What would be the appearance of the Moon xk38zf rk hu (k;2/hutif it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman ;y/-u(t ww r8hbn s,32n lxcinfleet in the harbor of Syracuse by focusing the rays of the Sun with a huge spwyc, b (n8iwhut -/sx nrnl32;herical mirror. Is this reasonable?

Although a plane mirror appears to reverse left and right, it d,hv.bw jbu7 ;soesn’t reverse up and down. svbuwj, .7b;hExplain.

If a concave mirror produces a real image, is the image necessarilpr02;71htpyl en. ecky inverted? Explhl2;.k 70eyrpn pec1tain.

An object is placed along the principal axis ofa90qg t3 br.fj /;/xoc5qrqjw 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 whichxqbo.0wj ;c agt3qqrr9 f/j5 / side of the mirror is the image located?

Using the rules for the three rays difriek95r*y; 33i voa sscussed with reference to (Fig. Below a), draw ray 2 forsy5o3 r*ei9akiv;r3 f (Fig. Below b).
(a)
(b)

What is the focal length of a plane mirror? What is thdntex nj1:aj*qs4acnv+hk/ . m;w 6p4e magnification of a plane mirror p4nq;.d1awnn6sm e*k h4+vjj /:caxt?

When you look at the Moon’s reflection from a ripply sea,itv)kx c1ly ;j5nxjadu)zg* t(/o5 w0 it appears elongated . E 5*k;j/axutvj )cni5zgw( lty) dx1o 0xplain.

What is the angle of refraction when a lightq.dbe- z(oln1j )i )cq ray meets the boundary between two materials perc1j l.)qbieod)(nz -q pendicularly?

How might you determine the speed of light in a so2z l rrwhja 1-k4cgfqn..9(folid, rectangular, transparent objl rn1joz -(ah9.4cgfrw .fk2qect?

When you look down into a swimm5b zl6fzmzfn,q1sb pu3 3zmi k3m3+.ling pool or a lake, are you likely to underestimate or overestimate its depth? Explain. znbl+fb3pz,3s m3kz 6mu1fz.lq5im 3How does the apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks bent when part o qp:+hww8 s4pm;d:epla: . vjof it is under water (Fij8s l: :pa.;v:o+dwqpmep h4wg. Below).

Your eye looks into an aquarium and views a fish inside. One ray of lxwbp-: 0avbp ;xw0 ff7ight that emerges from the tank is shown in (Fig. Below), as well as the apparent position of the fish. In the drawing, indicate the approxim7fa:v w0-x; bbp0px wfate position of the actual fish. Briefly justify your answer.

How can you “see” a round drop of water on d lnl1 2;f;nfsa table even though the water is transparent and colorless?fn; 1llsd n;f2

When you look up at an object in air from beneat ;h-ytehzqdzzb c78.(h the surface in a swimming pool, does the object appear to be the same size as when you see it dib;zh8.d tch(-zqe zy 7rectly in air? Explain.

How can a spherical mirror havqrn 0gg9cofnqnj 7z 94;76yspe a negative object distance?

Light rays from stars (including our Sun) always b9 f 8 xujino6fq*,(yfwel +/qtend toward the vertical direction as they pass through8o fejt/i*f+ yx fqnq,6(uw l9 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 sharp ima(* tb7pp dgq,kge of an objek(bp* g,tqdp 7ct very far away?

What type of mirror is showi 2dx i.b(0nepn in (Fig. Below)? Explain.

A photographer moves closer to hi9 n vmvxc8 bof;(k-3nns subject and then refocuses. Does the camera lens move m8 bkonvfvnc3-9; x(nfarther from or closer to the film? Explain.

Can a diverging lens form a real imv zn 5 1zit2g+87gkiwz(zel9uage under any circumstances? Explain.

Use ray diagrams to show that a real image formed by a thin lens is alwayse;4 y1yeigggv *;p(lct*s2qtk bs1g) inverted, whereas a virtual image is alwaygv1 cye bpg4gt *q;2s)*;gik(ety s 1ls upright if the object is real.

Light rays are said to be “reversible.4uqq6q r160jv dhv(5 )zdd vsw” Is this consistent with the thin lens eq d0jqdwv 1sh)v6vqzuqd4 r65(uation? Explain.

Can real images be projected on a screen? Can virtual imagvlo2 k wl8).ryes? Can either be photographed? Discuss carefuly82vlw kro )l.ly.

A thin converging lens is moved closer to a nearby object. c1f na5 g-kruq b(+fs0Does the real image formed chan(fa+c-k0ub5sg 1fn qr ge
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index ng9wr.vxghl0e/ 8 q25h+l dyt /no n*wof refraction n = 1.30 In air, it is a converging lens. Will it still be a converging leng80t/e.o2yrnd g*qwh/+n 9xw ll n5vh s if placed in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands fachd) .+yzj 8xozs nw. o.a2c0iw.o8x4f- p iakjing a converging lens. If the nose and the tail are each focused onxapkwj y+o0.c o f j)si8wxia 4on-8h.zd2..z a screen in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the ar9r qxgsdwb9/x kd2/+vsw / 8;an4vkdir 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 images;/wwxrg abvxd4vn9q/ ks dk+d9r /28 of the rest of the cat be?

Why, in Example 13, must the con* s 48ri )w gv3j40evcls7djtuverging lens have a shorter focal length than the diverging lens if the latter’s focal length is to be determined b*dsivts3 lj8 r u74cve0wjg)4y combining them?

Explain how you could have a vuk/i :pep;t6 z -(yitlirtual object.

  An unsymmetrical lens (say, planoconvex) forms an image of a nearby object.rs g 1gl1iq-2g Does the ima12g1girsq gl-ge point change if the lens is turned around? ----待选择----yesno 

The thicker a double convex lens is in the center as comparehfyo7- jur ue59(z yjs o6+w+qd to its edges, the shorter its focal length for a given lens diame+ ourjyys5oj+7wf ehz-(9u6 qter. Explain.

Consider two converging lenses separated by some distance. An object is plac+/xyi5: ns - e6bpw;spgkq6 yg3 )eyqwed 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, s56wkywy:y )ep6g- qbp3sgx ;e+ qin/where? If not, why not?

  Suppose that you want to take a photograph of b:7+ucb(g cj f)lwtf) yourself as you look at your image in a flat mirror 2.5 m away. For what distance should the camera lens w+)f( ccb ft)l jg7b:ube focused?    m

When you look at yourself in a 60-cm-tall plane mirror, you srv,vgu;hwr ,o+ l x yw;hv25/dee the same amount of your body whether y+lv o ;h;5uvdgh r2,vr/y wwx,ou are close to the mirror or far away. (Try it and see.) Use ray diagrams to show why this should be true.

  Two mirrors meet at a 135a/ vzgk+3d 0qll,ww -p *tdf)p$^{\circ}\,$ 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 abofovc sthn(-g/bp/o7)+y zqs.xu .1 u yve the floor stands 2.20 m in front of a vertical plane mirror whose bottom edge is 43 cm above the floor, (Fig. Below). What is the horizontal distance x to the base of the wall supportingosypyuu . /cqb(x1zn)og/. +s h-7vt f 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 mi8i5;fk/s l5fh (ypypw h+n u*brror. What area of the mirror is used to reflect the rays entering one eye from a point on the tip of your nose if your pupil diameter is 5.5pi*ky8+lhnub 5pw y;f s/f5 (h mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors meet ac4u:i/ :lcs 6kuk uv*wt 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*esfkvbc*5uvp m20j 1m/8vti concave mirror pointed at the Sun, focuses the Sun’s rays 18.0 cm in front of the mirror. What is the radius of the spherical surface fr/sji*1vm u v5bf82m0tpke v c*om which the mirror was made?    cm

  How far from a concave mirror (radius 23.0 cm) must an object be placed if itsh8(md3e864/ww qf wqjmt.bt o it6/m4f3qj8e t 8wwom .dq(wh bmage is to be at infinity?    cm

  If you look at yourself in a shiny Christmas tree ball with a diametew/7zv.g.uw k8x,dt9 oneqy+ tr of 9.0 cm when your face is 30.0 cm away ,qwn. y z+.tud87okv/9x twegfrom 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 any person who stja)*9wplmy )v ands 1.4 m in front of it. If the image is three ty*)ajml9wp )v imes 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 pr;rk xypnu6w,9 oduce 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 prod-vkjp 8xq--mju1afmn)o) y/ z uce images of cars behind you that are smaller than they would be if the mirror were flat. Are the mirrors concave o8vn-fu 1p aj)om xyjz/-mk )q-r 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 h2v yph7m24ulmm high is placed 20.0 cm from a convex mirror of radius of curvature 20m7l2 hhy u2p4v.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 tkr ux h zp+4hb)zcnye)e96 7/a store. You estimate the height ofrcyx z9uh )) 6p+/ hknzete74b 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 of a concave mirrorgy o8l qnnqz54 e;ec5lo)b6 *m so that it produces an image at the same location as the object? e5*4gm5;o 8cy b nl)zqe6q oln
(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 trp /t vq7gf9cjmg3*b/f6q.zgn ee is virtual and very small when viewed in a curved mirror. The image appears to be 18.0 cm behind the/g 69ct jgqzbfq vmfpn*/g37. mirror. What kind of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different tech3om m.m0:h2 gbimb.yn niques,
(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 magnify w ,tie2vs6ym(o:u a::pxg(+pd-su eication m of a convex mirror is $m=-d_\mathrm{i}/d_\mathrm{o},$ just as for a concave mirror. [Hint: consider a ray from the top of the object that reflects at the center of the mirror.]

Use ray diagrams to show that the mirror equation, Eq. 23qur) me3r/f eo2+qr0s–2, is valid for a convex mirror as long as f is cs0 rm qoq+ re2/e)ru3fonsidered negative.

  The magnification of a cg 8ge +l.w1 :a/egoy9h+xjzcoonvex 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 pkclz,s5xc9 c:laced 28 cm in front of a spherical mirror. It is desired to produce a virtual image that is upright kxz,c s 95lcc: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 magnif q5o7guyze5- ) nuekd+y your face by a factor of 1.33 when your face i-ze geo5)kq+ nyud u57s 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 in /dzq0v4: buiw
(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 isyws33.lkuoc-.izy6 afwo2 uwd5b 7: o $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain substance is 89% of itshp.k po d;nk1* value in water. What is t1*k;kp.pondh he index of refraction of this substance? n =   

  A flashlight beam stri 2tqm+nmttw59*wsawp8 : ;me/lj4wb n kes the surface of a pane of glass (n = 1.58) at a 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashlight upward from beneath the water at9 /d)jtfzddkrjbj5qjo)( 2fa.jq iv4f/ +zm; 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 d q;qy7r8 ruj 2(a5vhjangle of (j qq8rhda;uvrj7 y5266.0$^{\circ}\,$ 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 makeur)rp uu/e9b9 a 31.0$^{\circ}\,$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?    $^{\circ}\,$

  An aquarium filled with water has flat glass sides whose index of refrac, ,e 36mt0syfv dch.jqtion 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 thisse vy,fqjtm0c3.6h, d 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 botyq,ksm- k 8)bgtom of a pool at night, a watchman shines a narrow beam of light from his fl,kkbqmy) g8 -sashlight, 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 his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equilateral glass5jmat( 7k 7. mqwh;/jfau63yys 2veoa prism at a 45.0$^{\circ}\,$ angle to one face, (Fig. Below). Calculate the angle at which light emerges from the opposite face. Assume that n = 1.58.    $^{\circ}\,$ from the normal

  A beam of light in air strikes a slab of glass (n = 1.52) and is partially +ir( q+. t8cuw;4im w0vvqalsreflected and partially refracted. Find the angle of incidence if t v 4v8iam 0(t cq.lsiu++r;wqwhe angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam incident on a uniform layer of transpare,q5nqtrs(8py nt material, as in (Fig. Bel,p (q5s8q yrtnow), the direction of the emerging 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 piece of glass with index of refra3j m e5 :135j juqkja7hbo,ezoction n as inhojee:u m5ja qj5bjk ,7oz 133 (Fig. Below). 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 angmeagb*x6 252,ow sp jule for the interface between water and Lucite? To be totally internaj ,wse26*omb u5a2gpxlly reflected, the light must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–air surface is 47.7i1+ rsv9yv ym3q)dl4/m kk)ej$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in a pool of water z+yg ud*p4t oex- qg5,from a depth of 62.0 cm. Where must it strike the air–water interface, redg x4 -goy*5uq ,+ptzelative to the spot directly above it, in order that the light does not exit the water?    cm

  A beam of light is emitted 8.0 cm beneath the surface of a liquid and stri2iu* e peko9ui36)hutl7q xy3kes the surface 7.0 cm from the point directly above the source. If total internal reflection occurs, what can you say ek3xiup6eh u9i )3qy2 7 uol*tabout the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face of the prism in (Fl+ opy3vq8 2dq;a 8ijnig. 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 c dc 2/jknv(x+c7gh:gx,jc hvjg)4x)shown in (Fig. Below). Show that we can guarantee total internal reflection at the side surface of the material (at point a), if:+dvgc /hnc2cx)) ,v7jgk4c(hj jxg x 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 for a glass or plastxg wt+;b 6i7udic prism to be used in binoculars (ug67xw d t;b+iFig. Below) so that total internal reflection occurs at 45$^{\circ}\,$? $n_1$ $\geq$   
(b) Will binoculars work if its prisms (assume n=1.50) are immersed in water?  ----待选择----totally reflectingtotally transmitting 
(c) What minimum n is needed if the prisms are immersed in water? $n_1$ $\geq$   

  A sharp image is located 78.0 mm behind a 65.0-mm-focal-le : +u(r3:*se h(aa lplvt 1ozqlokt0-6q8gvnongth converging lens. Find the obje a( (q *og ltlra3vo6+:u0 nh8v-ptq:os1lk zect distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18prb5 v n 0sehorkfu9 *sl+094r.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 axkk5 i*s1ffd)v o:k *qn object 2.75 m away as an image 48.3 cm on the other side of the lens. What type of lens is it and what is i1fq dvxokfks)5k*: *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 20ao /o.j,xl 2 xn2kvfs35f-kyl .5-cm-focal-length lens? P =    D  ----待选择----converging diverging 
(b) What is the focal length of a lens? $f$ =    cm  ----待选择----converging diverging 
(c) Are these lenses converging or diverging?

  A stamp collector uses a converging lens with *oa0j.4 wi.tzutnk * 2ym:qxcfocal length 24 cm to view a stamp 1mitk 2j*.o q4:*u .0yacnzxwt8 cm 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. What are thefv,, fhc ved9;swxjt 7c11y5zu xru39 position, type, and height of the im 1w7, tefjc;xh93xuvzy1 9,fvdsc u5rage?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length len9y(cw2y09y.ro tzh.vp- xkof ( 6 hpchs is used to focus an image on the film of a camera. The maximum distance allowed b(t.pkryy6.-ho 9 p zcfc2wxo0y9h (v hetween 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 material by a factor of 2.5× when a w( r-hoq3 +lyo+w 1rp/kjz qy-book is placed y(+l-3yr+pro h-/ qkzo1jw wq8.0 cm behind a lens.
(a) Draw a ray diagram and describe the type of image this would be.  ----待选择----realvirtual 
(b) What type of lens is needed?  ----待选择----converging lensdiverging lens 
(c) What is the power of the lens in diopters? P =    D

  An object is located 1.5 m from an 8.0-D lens. By how much does the imageq1ktyujd8 r )8 move if the object is movektd)8ry uj8q1d
(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 dquaon s,/jm 3b4i69ca focal length of 25 cm should an object be placed to produce a real im4, b mn 9ucaiqj/d36soage which is the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-length lens8/d.yk j-pjg ep ),tvy must an object be placed if its image is to be magnified 2.00× and bey-pd jt.,vp/)ey g8kj real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm

  (a) How far from a 50.0-rdyjd fx,h z9ma ,yq8fgvjn7f272o . 8mm-focal-length lens must an object be placed if its image is to be magnified 2.00×zfd2r8j7f9xdo8ymjf hvq2, ,7ag .yn 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-len k c qpobd9+rdyk26u46,xcp:ugth lens. Where is the image, how high is it, and whrk,6:dyud+9 p cbc4u oxkpq 26at 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 con6ojt3(t j slhb-e)2snverging lens if the image tebjl s)n( th6so3-2j is 2.5× larger than the object and is real?    m

  A bright object and a viewing screen are separated by a distance of 66.ln,6gr) 2s be61 o(bfvc wtse20 cm. At what location(s) between the object and the screen should a lensvo6(1el c2 6n)t2 fsgbsbw,er of focal length 12.5 cm be placed 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 converg3i sd*(9fw mrding 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 secw*i9rmd3 f(d sond lens be located? What is the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens wit qx dno4j/.y(wi epl9/h $f=-31.5\mathrm{~cm}$ 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 converz(zg;5iw; xj fging lens is 21.0 cm behind a diverging lens. Parallel light strikes the diverging lens. After passing through t;f;(zxw zji5ghe converging lens, the light is again parallel. What is the focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Example 23–12 are now placed only 20.0 cm apart.bj8 1e 4vhmvb. The object is sti4 j81.vhbv bemll 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 to:azve dg 11v;he lens on the right is 20.0 cm, and the focal length of the lens on the left iso ez vga:1vd1; 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 :* 2v k3ynaqu04 b4ub bls*qsj is placed 12 cm to the right of a converging lens with a focal length of 18 cm. An object is placed 33 cm to the left of the converging y us2: bjusqlv4nqb04*ak*b3lens.
(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 kt w sks/;c6 +if,rd1uone diverging with focal length are placed 25.0 cm apart. An object is placed 6 s/f+ 1u6drsc;kk,wti0.0 cm in front of the converging lens. Determine
(a) the position    cm to the right of the diverging lens
(b) the magnification of the final image formed.   
(c) Sketch a ray diagram for this system.

A diverging lens is placed next to a converging lens of focal le:a1mhsb4pip p ws8:6 ength $f_C$ as in (Fig. Below). If $f_T$ represents the focal length of the combination, show that the focal length of the diverging lens, $f_D$, is given by
$\frac{1}{f_\mathrm{D}}=\frac{1}{f_\mathrm{T}}-\frac{1}{f_\mathrm{C}}.$

  A double concave lens has surface radii of 34.2 cm and 23.8 cm. What is the+;pz( vin- cbj focal length ifn+v(bzjcip - ; n = 1.52?    cm

  Both surfaces of a double convex lens have radii of 31.0 cm. If the focalbnsi 9gl -ua82ei08c/ elsn. r length is 28.9 cm, wha ilgns abcls 2r0e8e/ui.8n9- t is the index of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has i9l/4wgctf1q a focal length of -23.4cm. What is the radius of the concave surfatfwiq l/g 94c1ce?    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat sureq7zadniw :r6 ,1nf0jface and the other has R = -18.4 cm. What isf7 1ajz,eqn w0n r6:id the focal length?    cm

  A symmetric double conv(1crso; lpy r(ex lens with a focal length of 25.0 cm is to be made from glass with an index of refraction of 1.52. What should be the radius of curvature for each surfarys1p ;l(c(or ce?    cm

  A prescription for a corrective lens calls for +1.50D. Thaj peo64t0 :pre lensmaker grinds the lens from a “blank” with n=1.56 and a preformed convex front surface of r 60:jpepr4tao adius of curvature of 40.0 cm. What should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fig. Below). You standnx3kyh *lv0.k 1.5 m away from one of these mirrors and look into it. You will* xyk. k3h0lvn see multiple images of yourself.
(a) How far away from you are the first three images in the mirror in front of you?
$d_1$ =    m
$d_2$ =    m
$d_3$ =    m
(b) Are these first three images facing toward you or away from you?
the first image is facing  ----待选择----toward youaway from you ;
the second image is facing  ----待选择----toward youaway from you ;
the third image is facing  ----待选择----toward youaway from you .

  We wish to determine the depth of a swimming hkj7yy 0iqn-.o .xd)n pool filled with water. We measure the widy-.oji k7nd.q hy0x)nth (x=5.50m) and then note that the bottom edge of the pool is just visible at an angle of 14.0$^{\circ}\,$ above the horizontal as shown in (Fig. Below). Calculate the depth of the pool.    m

  The critical angle of a certain piece of pl cux oh;w 2l9m/c4mj8,fvp ei/astic 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 limi1 ivsvq7o m)jis ,5a;hting case of a spherical mirror. Specify whatiqm7;j1s v v),5iahos 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 mi4i /jcbg z,dh+rrors 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 th1uvib.ov ;vr5jp ) b,9. idxe) wyf5rlat a diverging lens can never form a real image of a real object. Can you describe a situation in which a diverging lens canjd,lw)ue b;ivyv).oxrfvb r ip5 9.5 1 form a real image?

  Each student in a physics lab is assigned to find the location where a r g3,l7n lkv,cu+udjh (ie eiir05r(/ bright object may be placed in order that a concave mirror with radius,ce ru v5ik(hi3el0j/rd,+gr u7n l(i 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 p0b*ysyge5 1zl.;wtso b od, -e)*ogba 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 glqm br)1nt*-x/gmz5p dz9 skq2 ass 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 9fj x/0u7pso2tmcy- .4 bx wko33 cm in front of a converging lens of focal length $f_1=15\mathrm{~cm},$ which in turn is 55 cm in front of another converging lens of focal length $f_1=15\mathrm{~cm},$ (see Fig. Below).
(a) Draw a ray diagram and estimate the location and the relative size of the final image.
(b) Calculate the position and relative size of the final image.

A bright object is placed on one side of a convejg;4q4: 3s t amyjap:+,tc. llcf6crzrging lens of focal length f, and a white screen for viewing the image ifp:lz g 4tacc4.6 ;3 qmct:,sl yj+rajs 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 fswf2hqj6f k* g zua511ilm acts as the object whose image is projected on a screen (Fig. Below). If a 105-mm-focal-length lens is to project an image on sq2j z*k fu161agw 5hfa 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) is to be projected on a s5cpaphx9/c m,3 5lqvj creen 1.80 m by 2.70 m placed 7.50 m from th j x/,h39pacvp5m c5lqe projector. What focal-length lens should be used if the image is to cover the screen?    cm

Show analytically that the image formed;2p 4rcc6yqa( tmva6n by a converging lens is real and inverted if the object is beyond the focal pct n6c6aa p4q2;rymv(oint $(d_0>f),$ 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 shootinpfbwv;d0i dt +.jmd4 nh48mc -g pictures of her at home. She claims the reporter was trespassing. To prove her point, she gives as evidence the film she seized. Her 1.75-m height is 8.25 mm high on the film, and the focal length of the camera lens w +bm04 i8dp4.j-fh n;cwvddmt as 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 cy)nlf dm0vuli4 5+5q namera 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 i 4f83(8e7u qx;d p(mk bqgx9jkvrw1x1gwh ys 1s imaged 8.20 cm in front of that lens (on the same sxbkv;g1j84qku18(rf(dw w sme9h73x pxqyg 1ide as the object). What type of lens is this, and what is its focal length? Is the image real or virtual?    cm (diverging)  ----待选择----virtualreal 
(b) If the image were located, instead, 41.5 cm in front of the lens, what type of lens would it be and what focal length would it have?    cm (converging)

  When an object is placed 60.0amff75 vsq274 pie,k g zm67hx cm from a certain converging lens, it forms a real image. When the object is moved to 40.0 cm from the lens, the image moves 10.0 cm farther from thvp6 hk7 m,g7 27a5s fzmfix4qee lens. Find the focal length of this lens.    cm