b kq) gui2rror of radius of curvature 20.0 cm. :f3)j:bwi7 ig2quhd k
(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 securgg)mf iq1,uuiz64em57w ij 4vity mirror in a store. You estimate the height of your image to be ha)eg u i176uqzmiv ,544fwij gmlf of your actual height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object bedyy;ghya +hq0 (hk2px+ y8q3(irp zk( placed in front of a concave mirror so that it produces an image at the sqpy(+8h(qd2gxihp3( z+y khy kry0;aame 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 26dvxhu1,w (ot *nj jbgpjj;-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 what is its nhg6*o xjp2vj1t ;wbj-(udj,radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different technique;qh1:xyatix a1pf :xw ./ v)jis,
(a) a ray diagram,
(b) the mirror equation, to show that the magnitude of the magnification of a concave mirror is less than 1 if the object is beyond the center of curvature $C\left(d_0>r\right),$ and is greater than 1 if the object is within $ C (d_0 < r) $.

Show, using a ray diagram, that the magnification m of a convex mirro 6cu1cri;p g/xr is $m=-d_\mathrm{i}/d_\mathrm{o},$ just as for a concave mirror. [Hint: consider a ray from the top of the object that reflects at the center of the mirror.]

Use ray diagrams to show that the mirror equation, Eq. 23–2, is vali8plp ovh1wtd5x/v 99z6)l5nf9 tzesrd for a convex mirror as long as p5vv5pz /tnwt srod9z)xef691l9 8l hf is considered negative.

  The magnification of a convex mirhr3hh2e 8 ndq6ror 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 spherical mirror. It iee/zrqk8. mq lcs *x12s desired to produce a l1qq82/ eksz re .cm*xvirtual 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 fayuuord , iblj0/7j *)abf:jy9ctor of 1.33 when your face is placed 20.0 cm in front )j,j0a97u yd:*fou/b j il rbyof 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 in,kbuwgqe2o n5tx0q p :/cp;6ilbuq 81
(a) crown glass,    $ \times10^{8 }\;m/s$
(b) Lucite,    $ \times10^{8 }\;m/s$
(c) ethyl alcohol?    $ \times10^{8 }\;m/s$

  The speed of light in9xlr) ql2wrk ( ice is $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain substance is 89% of its value in water. )gkc 7,v0nnlu- rf3 j;it,vu* vf 0wldWhat is the index of refraction of thi f wvnjt nv i,7cdr0fl;l)0ku,g3u-*vs substance? n =   

  A flashlight beam strikes the surface of a pane of gl*g 4d*xk. npuqass (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 upwa ezi:yn2d4,t jrd from beneath the water at a 42.5$^{\circ}\,$ angle to the vertical. At what angle does the light leave the water? $\theta_2$ =    $^{\circ}\,$

  A light beam coming from an underwater spotlight exits tt2/7 54(zn9rtwj pvuqdpo,uahe water at an angle of 6z2vu (ao q9nut p5t4j7d,pw/r6.0$^{\circ}\,$ 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 seen to make a 31.0tlxxs6 2mnb40ct a+g8$^{\circ}\,$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?    $^{\circ}\,$

  An aquarium filled with water has flato66y)/busz jn/k+b4 atjux /t glass sides whose index of refraction is 1.52. A beam of light from outside the aquarium strikes the glj/s/+6 u /oykjbxa)bnttz64uass at a 43.5° angle to the perpendicular (Fig. Below). What is the angle of this light ray when it enters
(a) the glass, $\theta_2$ =    $^{\circ}\,$
(b) the water? $\theta_3$ =    $^{\circ}\,$
(c) What would be the refracted angle if the ray entered the water directly? $\theta_3'$ =    $^{\circ}\,$

  In searching the bottom of a pool at night, a watchman shines a narrow beau;*u c3ha scr.m 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 r sh; u.ucca*3of 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 equilate/ lfne)i5u3:v,xou a4g e6qecral 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 strikes a slab of glass (nzuyr5oq7 oj4 7 = 1.52) and is partially reflected and partially refracted. Find the angle of incidence if the angle of reflection is 74uzqoy jr7o5twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam in0stj5s* enr xyi 1g2+z p,2r.lzpq ek8ak9-aqcident on a uniform layer of transparent material, as in (Fig. Below), the direction of the emergik2t*zr.5p,0-qaie +xpegkr812 q9jny sa l zsng beam is parallel to the incident beam, independent of the incident angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on a flat pxvy(n;sz xsq qb- 35 1a7cop6hiece of glass with index of refraction n as in (Fig. Below). Show thay ( sxpv;-xqh65qcsoz3b1 n7 at if the incident angle $\theta$ is small, the emerging ray is displaced a distance $d=t\theta(n-1)/n$ from the incident ray, where t is the thickness of the glass and $\theta$ is in radians. [Hint: for small $\theta,\sin\theta\approx\tan\theta\approx\theta$ in radians.]

  What is the critical angle for the interface between water and Lucite? To bm mq:d,g+qvnw-ix s9/e totally internally reflected, the light must start in which xqnsm,wvg- / mqd9: i+material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for /gd)svbiarug eiqja g.d7:o:u n+81; 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 water fro74bld eq6xa0 ,exh00e:kjevo m a depth of 62.0 cm. Where must it strike the air–water interface, relative to the spoqeeoed:7x 4vajh0b60k,ex l0 t 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 striks z uvp8k1u3x*tyyr.3 es the surface 7.0 cm from the point directly above the source. If total internal reflection occurs, what can you say about the index of refraction r zpu*syu1y kv8. xt33of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face of t/s 6 mml.ak.oihe 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 ende b88ooseq1gt(+ fm3 p/fxkv3 of an 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 greatvsgeqxom (f b3f1t /3o+8pe8ker 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 indo kjf(ig enur, )8)nj9ugtf08 vi4ye1ex of refraction for a glass or plastic prism to be used in binoculars (Fig. Below) so that total internal reflectio,)fenio1j9gt 8unf8 (kje viy4 g0r u)n 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 1 ,wstdkz0*h y72fvllconverging lens. Find t k02ts,l7fy 1dl z*vwhhe object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focuzuv:axh/6g(x 7 wfjerv,9x+ v s at a point 18.5 cm behind a lens.
(a) What kind of lens is it?  ----待选择----converging lensdiverging lens 
(b) What is its power in diopters? P =    D

  A certain lens focuses light from an oz7j 6snac )7p r+fmp9gbject 2.75 m away as an image 48.3 cm on the other side of the len+mcg6snrp z9jp a7f)7s. 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-len:vzkp3v i 4whn, 5nqx7+smx t z81n5yhgth 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 len,x wie,inyl+:gth 24 cm to view a stamp 18 cm in front of ,wilin:e ,+yx the lens.
(a) Where is the image located?    cm behind the lens (virtual)
(b) What is the magnification? m =   

  A -5.5-D lens is held 14.0 cm from an object 4.0 mm highgaaf-a,0v/bkb x; ei5. What are the position, type/viafakxb0 5b;eg- , a, and height of the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to focus aev:s c+bd tq0j(hi aeje*5h86n image on the film of a camera. The maximum distancqsv:hej8be (5c 0a+ thi6e* jde 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 readsi 6*g;e+jt( itukde)ing material by a factor of 2.5× when a book is placed 8.0 cm behind aiitd()*u kg;+j 6etse 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 anz7:hp; srky/f 8.0-D lens. By how much does the image move if the object is kp:zr;fh/7 symoved
(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 ot (-cm, bsd/nz 0:zn5rpzy+ tfocal length of 25 cm should an object be placed to produce a real image which is the samz-+msp(cnn d tbzoz: yt/r50,e size as the object?    cm

  (a) How far from a 50.0-mm-focalpwd6spbiav2+1 c no3 0-length lens must an object be placed if its image is to be magnifiedpi01+swv 326aodpb cn 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 lense 8ezp)j,rb3- wcjr (e must an object be placed if its image ij-e pjb8c,r(z)w3ee rs 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 froa tv0r.p e v)qlelk5,,m a 135-mm-focal-length lens. Where is the image, howq pvtr)l5.0l,e, ka ve 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 all+ pne kd9:;gnd an image formed by a 75-cm-focal-length converging lens if the image is 2.5× larger than the object p+le 9nld k;:gand is real?    m

  A bright object and a viewing screen are separated by a dis y) s7izwog mcp,icu:c r+813dtance of 66.0 cm. At what location(s) between the object and the screen should a lens of focal length 12.5 cm be 7cpm 3i y uo)wc8i+:dszrc g,1placed in order to produce a crisp image on the screen? [Hint: first draw a diagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length convergipqfik/k(ttw hk*uh6c- p/ )2rng 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 lens be located? What is the total magnificatpkf-(6 whc)uhkq/ /pi*k 2rttion?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens with 8z5(uza. him l;kt:(:)hfc k itfpgi0$f=-31.5\mathrm{~cm}$ 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 divergincc :mgfmvq (. v(80 ht .d451rjcuifqwg lens. Parallel light strikes the diverging lens. After passing through the convejr 4g:f(iwdvuq5vc qt.f0cc( h1 8m.mrging 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 2f 2ywft,1v3vg g 1z1g*imlq, n.d2mr z3–12 are now placed only 20.0 cm apart. The object igz ny,3vv2dmzt r1l,mff . wg2gq* 1i1s 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 lbh 8xr.i 2dl6fens 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 or 2bi.rlx8 df6higinal object?    cm

  A diverging lens with a focal length of is placed 12 cm to the right of a e-3pt9+ ji pktconverging lens with a focal length of 18 cm. An obt-p9ekp+3 j itject 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 length 20.0 cm and one diverin nc hnf7w;o4+7k,9x lewp9jging with focal length wnn w7ck,n9o+l9e ;f xi74jhp 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 convetwdm:d.h0 / trrging 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 34 w q+jrdccve)b5 3aupfx6 r)/fd 3/h-her2m -f.2 cm and 23.8 cm. What is the focaha6 )3c fjhfwpq+mf)vd uxrre d- 23/ 5-/recbl length if n = 1.52?    cm

  Both surfaces of a doubn 3 yy0reh/br;aamb/8 le convex lens have radii of 31.0 cm. If the focal length is 28.9 cm, what is the index of refraction obh 8 m/;nrbe0 yaay/r3f the lens material?    cm

  A planoconcave lens (n=1.50) has a focal length of -; to4 *e g9vdrcw13oej23.4cm. What is the radius of the concave c4*dog;9rv eo3tw j1e surface?    cm

  A Lucite planoconcave lens (see Fig. Belon kczr+6;tuele bqw. v xb(9og34s11uw) has one flat surface and the other has R = egtqw6s39rcxb.(uol e1 ;n4b+zu 1 kv-18.4 cm. What is the focal length?    cm

  A symmetric double convex len8hdwp9k o41oh93jknc- 7 u iekrzp+en1a;w b- s with a focal length of 25.0 cm is to be made from glass with an index of refraction of 1.1c p 9r;7w p+ j41nokzki8ek dhheo--w9anbu352. What should be the radius of curvature for each surface?    cm

  A prescription for a corrective lens calls for +1.50D. Th.n 6:bqu *yw2wrskj 6de 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 of the other surfb w6 :d2rknq j6.*wysuace?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fig. Below). You xctx (0) :xcf-znjah*stand 1.5 m away from one of these mirrors and look into it. You will see multiple images of yourself. c(cxtf:)*xj- 0azxh n
(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 fila*gr mlic:-(9lnflt d)2ee 0 9msah -y,wh k0cled with water. We measure the width (x=5.50m) andw,2 -0llrg * ma:ak9c0 de(-fh ct9se)nl ihmy 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 piryai mvwv9 g7o0lh*kdakd*4.v24 bv*ece 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 limiting case of a sph.m0x n 8g tjifi+mjj*/erical mirror. Specigj/ m.n+8fjtij *0x imfy what 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 for-le1)5auw vokm a 90$^{\circ}\,$ angle as in (Fig. Below). When you look into this double mirror, you see yourself as others see you, instead of reversed as in a single mirror. Make a careful ray diagram to show how this occurs.

Show analytically that a diverging lens can never form a real r v15k7v klvjw()ln+dimage of a real object. Can you describe a situation in which lv)+ vl15vkk( dnj7wra diverging lens can form a real image?

  Each student in a physics lab is assigned to find the locatikiqgp np c,ktk*;;5,fon where a bright object may be placed in order , p5pkk;ntq*g,c i f;kthat 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 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 acu scls g ++ r/rc n9fy8,t6k;a8-jpkf prism is $\phi=72^\circ$ see (Fig. Below), what is the minimum incident angle for a ray if it is to emerge from the opposite side (i.e., not be totally internally reflected), given $\mathrm{n=1.50~?}$ $\theta_1$$\geq$    $^{\circ}\,$

The end faces of a cylindrical g s 6(sqw*evf8jlass rod $(n=1.54)$ are perpendicular to the sides. Show that a light ray entering an end face at any angle will be totally internally reflected inside the rod when the ray strikes the sides. Assume the rod is in air. What if it were in water?

A lighted candle is placed 33 cm in front of a converg)jiaqhl j(k8+ ,c,n:b sbc;rling 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 orpvpt+ -cqz **js3 ni,f focal length f, and a white screen for z+ ,jsr* q*pnv3-pcitviewing the image is on the opposite side. The distance $d_T=d_i+d_o$ between the object and the screen is kept fixed, but the lens can be moved.
(a) Show that if $d_{\mathrm{T}}>4f,$ there will be two positions where the lens can be placed and a sharp image will be produced on the screen.$d_T$>4$f$
(b) If $d_{\mathrm{T}}>4f,$ show that there will be no lens position where a sharp image is formed.
(c) Determine a formula for the distance between the two lens positions in part (a), and the ratio of the image sizes.

  In a slide or movie projector, the film acts as the objemr zylcy ll.9g-p:/u ,ct whose image is projected on a screen (Fig. Below). If a 10 py:-mz.lrcl,l/9u y g5-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 actually 24 by 36 mm) +jxlr 4 iy+nf7is 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 beyif 4x7+r ljn+ used if the image is to cover the screen?    cm

Show analytically that the image formed by a converging len7sh 1i,a,d t5ocujiw +2j3g ats is real and inverted atacjdwi , j3gu i7,ot251s+hif 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+m4 *ie u,o)ujyyhz/j 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 the focal length of the camera lens was 210 mm. How far away from the subject was the reporter )e oyyh/4 *,ujijuzm+standing?    m

  How large is the image of th ey xbeziwi6gc9p5* 57e 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 certwa.z:actxq ah +)t1g/ ain lens is imaged 8.20 cm in front of that lens (on the same side as the object). What type of lens is t1)qz/ g a: t+.haatcxwhis, 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)