What would be the appearance of the Moon if it had tt5.u)kk;t:h)n+z5s lymwe e
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fleet in the harbor of Syraswg.+s j,t1xu cuse by focusing the rays of the Sun with a huge sphers. jt1wgx,+usical mirror. Is this reasonable?

Although a plane mirror appears to reverse left and right, it doesn’t rj *-, (gwloc8g4rb i8as;zzozeverse up and doc;zl 8za ,o w jg(r8io-4gzb*swn. Explain.

If a concave mirror produces a real image, is the image necessarily inver5poe 3df q*xsyq;8 :mlted? Ex:x5s em;3y o qdflpq8*plain.

An object is placed along the principal-g oht/nd-sq16 lye, q axis of a spherical mirror. The magnific-yoh ,d/ngs 6-t1 qqelation of the object is -3.0 Is the image real or virtual, inverted or upright? Is the mirror concave or convex? On which side of the mirror is the image located?

Using the rules for the thrkq j(g8b u -y6/dev4zfee rays discussed with reference to (Fig. Below a), draw ray 2 for bu4/yv6kqd-ze ( fj8g(Fig. Below b).
(a)
(b)

What is the focal length of a plane mirror? What is the/idkc-39 ld 0p)iuw;cmtz /qy- qe5d7ph vii0 magnification of a plane mi-muicl/d)vk; pq ztd wc9-dpy 3iq 5ei0/70hirror?

When you look at the Moon’s reflection from a ripply sea, it appears elongated .z,w 3zaqp h44fl0zjb+ 4lhjz4aqw,fp z+3z 0b Explain.

What is the angle of refraction when r :k)c-)elawfa light ray meets the boundary between two mat) a)l:ec -rwkferials perpendicularly?

How might you determine the speed of light in a solid, rec+kf9o/i 5w8yw p rl-m6,qd,i3tzjjivtangular, transparent obl +m8ji pjydq w9ii 5fo3zv-/6,k,tr wject?

When you look down into a swimming pool orwa)mh .x; a-yxuc4;ak a lake, are you likely to underestimate or overestimate its depth? Explain. How does the apparent depth vary with the viewinxy;4m- h.a)aw kcua ;xg angle? (Use ray diagrams.)

Draw a ray diagram to show why xoh(nrsym;fij d w96 kznx(0n 6o2(j/a stick looks bent when part of it is under water (Fi y ji6mjs(fwn(( 2xn / r0do;96hknxozg. Below).

Your eye looks into an aquarium and views a fiel o vr)c1p1(:39ynoc9f39 sszgixw ksh 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 act y9ilgxv:rz) ef cn3w1s 1p9cok3so(9ual fish. Briefly justify your answer.

How can you “see” a rolr w -on-,23+kuquq/y 7epxh iund drop of water on a table even though the water is trans-oy p/l 2whquqin+r x37ku-,eparent and colorless?

When you look up at an object in airw ka(: pvq1k+p from beneath the surface in a swimming pool, doew(+ pvp1k :kaqs the object appear to be the same size as when you see it directly in air? Explain.

How can a spherical mirror have a nec;v 7b9xj+dsxgative object distance?

Light rays from stars (including our Sun) always bend toward the l tjozf7-uo,eb dz1/, t:q*wcvertical direction as they pass thqzjc:fwt/z*lo1 ,o t b ,7du-erough 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 c 5lbdq,l9mwf+amera lens is to make a sharp image of an object very far awayl+ m9db5lf,w q?

What type of mirror is shown in (Fig. Below)? Exv(d)s pi dm0512 upmrnplain.

A photographer moves closer to hi4(4) : sfipmti nt+norjvn;r-s subject and then refocuses. Does the camera lens move farther from or closer to the film? Explai4sntm:4+n) ir;tp r -(ijnovfn.

Can a diverging lens form a kh nvxmpo3eu- fy9y/z72:et) real image under any circumstances? Explain.

Use ray diagrams to show that a real image formed by a thin lens is dh/fsn9c1 why6+d *io)wh( y aalways inverted, whereas a virtual image is aihf (achn9 d6h1s *+oyw /w)dylways upright if the object is real.

Light rays are said to be “reversible.” Is this consistentbgxr(cp07 duq (;4bqk with the thin lens equat4(br7 dq(uxc; p 0qgkbion? Explain.

Can real images be projected on a sc 8r2io;n3dbfl reen? Can virtual images? Can either be photograp8r ;2ib 3onfdlhed? Discuss carefully.

A thin converging lens is moved cl/;bcp)ua cse )oser to a nearby object. Does the real image formed)c;p/ c bseu)a change
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an 3epk l 5h-f*hyindex of refraction n = 1.30 In air, it is aph*y l-f h5ke3 converging lens. Will it still be a converging lens if placed in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail i:mt6**gmk6udsrqii6 els v 5 .mmwbc8vut-,:n the air stands facing a converging lens. If the nose and the tail are ea stm-b6e:d,lm5wv.*tq 8*v 6:g cu mii6mrskuch 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 converging lens. Uv96 1 jso, qzx-z/hktv q,jh6jnder what circumstances (if any) would the ima,hjkxo ,vs/ q-h 9j 6z6tzjv1qge 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 have a shorter-w4 6n,4om wd+icb8 *cablh jw focal length than the b,8i -lnbco mj+64whc4 waw*ddiverging lens if the latter’s focal length is to be determined by combining them?

Explain how you could have a virttl xjq9xk4 o4:. y;klkual object.

  An unsymmetrical lens (say, planoconvex) forms an image of a nearby 6ya ceut ,g7mk+dj::r*r )pwdobject. Does the image point cha :w:kpg 6, r+)eud*7tdaymr jcnge if the lens is turned around? ----待选择----yesno 

The thicker a double +a xtx1z4t52qo tcf5 wconvex lens is in the center as compared to its edges, the shorter its focal length for a given lens diam4 t+octqaft 55xzw12xeter. Explain.

Consider two converging lenses separated by some distance. An y(nd2:wuor*;o nkgvi-/ xh-jv yc 47 nobject is placed so that the image from the first lens lies exactly at the foca nunow j(yyrg:kvvh*o-4;d x ci72n- /l point of the second lens. Will this combination produce an image? If so, where? If not, why not?

  Suppose that you want to take a pp*o jnq +tc7; b;lcm4vhotograph of yourself as you look at your image in a flat mirror 2.5 m aw b;+tcq;o4 7mvl*pncjay. For what distance should the camera lens be focused?    m

When you look at yourself in a 60-cm-tall pfkv q*ob+( co1lane mirror, you see the same amount of your body whether you are close to the mirror or far away. (Try it and see.) 1c(kvoo+*q bfUse ray diagrams to show why this should be true.

  Two mirrors meet at a ,ootf-i,oh0 y135$^{\circ}\,$ 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 txb+ rq799ph8 srt ccn7v3/hf kg,g7pkhe 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 pq/h7gck7h8xfvrk p9, gn 9r 7c+sb3t x to the base of the wall supporting the mirror of the nearest point on the floor that can be seen reflected in the mirror?    cm

  Suppose you are 90 cm from a plane mirror. What area of the mirror is usedvo0rg u2 w.oh su5i72b to reflect the rays enter.o 22b0vwisruhg5 ou7ing 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 mirrors meet at an ahnhe4ro7 4hzi44j 5jb ngle $\phi$. 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 mirrols r vk,it5e/zxtl( +7r pointed at the Sun, focuses the Sun’s rays 18.0 cm in front of the mirror. What is the radius of the spherical sursl k7tx,rv+ze/t 5( ilface from which the mirror was made?    cm

  How far from a concave mirror (radius 23.0 cx; ka9w*p*2jb* +hbwgj9p 2 oonua1 sum) must an object be placed if its image iwb+**au2 ops g2wuj;*opbj9ah91x kns to be at infinity?    cm

  If you look at yourself in a shiny Christmas tree b-qiq0ocg p oq4yh0( /k:iqou5all with a diameter of 9.0 cm when your face is 30.0 cm away from it, where is your image? Is iqoq(u :-h/o0 qik5c0y 4q poigt real or virtual? Is it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusementm64bdv ugn4up)6ea4x.k(oa h park shows an upright image of any person who stands 1.4 m in front of it. If the image is three t4e 46p6ak .auugm4 d)bv(nxoh imes the person’s height, what is the radius of curvature?    cm

  A dentist wants a small mirror that, t 7n4 +vorm9nnwhen 2.20 cm from a tooth, will produce a $\text{4.5×upright}$ image. What kind of mirror must be used and what must its radius of curvature be?
 ----待选择----convexconcave 
r =    m

  Some rearview mirrors produce images of cars behind you that arcn63v jzwd k)6an)c t0e smaller than they would be if the mirror were flat. Are the mirrors concave or convex? What is a ) 6zj6n3 0w ckcadt)nvmirror’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 plac 1erep 0;i32bq4q/vusvau4l j5.gd q ied 20.0 cm from a convex mirror of radius oe2l1.50rgi3iu;a q4pjvqdsvbeuq 4 /f curvature 20.0 cm.
(a) Show by ray tracing that the image is virtual, and estimate the image distance.    cm
(b) Show that the (negative) image distance can be computed from Eq. 23–2 using a focal length of -10.0cm
(c) Compute the image size, using Eq. 23–3.    mm

  You are standing 3.0 m from a convex security mirr98t jguf 1pli1or in a store. You estimate the heighp 8gtfl9 j1u1it of 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 mirror sojziqd/ji3.903icf 1:n orm7g 4b bu fv,:axcs that it produces an imag:,v. c1 ous0 q:9j/g dmfii334 zai7 cxfrjbbne at the same location as the object?
(b) Is the image real or virtual?  ----待选择----realvirtual 
(c) Is the image inverted or upright?  ----待选择----invertedupright 
(d) What is the magnification of the image?   

  The image of a distant tree is virtua ep* ae:4.rg.wg o*vekl and very small when viewed in a curved mirro*4 vra.*eew.ok:g pger. The image appears to be 18.0 cm behind the mirror. What kind of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different te6sv(flwg;ex)(lgem9 yc8 6a zchniques,
(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 conve1k gijc*c,1g j)im ek2x 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 tha,+ bw80nu1dmhpdob) p8a ll n)t the mirror equation, Eq. 23–2, is valid for a convex mirror as long as f is nb )n 0d18)poa,hl p+uw8lb mdconsidered negative.

  The magnification of a w7 5:2plu :hz bb:sq1mpsfl i/convex 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 spherical mirror. It is d*8ki6 dndi: pfesired to produce a virtual image that is6d*ipi:kd8n f 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 /.9emn9yh j (th0m tcnp5y-yiby a factor of 1.33 when your face is placed .ptn5 mt/y 0(-hmje9c9nyih y20.0 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 of4zn n8-;skbbql/1e ap light in
(a) crown glass,    $ \times10^{8 }\;m/s$
(b) Lucite,    $ \times10^{8 }\;m/s$
(c) ethyl alcohol?    $ \times10^{8 }\;m/s$

  The speed of light in ivqi rd:7 b.du oj(in6(ce 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 89xfgz5 l jln9:)% of its value in water. What is the indf:zlnl j5 g9x)ex of refraction of this substance? n =   

  A flashlight beam strikes thehgr+f+p01 ;ls43igb 7plv yni 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 watg02f+mtdxsl7k 471oer ,9 ijsd ch l6ver 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 underwateh52z)prsq( g6i(sf i ir spotlight exits the water at an angle of 66.0q2rpf((isgsih ) 6 zi5$^{\circ}\,$ 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 3y+ n8;1caa kap1.0$^{\circ}\,$ 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 whujzops7z(j 3,i b2oc d/h+z.m;.xusk ose index of refraction is 1.52. A dz2s.ki/c p3 (.zoz7,ouhj x+bu;smj 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 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 beam o3g zs rw:*gq*v4eyea4 f 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 e4a wqreg3s :4zv** ygbeneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equilateral glass prikymky ja:4v+y-zre)1q; u8 eoqyt; (ysm 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 stricae q0 i4py3j3*r1orqdf 2s,-nqj h/o kes a slab of glass (n = 1.52) and is partially reflected and partially refracted. Find the angle of incidence if the angle of refleccj4 edp-f rq 23jr qoqy10an ish/,o*3tion is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam incident ole t*ied /5+z.tchjbqw)bvov15r0i9 px5 5 wdn a uniform layer of transparent material, as in (Fig. Below), the dire 90qwxbw .zi*vd dl5hroptjvc/b5t51) +5ieection 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 incidh,;zkbdm, s,uent on a flat piece of glass with index of refraction n as in (Fig. Below). Show that if the incid, uzk;,d, sbhment 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 be toe)+ :6rfpa ;5yysqpp:c h+f mht5; yf6:mr)f pq:pc sa hpyh+e+ally internally reflected, the light must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–air surface is 47.-s+ou5khgzf; hse,-xk19 ylr 7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in a pool of water from a depth of um3 9)b ouqa5zi+nm5 80wsk yk62.0 cm. Where must it strike the air–water interface, relative to the spot directly above it, in order that the light does not exit the water?5)8mas3 bnky uwzu 590q i+kom    cm

  A beam of light is emitted 8.0ld y3t8z:ghnsrxuph8 p 754 go8v, z8r cm beneath the surface of a liquid and strikes the surface 7.0 cm from the point directly above the source. If total internal reflection occurs, what can you say about the index of refracti4 h7vpryo8ptu8dr gsg53x8h znzl,: 8on of the liquid? $n_{liquid} \geq$   

  Suppose a ray strike(f.fid3 ;:yj5qiezu n s the left 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 shown in (Fig. Below). Show/ dbe( hms;fbp gtsm 5)f,zqc450r5 wu that we can guarantee total internal reflection at the side surface of the material (at point a), if the index of refraction is greater than about 1.42. In other words, regardless of the angle the 5wc5gbfsbhpf;s5 m(rm4/uqez ,td0) light beam reflects back into the material at point a.

  (a) What is the minimum indw()qu4)mn r9 v wz+rn4hek8mzex of refraction for a glass or plastic prism to be used in binoculars (Fig. Below) so that total4mwhnurn)z w (r8v qe)49zk+m 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-len4brb0pzf bo(- 1m 1sbkgth converging lens. Find the ob4bkob(bspf- 0m11r bzject distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point qdr0j j,x, sd,xu g ,,6nidpi318.5 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 ipk4) zuh o du59zv(zg3*r+lufrom an object 2.75 m away as an image 48.3 cm on the other side of the lens. What type of lez9dz lu53r(hvk +4ugpo uiz)*ns 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-cmzolcosko s:*i- 5 h15r-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 focal length 24 cm to view a stacm f (w6copiy+1 z5t;pmp 18 cm in front of the lens. y6 m1fi+tpcozc5( pw;
(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 oqrp53u 1k xc+ckleofu;pw 9r47g8v ;dbject 4.0 mm high. What are the position, type, and heil d cx +guew;uk rfqo;crppkv4935817ght of the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to focus an image on the 5+37upfa9nva 3g taihz-xl1i film of a camera. The maximu7 g+a- xzht ipauifa331n5l9vm distance allowed between the lens and the film plane is 120 mm.
(a) How far ahead of the film should the lens be if the object to be photographed is 10.0 m away?    mm
(b) 3.0 m away?    mm
(c) 1.0 m away?    mm
(d) What is the closest object this lens could photograph sharply?    mm

  It is desired to magnify reading material by a nqkl 5v8.cwgx- z2pxpz5d*-l factor of 2.5× when a book is placed 8.0 cm behindp5pzqlgx8 x.c-5l-wd z* kv2n 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 8.0-64q1 dfeglpn8*;vms*kzse)(c/zzr mD lens. By how much does the image move ieqv )*pmc* nz/ zs elz1(64rf8;gmkdsf the object is moved
(a) 1.0 m closer to the lens,    cm away from the lens
(b) 1.0 m farther from the lens?    cm cm toward the lens

  How far from a converging lens with a focal length of 25 cm should an objec5tuseb4n x2b +t be placed to produce a real imagb 4ubsn25t+exe which is the same size as the object?    cm

  (a) How far from a 50.0-mm-focal-(guh*dwnhzbp9 :*)2hdou ; bhjxv;a *length lens must an object be placed if its image is to be magnified 2.00× and be real? hzvhh jbg(hx9n2)* *pd* uwd; u:ao; b   mm
(b) What if the image is to be virtual and magnified 2.00×?    mm

  (a) How far from a 50.0-mm-foca4 9ou; zcqwhd53 pj6hyl-length lens must an object be placed if its image is to be magniqhh6ow 9z 45c3upjyd ;fied 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 frouz ll k,c-m :(+xzn,sgm a 135-mm-focal-length lens. Where is the image, how high is it, and w cu z xn+l-s(,,mlz:kghat 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 rz/ ttur7gtq -q(ji)3n oat/1 75-cm-focal-length converging lens i/ )n1ottquriat(3g7zq/r - t jf the image is 2.5× larger than the object and is real?    m

  A bright object and a viewing screen are separated by a distance of 66.0 cm. 3d r)l* tbam3uAt what location(s) between the object and the screen should a lens of focal length 12.5 cm be placed t dlmu3* ab)3rin 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 converging lekx3p6kv-v e9n q1,3 jjxqajf1nses are placed 16.5 cm apart. An object is placed 36.0 cm in front of one lens. Wheqx39-k1jv6jak e pnxfq13,jv re 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 wit1/p:n mzlwkkh xr:3*bh $f=-31.5\mathrm{~cm}$ is placed 14.0 cm behind a converging lens with $f=20.0\mathrm{~cm.}$ Where will an object at infinity be focused?  ----待选择----realvirtual ,    cm beyond second lens.

  A 31.0-cm-focal-length converging lens is 21.0 cm behind a diverging lens. s7zhxwjua5,hie ;7lr9 v*fk-2xz,dlParallel light strikes the diverging lens. Aftv,rx ;9i zl5,x *uwe j7a7-2zdlsfhkher 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 23–12 are2+ab urhbzp 17 now placed only 20.0 cm apart. The object is still 60.0 cm in front of the fibb1 a+pzuh72 rrst 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 + 23jbl:9nqsao o0e eoapart. The focal length of the lens on the right is 20q :eo2bo j+an 0o93lse.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 original object?    cm

  A diverging lens with a focal lvu x,yts4/jirv0*6pw ength of is placed 12 cm to the right of a converging lens with a focal length of 18 cm. An ots,uvx6/pvjy04 rw*i bject 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 divergi*ob 4sspw4- slt c*8mjng with focal length are placed 25.0 cm apart. An obje84sw**bl4stpsom j c-ct is placed 60.0 cm in front of the converging lens. Determine
(a) the position    cm to the right of the diverging lens
(b) the magnification of the final image formed.   
(c) Sketch a ray diagram for this system.

A diverging lens is placed next to a converging lens of focal lengzo ,q6b-r9p,1npj ;v/qo okjgth $f_C$ 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 cn e+h:gbr39 7twek+; gdcn 1kzm and 23.8 cm. What is the focal length if1t gedkh bn7nr39ew k;:zg+c+ n = 1.52?    cm

  Both surfaces of a double convex lens have (8ibk7q j s;j35. a8rnrifsw/gp(ujaradii of 31.0 cm. If the focal length irj/8 7b(n uqw8j.(;kafagjps3sr5 i is 28.9 cm, what is the index of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.49 c 86rfdz* ukpe:sk-8hfz9 wvcm. What is the radius of the concavz: zcd8wf9k89ue hr- psvk*f6e surface?    cm

  A Lucite planoconcave lens (see Fig. Below) hi 4jtpx7ag*6izpqw z,:/o ;kl as one flat surface and the other has R = -18.4 cm. What isp ,i zw otijpz4xkg:ql7;/6a* the focal length?    cm

  A symmetric double convex lens with a foc3ytl /* .udvrcal length of 25.0 cm is to be made from glass with an index of refraction of 1.52. W.yuvr*3 l/dcthat should be the radius of curvature for each surface?    cm

  A prescription for a corrective weern0 ny /+ aurrm83sd u:nv*;mn4t2 lens calls for +1.50D. The lensmaker grinds the lens from a “blank” with n=1.56 and a preformed c;mn3uvm0:8w e 2nte+sn/4 *urynr dra onvex front surface of radius of curvature of 40.0 cm. What should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fig.z3,e4x pv)yljns/m .w Below). You stand 1.5 m away from one of these mirrors and look into it. You lex.pm43)ynz w/,sv jwill see multiple images of yourself.
(a) How far away from you are the first three images in the mirror in front of you?
$d_1$ =    m
$d_2$ =    m
$d_3$ =    m
(b) Are these first three images facing toward you or away from you?
the first image is facing  ----待选择----toward youaway from you ;
the second image is facing  ----待选择----toward youaway from you ;
the third image is facing  ----待选择----toward youaway from you .

  We wish to determine the depth of a swimming pool filled with waepjh/5yk w 4h,dzw2; pter. We measure thdh,w4zeyj5w /;p h p2ke width (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 certaiuyn6yx: d e 0o5tfnxz49d d.z(n piece 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 lod+z mybw+0g-qdq7 ) a spherical mirror. Specify what thiqz0+ qm )ogdy7w-+b dls 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 form a6qzsk osid:n)t 92nl;i8c-fr 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 a1eboetc6qme 384el+ xvd :ve 3 diverging lens can never form a real image of a real object. Can you des c+ml1:4ev e38dvt eb6xqo 3eecribe a situation in which a diverging lens can form a real image?

  Each student in a physics lab is assigned to find the l 0xck-d0ul f; j(7h9negg yu4qocation where a bright object may be placed in order that a concave mirror with radius of curvature r = 40 cm will produce an image three times the size of the object. Two students complete the assignment at different times using identical equipment, but when they compare notes later, they discover that their answers for the object distance are not the same. Explain why theylqgfh0k 7dgenc(x; -uj40 y9u 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 prismm9g vs m os:.s8.zc6pna7nh+i 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 cylib ff0qz8+ya(xi3fc 9 gndrical 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 focal length ; anjpds oef;g7 m02h2$f_1=15\mathrm{~cm},$ 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 o*7+ddfflv5 ox6 w3ab9khp as1 n one side of a converging lens of focal length f, and a whitel f3x9 dv+f obawak5617dh* ps screen for viewing 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 the8cs:u8t qwz) h object whose image is projected on a screen (Fig. Below). If a 105-mm-whc)z8ts8 : uqfocal-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 actuallyzr( x h-vhf5 ,y.cfy2k 24 by 36 mm) is to be projected on a screen 1.80 m by 2.70 m placed 7.50 m from the projector. What focal-length lens should be u fy5 vx(crfhy,zkh.2 -sed if the image is to cover the screen?    cm

Show analytically thatf 3iomd ,s8zupt.0fh .3eopc7 the image formed by a converging lens is real and inverted if the ofe.38 s.3 fph0ictm, 7ozpudobject 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 5/c2ixu ui 0 6fgp,c,k3swn azat 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 focfa2uci,/kw0us3g65z i n,xc pal 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 Sund.5 qmc tf3a5m on film used in a camera with
(a) a 28-mm-focal-length lens,    mm
(b) a 50-mm-focal-length lens,    mm
(c) a 135-mm-focal-length lens?    mm
(d) If the 50-mm lens is considered normal for this camera, what relative magnification does each of the other two lenses provide? The Sun has diameter $1.4\times10^6\mathrm{~km},$ and it is $1.5\times10^8\mathrm{~km}$ away.    for the 28 mm lens    for the 135 mm lens.

  (a) An object 34.5 cm in front of a certain lens is imaged7/m.dxdawb 6m 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? Is tm dax67./dmw bhe 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 certainr,y eyf 6 zme/i .hhrly4x0r,. converging lens, it forms a real image. When the object is moved to 40.0 cm fromhx , efil/z.y .4y m,re6rh0ry the lens, the image moves 10.0 cm farther from the lens. Find the focal length of this lens.    cm