What would be the appearance of the Moon if it had rqe e)25l lmobqn(5z g x8b8vt;pzy:/
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to hag66uw+ s4nibysm *()n0yock 0l iooy:ve burned the whole Roman fleet in the harbor of Syracuse by fosok:b (cl0moy4* +)n 6unwo0iisg6y ycusing the rays of the Sun with a huge spherical mirror. Is this reasonable?

Although a plane mirror appears to reverse lef- (peydowt:l9p3 f1jw t and right, it doesn’t reverse up and down. Ejpo3e- yf w:(pl91twdxplain.

If a concave mirror produces a real image, is the image necessarily 3 4yvu c6e*bt i+nvx1ginverted? Explain.1c 4vi6uby n*ex3 +gvt

An object is placed t 1r;d 6-.ldt3qxb4jk1.j cllrv l9 j4zymxg*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 concave or convex? On which side of 4l1tkg v1jc rl4 y. djdr;l*.xq6lm3b- zj9xtthe mirror is the image located?

Using the rules for the three qdvr qb*2.mu5d9g+lh. mzu )g rays discussed with reference to (Fig. Below a), draw ray 2 uq5hm2d9vumqz*rdg .l g)b +. for (Fig. Below b).
(a)
(b)

What is the focal length of a yet9u36qp:c q45 vbr9wg5x yqplane mirror? What is the magnification of a plane miqqet5gr6 pb9vxcyw :4uq9 5 3yrror?

When you look at the Moon’s reflection from -d; ni njehj*/hz jp ua:zc5c,:6 wb6ja ripply sea, it appears elongated . Explaijc;zpn 5h ju/ebdaih:jn-cw, j*6 6:zn.

What is the angle of refraction whrse:0+n h wawqqd)go27g d:0;pqumgud1,s s* en a light ray meets the boundary between two materials pe+ )upqsd,2r has;1dqm0 *n g7gwu0 g o::dqwserpendicularly?

How might you determine the speed of light in a sdnd6uix2 u)(vx5 gn; lolid, rectangular, transparent object2lin5 d)duvuxg(n x; 6?

When you look down into a swimming po/2h x i3y)8gp zphfqi6ol or a lake, are you likely to underestimate or overestimate its depth? Explain. How does the apparent depth vary with th/pzigf3 p 8ix h2)qhy6e viewing angle? (Use ray diagrams.)

Draw a ray diagram to s*8oxqfk cm)j, how why a stick looks bent when part of it is under water (* , fkc)oq8mjxFig. Below).

Your eye looks into an aquarium and views a fish inside. One ray -9ka)wne;p b kof 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 pnak ;e9kwbp-) osition of the actual fish. Briefly justify your answer.

How can you “see” a round drop of water on a table even though the water is.j8;xajg1sasuxe; - h transparentxxghj.aseu;- ;j 1 8sa and colorless?

When you look up at an object in air from beneathlgrf .:e f- 8s3ii6vem the surface in a swimming pool, does the object appear to be the same size as whrv lf sg.ie: 86fe3-mien you see it directly in air? Explain.

How can a spherical mirror have a negative .eer/:lo)h9sz gg ys 5q) 5fpzobject distance?

Light rays from stars (inclqs98 2lemybxrs 2bn7;uding our Sun) always bend toward the vertical direction as they pass thros8q29;mx yb7bsn e r2lugh 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 plx b)(:;n:ru k9lh1rb3ghevk yaced if a camera lens is to make a sharp image of an object very faueh vkx);blh:n3: k9y bg r(1rr away?

What type of mirror is shown in (Fig. Below)? w5t8gd*0u2 rewzf 3* 14equ/retxlbmExplain.

A photographer moves closer to his subject and thelzheap r0ey0ch :) ;x7e6(lu)2zg.kesm4rl rn refocuses. Does the camera lens move farther from or closer to thkrs;l0 az ()6mglpr02ly )eeeeh.ur hz:c74x e film? Explain.

Can a diverging lens form a real image under any circumstances? Expd,kqzbwt j43aa t75i+ skx7-rlain.

Use ray diagrams to show that a real image formed by a thin lens is ae;2 oxzyp80ooww ib05ya 0r, zlways inverted, whereas a virtual image is always upright if the object is reab x5oo8 0wai20y;roe,p 0yzw zl.

Light rays are said to be “reversible.” Is this consistent with the 98pm4nvf +exb thin lens equation? Explain.n4xep f 8vm+b9

Can real images be projected on a screen? Can virtual images? Can eitherz dx2b9 v0- wloancb65 be photogr65lnzv0-ao9 xc wb d2baphed? Discuss carefully.

A thin converging lens is moved c6 g vcw*n0bcw(loser to a nearby object. Does the real image forcg0c 6n (*bvwwmed change
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an ins8y hv-n,i;f,:licq q dex of refraction n = 1.30 In air, it is a converging lens. Will it still be a converging lens if ,;ynfq,- il8v:hiqsc 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. Ikbi4 .e, r(xkaf the nose and the tail are e(,bkei.r 4kaxach focused on a screen in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facing a convhp8e5l:mn*i b4 gq(e.dc ep:ja1nt 4nerging lens. Under what circumstances (if any) would the image of the nose be virt4qh n41:cj* mgb5dtn8(alnp:e.ie ep ual and the image of the tail be real? Where would the image of the rest of the cat be?

Why, in Example 13, mte5rxow 5/ls*ust the converging lens have a shorter focal length than the diverging tw/x5oe5 s l*rlens if the latter’s focal length is to be determined by combining them?

Explain how you could have medj ozgh;o0ue --8/p a virtual object.

  An unsymmetrical lens (say, planoconvex) forms an image f-k 5crle*tdk usg26nf : oun:6 xvh//of a nearby object. Does the image point change if the lens is turned aro2-nk6e:6dsfxr*u n/vc5ot/: fk gh luund? ----待选择----yesno 

The thicker a double convex lens is in the center as co;d0w,s+o9nps w1 k2 xn1ctlzjmpared to its edges, the shorter its focal length for a given lens dij cpw2tso+k lsnx , zwn1d901;ameter. Explain.

Consider two converging lenses separated by some distance. An obm).pcr0o wj xswu i)+lvq55 6c++y gytject is placed so that the image from the first lens lies exactly at the focal point of the secondw++. tpgq0svocjr)u)yil yx+m5w5c 6 lens. Will this combination produce an image? If so, where? If not, why not?

  Suppose that you want to take a photograph of yourself as you look at your exg 21d;( xxgryp(v:ww 87p pkew-,znimage in a flat mirror 2.5 mdr w;2x(g nwg:wzx(7e,8 pxkve-yp1p away. For what distance should the camera lens be focused?    m

When you look at yourselfre m*ejb/ rrrc1gf7;7uwl37z. kby i( in a 60-cm-tall plane mirror, you see the same amount of your body whether you are close to the mirror or far away. (Try it and see.) Use ray diagrams to show why this should be*c z 7 ere1j /kbrl7brf3( rugwm7;iy. true.

  Two mirrors meet at a 1wivoaa+hx8+4 35$^{\circ}\,$ 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 abovezy.jm dl p- p7fl20bl7 the floor stands 2.20 m in front of a vertil7 2ydm-7fplb0z. l jpcal 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 mirror?    cm

  Suppose you are 90 cm from a plane m 2wnz(2r wpx4mirror. What area of the mirror is used to reflect the rays entering one eye from a point on the tip of your nosen w2w2xrpz (4m if your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors m/vi la f1f,matr0 jb8,eet at an angle $\phi$. a single ray reflected successively from both mirrors is deflected through an angle of $2\phi$ independent of the incident angle. Assume $\phi<90^{\circ}$ and that only two reflections, one from each mirror, take place.

  A solar cooker, really a concave mirror pointed at the Sun, focuses the Su*p0 m qy.uq)g9ct/kumn’s rays 18.0 cm in front of the mirror. What is the radius of th0mu q/9p .mcg) ku*yqte spherical surface from which the mirror was made?    cm

  How far from a concave mirror (radius 23.0 cm) must an object be placednz- )by9a9bh- hvlx9h if its image is to be at infinityby a -x-9)9h9znh hvlb?    cm

  If you look at yourself in a shiny Christmas tree ball wy93- gjp; pjyiith a diameter of 9.0 cm when your face is 30.0 cm away from ipy j39-yi; jgpt, 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 amusemf/q,giz7/ -y i.lwpf 46qclp sent park shows an upright image of any person who stands 1.4 m in front of it. If the image is three times4pg6ly,w-lc/7 f . pz/iiq sqf the person’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror that, when 2.20 c(u 9h4 m/qj )hitepn)km 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 thf)f p wqd3m2:q*aikn* evgto n5.( by/at are smaller than they would be if the)/dvgaq5e:bnfmtyk n.w(oqf* 3 2i *p mirror were flat. Are the mirrors concave or convex? What is a mirror’s radius of curvature if cars 20.0 m away appear 0.33× their normal size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is placed 20.0 cm from a convex mirror of rvdazirxyi+j3+0l.,k 2(b sd aadius of curvature 20.0 2jd.v sdb l +ay+(0r ,z3iikaxcm.
(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:ff7sp(np99j mf ak6 v from a convex security mirror in a store. You estimate the height of your image to be half of your actual height. Estimate the rfajk76npf(p9s : m9fvadius of curvature of the mirror.    m

  (a) Where should an object be placg:nc9 a svk8h.ed in front of a concave mirror so that it produces an image at the same location as the object? .:8nva9cgh sk
(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 virtual and very small when vqa+d p8ftia:f y8e)y .l3zgy4 iewed in a curved mirror. The image appeaya)ag yf348 yd ftz.pl 8q:+iers 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 technidddqg9+k)1 e r6r2fbd ques,
(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 diageg)e h.q4d r9lram, that the 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 mirror equationmbtr lx,k807kk5 jr5f, Eq. 23–2, is valid for a convex mirror as long as f is consider ljr85m 5k0rf7xtkkb ,ed negative.

  The magnification of a c + zx:fesfgtlt4+n:)/,/f-xlhbque u onvex 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 placed 28 cm in front of a sphero23 p fqttk 8o.*,dkvmhq4b7a ical mirror. It is desired to produce a virtual image that is upright and 3.5 cm k2fthbkq otp34q8*, v om7 .adtall.
(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 fac;v f*se8/pxn de by a factor of 1.33 when your 8xp*v/e ds ;fnface is placed 20.0 cm in front of it.
(a) What type of mirror is it?  ----待选择----convex mirrorconcave mirror 
(b) Describe the type of image that it makes of your face.
(c) Calculate the required radius of curvature for the mirror. r =    cm

  What is the speed of light d/- 2cw e7xiooin
(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 is a ei79(;emboy $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain substance is 89% ofdm41gju, xi nss0 ,p3o its value in water. What is the,dj p3oug1ssn0x,mi 4 index of refraction of this substance? n =   

  A flashlight beam strikes the surface of a pane of glass (n = 1.581x9b dd2apm a1) 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 wq ) trwjly;q.5m/xhyr +xta 18ater 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 the water at an nes63h q3wy:qhd 73ah angle of 66.3q3hyansedwh:7 h 36q0$^{\circ}\,$ 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 sjze2170a3 met qyhxh-een 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 withpk yo 0,8/f(phnksgk , water 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 this pohf,kksnk(y80,p g / 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 na ;**smerh jpm4rrow 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 the bottom of the pool, measured from the wall beneath *r4j p hm;*emshis foot, if the pool is 2.1 m deep?    m

  Light is incident on an equilateral glapg0ex-7+x w.9jvrdie- v l7mzss 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 :13 xkdrpugz: (n = 1.52) and is partially reflected and partially refracted. Find the angle of incidence if the angle of reflection is r:z3pu:dxkg 1 twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam incident on a uniform laye8-lq3yk.bc/m4h dlwlr of transparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the incident beam, independ3 l-h.y4k8cdwql m/b lent 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 z:jao6p/+pc-1cjm 9d;a an.gd bt x,y of refraction n as in (Fig. Belowpm,c1dab nzapc ;. 9+dgtya6:/joj x-). Show that 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 fcflp0u;h g*-(gsb6*gmn zv 4and Lucite? To be totally internally reflected, t6 lfvm sug(;h0* *-gpfbznc 4ghe light must start in which material?
$\theta$ =    $^{\circ}\,$
 ----待选择----waterLucite 

  The critical angle for a certain liquid–air surface is 47.dy/7bqe jq2g3 7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in a pool of water fromi vc /2ra(4fol 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 ligh(r/ i4lfovc2at does not exit the water?    cm

  A beam of light is emitted 8.0 cmq 4ax6ofo87 su beneath the surface of a liquid and strikes the surface 7.0 cm 6uf 8qos4a7ox from the point directly above the source. If total internal reflection occurs, what can you say about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the lef4-y daxd.aas 5w0:khfk(okh3 t face of the 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 sx+isu28 frl( phown in (Fig. Below). Show that we can guarantee total internal reflection at the side surface of the materiar8 ui2fs+xp(l l (at point a), if the index of refraction is greater than about 1.42. In other words, regardless of the angle the light beam reflects back into the material at point a.

  (a) What is the minimum index of refraction ff t448c32x7ypbji fxa yv8:kna*vc( nor a glass or plastic prism to be used in binoculars (Fig. Below) so that total internal reflection occurs at * faj28ia3vtxfnnb: v4 kcx p487( yyc45$^{\circ}\,$? $n_1$ $\geq$   
(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. ,7xdz1j-nr2qw 2 n2 dnjdxw*h0 mm behind a 65.0-mm-focal-length converging lens. Find the object distan 7zwwjh - nnx*q2n 21r2xjddd,ce
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.5 cm behindwawxh3b o;86d 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 ob(8epd2 5 -zoyagc+l/6auaaopject 2.75 m away as an image 48.3 cm on the other side of the lens. What type of lens is aaug/eolp6 (ay-2d+8zpc5oa 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? Pddwq9ajt).i0zu,/e l. p )i 9qdm8x gz =    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 convergin-d.hy;3cz+(fj d a axyg lens with focal length 24 cm to view a stamp 18 cf(3 had;cyyda+ .z-xj m in front of the lens.
(a) Where is the image located?    cm behind the lens (virtual)
(b) What is the magnification? m =   

  A -5.5-D lens is held 14.0 cm from an object 4.0 mm high. Whatdwatpo(xfs r .)93/u o are the position, type, and height of t o3)tpasf(w9 ./ruo xdhe image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to focus an .dex*d sm, vl6tlbi0ji 4 k1+uimage on the film of a camera. The maximum distance allowed between the lens and the film pb i, 0e 1.stlmx+i 6u*kddv4jllane 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 material by a factor of 2.5× when a book y/cj rv.6l,k*yvxpk8 is placed 8.0 k/jxyk86lvvpy *,.c r cm behind a lens.
(a) Draw a ray diagram and describe the type of image this would be.  ----待选择----realvirtual 
(b) What type of lens is needed?  ----待选择----converging lensdiverging lens 
(c) What is the power of the lens in diopters? P =    D

  An object is located 1.5 m from an 8.0-D len 1;+pwa0 st tbv1r-33xwyu bzis. By how much does the image move if the o it-b1wwraup 1s0;33+tbyz vxbject 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 25 cm should8 l x2te wn89ylgm0y/vj+xu7b an object be placed to produce a re vexuylx +gmyt0 8 9bw8n/jl72al image which is the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens must an object be placed i(9*sv+o2 n1 lhssrppif its image is to be magnified 2.00× a+s lp(sno9r*21i ph svnd 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 be5f.l qahm z6m zjic2q1u+mz*0 placed if its image is to1 ujqmiqcfzmm*.56+l zz0a2 h be magnified 2.00× and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm (formed by some other piece of optics).]

  (a) A 2.00-cm-high insect is 1.20 m from a 135-mm-focal-length lens. W .sh m wspt;:y gcl,x7bx1-m+dhere is the image, ho;s7bp1 dg s +lx.t-wmy, mc:hxw 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-length co /dpl6jhkkqvle ,/, ;jnvergik/jv, dl6 eqj ,;plhk/ng lens if the image is 2.5× larger than the object and is real?    m

  A bright object and a viewing screen are separated by a dis im s13kr z-a0j-(gbyytance 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: firs3ji yms1-b0gy-k(za rt draw a diagram.] lens should be placed    cm or    cm from the object

  Two 28.0-cm-focal-length converging lenses are placed 16.5 cm diu.vs (ynq(m8m za i/-)bk3d apart. An object is placed 36.0 cm in front of one lvqbm) u smzd (aniy/d-(8.3k iens. Where will the final image formed by the second lens be located? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens with1xbr,pd2ell/z,6c 0b w ucx 4i $f=-31.5\mathrm{~cm}$ 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 divergyk zt/(u0;cve gbw( w)n+e jc;ing lens. Parallel light strikes eb;(e t/czk vw()jcw0 nug+; ythe diverging lens. After passing through the converging lens, the light is again parallel. What is the focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Example 24am:h cna+9lp1 d,tmf 3–12 are now placed only 20.0 cm apart. Thenm,1 tpa:lhf9damc +4 object 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 y1cgs4nxllo4s .7a wu 77ps/ulens on the right is 20.0 cm, and the focascson/.47u74lwa s1ux g7p yl l 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 original object?    cm

  A diverging lens with a focal length of is placedozkcjym- 12 k9+.uc yg1:re he 12 cm to the right of a converging lens with cjemryo21k 9ey-:.k z +c1ugh a focal length of 18 cm. An object is placed 33 cm to the left of the converging lens.
(a) Where will the final image be located?    cm to the left of the converging lens
(b) Where will the image be if the diverging lens is 38 cm from the converging lens?    cm to the right of the diverging lens

  Two lenses, one converging with focal length 20.0 cm and one c( g5 qz3: qmf8qgti;cdiverging with focal length are placed 25.0 cm apart. An object is placed ct3:8qmzgqqfc ;i5 g(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 e:+d lq2ustus ;s a5/dplaced next to a converging 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 surfac 5s kor y4cg;q n2i;tvlrm50li0uv4q3e radii of 34.2 cm and 23.8 cm. What is the focal length if n = 1;qrcq4l3m45i ogsvrn0;0lt5 k 2vuyi .52?    cm

  Both surfaces of a double convex lens have radii of 31.0 cm. If the focaj3)/.rr .0 avj: wpuf.zojpb sl length is 28.9 cm, what is the index of refro . 3bp/ u.0jsj.fawzvprjr:)action of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm. What is thqb 2i+zgjca w+w+f9v*e radius of the concave surface? *2bfa9c++wivg w zqj+    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat s0j 3t67fw nnjkurface and the other has R = -1tnfjw0 n67j3k 8.4 cm. What is the focal length?    cm

  A symmetric double convex lens with a focal length of 25.0 cm is to ee3yko/ a n,g9be made from glass with an index of refraction of 1.52. What sho a3ge9 kn,/oeyuld be the radius of curvature for each surface?    cm

  A prescription for a corrective lens calls for +1.50D. The lensmaker grinds theoh1bfo 0l3xl n(. ezk7 lens from a “blank” with n=1.56 and a preformed convex fnob.z37l 10 lxfheo(kront 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 api a(m:1tz jo v24g:utuart as in (Fig. Below). You stand 1.5 m away from one of these mirrors and look into it. You will see multiple images of 2 vtmjiuazt:u1:o(4 g 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 fille)np1uaj6 9gbl kq,o0b.nsbnvm :kx89 / n.g nwd with water. We measure the width (x=5.50m) and then note that the bottom edge of the pool is just visible at an angle kbjug8 )9b6 obp.n0nsnk:m.w/ qx 9avn, nl1g of 14.0$^{\circ}\,$ above the horizontal as shown in (Fig. Below). Calculate the depth of the pool.    m

  The critical angle of a certain piece of plastic in a vblt(ng7bn 6. 7nek9nir 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 spherical mirror. dkxzd-p 4-d+y Speci-kdyd-4 +xdpzfy 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 sov-ej4exjz j;0k6a a/oe/+ naxqf zf 26 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 form a real image of a r l(ar 16b-i afhhux8m9eal object. Can you describe a situa1 rxfhl86iu- ma (abh9tion in which a diverging lens can form a real image?

  Each student in a physics lab is3p6m 7b3s 8ifunc6nbmrme l-/ assigned to find the location where a bright object may be placed in order that a concave mirror with radius m3fm 6bsr7li -8pu 3nb/mcne6of 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 prisw0 5h-99saqn.adxm*8g a3hn 5mcaq 8jbt) snnm 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 cyls*z bd2r3qjlm-imy *8indrical glass rod $(n=1.54)$ are perpendicular to the sides. Show that a light ray entering an end face at any angle will be totally internally reflected inside the rod when the ray strikes the sides. Assume the rod is in air. What if it were in water?

A lighted candle is placed 33 cm in front of a converging lens of focaudu 1j ,ag -kt+9dkq:sskad+5 l 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 p -d + kw-l9ktz8oq1;mvvy 8jbplaced on one side of a converging lens of focal length f, and a white screen for viewing the image is on the op;1wyq8v otpvzd9-j 8 kl-k b+mposite 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 objec)zj -jf(hj( hit 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 thf)jz (ji(h jh-e 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 (picturl 3y 0am kkc24m/)axtff0 g2cke size is actually 24 by 36 mm) is to be projected on a screen 1.80 m by 2.70m / yak2g)l4cm30 cxk0ftka2f m placed 7.50 m from the projector. What focal-length lens should be used if the image is to cover the screen?    cm

Show analytically that the image formed by a converging lens is real and in v7g3)sgm -wtkverted if thet7gvgsk)3-wm 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 shootinghl.1se*d fckr 7;l2;izq 0 58qpv vemk 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 mme r zd*lm ;sv15fk20eq 7lvc;iphkq.8 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 Sun on film used in a camera zwkt:qu/tm h 7/3i+rhwith
(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*wn r7vuz 7mr7 a certain lens is imaged 8.20 cm in front of that lens (on the same side as the object). What type of lens is this, and what is its focal length?77 *mvw7 rzrnu 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 jso bln )( (g3yjgn+q5converging lens, it forms a real image. When the object is moved t+ogj(qb3 j(n s)y5g nlo 40.0 cm from the lens, the image moves 10.0 cm farther from the lens. Find the focal length of this lens.    cm