What would be the appearancelhc5d1oge7qbri0t1y 0ip, / u of the Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fleet in thg,/5ia7 p vfk5e5vzgu e harbor of Syracuse by focusing the rays of the Sun with a huge spherical mirror. Is this reason5 fa guvizvk,gp5 e/57able?

Although a plane mirror appears to r ei:aj m1*h4nreverse left and right, it doesn’t reverse up and down. Explaiinr*ahj e :m41n.

If a concave mirror produces a realen21umr(uy k;m n1k;xvr9d.y image, is the image necessarily inverted? Explain.n (y1mre ;mr9ku2un.vy;k x1 d

An object is placed along the principal axis of a sphericalu.cih oze +(+e 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 teo+ cuiezh(+. he mirror is the image located?

Using the rules for the three rays discussed with referends-9iw5b2djs s xi) j3ce to (Fig. Below a), draw ray 2 fo 93 5swi jj)bixds2ds-r (Fig. Below b).
(a)
(b)

What is the focal length of a plane mirror? What is the magnificati4ly9biizr 5 ex. ,a;ybon of a plane mirr ,i9.xl4zry;b ieaby5or?

When you look at the Moon’s reflection from a ripply sea, it appears elongay59 u* 0uobqdcted . Eq5udu y 9*bc0oxplain.

What is the angle of refraction when a light ray meets the boundaixh*:a; 5b,mj1oh goqry between two materials pexbhmoo5:1aih,j g*;qrpendicularly?

How might you determine the speed of light in a solid, rectangular, transparen0sr div;48sub t object?48vrss; ub id0

When you look down into a swimming pool or a lake, so gbaqur5yh8u ;9+ c+nnez /aa47-ym are you likely to underestimate or overestimate its depth? Explain. How does the apparent depth vary with the viewin/457+g+cmo q ysbu- n8a eahyn;9 zaurg angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks bent when p7/ve0nd d9auj5n8yihm z;x ca0v (yg8art of it is under water 5yn ci9j0a8 anu7ve8 / 0xmdvhgzyd(;(Fig. Below).

Your eye looks into an aquarium and views a fish insex-d-bo ls -)hide. One ray of light that emerges from the tank is shown in (Fig. Below), as well as the apparent position of the fish. In the drawing, indicate the approximate position of the actual fish. Briefl )oxeb--s -hdly justify your answer.

How can you “see” a round drop of water on a table even though the waterh*vv6dws -ze*xa51klw k 9 e2v is transparent and color-x k9ev vh *lv akd*e15z26wwsless?

When you look up at an objeux se,m9vsi1,re4q7 sct in air from beneath the surface in a swimming pool, does the object appear to be the same size as when you see it directly in air? E1ssem s9i ,q,ev 4x7ruxplain.

How can a spherical mirror have a negative objyys:y ru5mcx 6zy 30vga.u03ject distance?

Light rays from stars (including our Sun) always bend toward the vertical dg 2js)f 67a.wq tel6sgx7jx -airection as they pass through th-g 7fe 6 lj6w xajs)x7gtqs.2ae 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 ma mvnp2isph *q f4d5a243 9*kth+zctvkke a sharp image of an object very fak44*dnvh t 9z*fsp2i3t p25 +vqc hkmar away?

What type of mirror is shown in (Fig. *l.3vhozl.;8zhtd ) k:ij p kqBelow)? Explain.

A photographer moves closer to his subject and then refocuses. Does the cak+uy.zjq.s . umera lens move farther from or closer to tu.sju .z.kq+ yhe film? Explain.

Can a diverging lens form a real image under any circumstancegx . wgq 8l2*wny-cq4zs? Explain.

Use ray diagrams to show that a +0krqzujl y: b)ml(pth)(-a)xj, tp oreal image formed by a thin lens is always inverted, whereas a virtual image is always upright if the object is re-:j)x + rutbopl)j )p0, ((qlkthmz ayal.

Light rays are said to be “reversible.” Is tlf*n )sj: ffl,his consistent with the thin lens equation? E s:n f,j*l)fflxplain.

Can real images be projected on a scregpnvozn1 bq+ c4 y843 jx0;hgeen? Can virtual images? Can either be photographed? Discuss ca41yox gbnp8gz+ n;43 jv0eq chrefully.

A thin converging lens is mom,*r p -on6e1claex2dwi rt..ved closer to a nearby object. Does the real image formed ch.p6em dn2txerwcr o.-*l a1,iange
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of refraction n = 1.30 In air,x54tr/lai/ ju it is a converging lens. Will it still be a converging lens if placed iniu/jax/ lr 54t water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands fa3mda-* 4lbix b8ifxb ) 9dasl-cing a converging lens. If the nose and the tail are each focused on a screen in mi 4*a3dslfbb)a lxidb-x98 -turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands 3n.wi9(tg k xjfacing a converging lens. Under what circumstances (if any) k9 g i(.nj3twxwould the image of the nose be virtual and the image of the tail be real? Where would the image of the rest of the cat be?

Why, in Example 13, must the converging lens have a shorter focal lengvvv4x6n**n+lr0cfu +j w( tuzth than the dive++wv ulx 0(6 4vrz*jfn tvnuc*rging lens if the latter’s focal length is to be determined by combining them?

Explain how you could ha*sner8 x:w1f(n .mjl cve a virtual object.

  An unsymmetrical lens (say, planoconvex) forms an image of a nearby object.fmuulg1uuo5 b*n,5 i7 Does the image point change if the lens is turneui5fu7l*nm u bu, 15ogd around? ----待选择----yesno 

The thicker a double convex lens is in the center as compared to its emiv.jsvvcpe6u+y+py9uc 4 pi 3o )t0) dges, the shorter its focal length for a given lens )9+o0y. c)mvyip+v e ti3s4u6ppcvujdiameter. Explain.

Consider two converging lenses separated by s;1-ba1zzx* q dkqc d8dome distance. An object is placed so that the image from the first lens lies exactly at the focal point of the second lens. Will this combination produce an image? If so, where? If not, wd axbk*q-cd 8z;1z 1dqhy not?

  Suppose that you want to take a photograph of yoursestyl1)1q emjopsu19 (lf as you look at your image in a flat mirror 2.5 m away. For what dista1to)q(l pseuy mj1 s19nce should the camera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mirror, yo:sr uua vkp hdwcw*5p+ l1j,utt;)8;hu see the same amount of your body whether you are clu,huk581;p dau twl) tjrp chs*:+;wv ose 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 (nj0.8xarm8f wp2wk mm02a br 135$^{\circ}\,$ angle, (Fig. Below). If light rays strike one mirror at 40$^{\circ}\,$ as shown, at what angle $\phi$ do they leave the second mirror?    $^{\circ}\,$

  A person whose eyes z p968 iri4fkbare 1.68 m above 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 694 8biifpzrkbase 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 az/fo85tzgu0s ho 3m j1bq2k m vjq-o08 plane mirror. What area of the mirror is used to reflect the rays entering one eye from a point on the tip of your nose3zqv8o o1g m f-mths25zoj 8qkju/b00 if your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirf/rgr70d3k q nrors meet at an angle $\phi$. a single ray reflected successively from both mirrors is deflected through an angle of $2\phi$ independent of the incident angle. Assume $\phi<90^{\circ}$ and that only two reflections, one from each mirror, take place.

  A solar cooker, really a concave mirror pointed at the Sun, focuses the Suko w /28z+1c kzhm,ysin’s rays 18./ c,y 8km2kw1oshzi z+0 cm in front of the mirror. What is the radius of the spherical surface from which the mirror was made?    cm

  How far from a concave mirror (radius 23.0 cm) must od7-gk.(( ve+rui zlsan object be placed if its image is to be at infii (lo eds7u+-(kgzr. vnity?    cm

  If you look at yourself in a shiny Christmass -nh1 vdeb:(tzb dirs98x;x1 tree ball with a diameter of 9.0 cm when your face is 30.0 cm away from it, where is your image? Is it real or virtual? Is it uprig- 1sdstbbhxx devi;8n(1r9 :zht or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusem cl huqij0fb:xo/v;41ent park shows an upright image of any person who stands 1.4 m in front of it. If the image is thh:uil 1vf0 jxcb;4oq/ ree times the person’s height, what is the radius of curvature?    cm

  A dentist wants a smalsn/;nz+ ui ;emc s:r5dl mirror that, when 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 -o 4epwx:,ff,*xpb cwbehind you that are smaller than they would be if the 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 si,pc -*pobw x,:wxffe 4ze?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is placed 20.0 cm ;cc uk.q: ft*tfrom a convex mirror of radius of curvature 20 :tkccu*qf.t ;.0 cm.
(a) Show by ray tracing that the image is virtual, and estimate the image distance.    cm
(b) Show that the (negative) image distance can be computed from Eq. 23–2 using a focal length of -10.0cm
(c) Compute the image size, using Eq. 23–3.    mm

  You are standing 3.0 m from a convex security mirror in a store. You estimatzh)e1a3gk jl6 :u79ejhcc y+de the height of your image to be half of your actual height. Estimate the radius of curvature of th+ u d1jga e lcyejk)796zhc3h:e mirror.    m

  (a) Where should an object be placed in frong;++/yh wn- xksf17wmqfxd;s t of a concave mirror so that it produces an image at the same loca1wf xm/x-+nks qf+d y7;ws;hgtion 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 virtual andidu a r4g9rhv y)k52)l very small when viewed in a curved mirror. The image appearshiy9ul5)4d)ak g2rv r 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 tec. bhwto t*pwkqrnxy1 s;.3 s w8)oj88cv.jf 7ahniques,
(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 dir:(zn4g 8xnm p 4s-mqvagram, 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 equation, Eq. 23–2, is valid for a ,:8s +rcakct2l)zvdrg r (x ,dconvex mirror as long as f it8sgr rk+r, ld)xdacz v(,c: 2s considered negative.

  The magnification of a ;vo )58oknt 44k qrogshft67f 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 placeu*q0wtd3tq : sgm;ng7d 28 cm in front of a spherical mirror. It is desired to qt :us3m 0w gqgdt7*n;produce a virtual image that is upright and 3.5 cm tall.
(a) What type of mirror should be used?  ----待选择----convex mirrorconcave mirror 
(b) Where is the image located?    cm behind the surface
(c) What is the focal length of the mirror? $f$ =    cm
(d) What is the radius of curvature of the mirror? r =    cm

  A shaving/makeup mirror is designed to magnify your face by a factor of 1q.ebg 58j/wu o7 3vyfop w3g4q.33 when your face is placed 20.0 cm in front of it.y g5 wg38obepquf/ .3w7jq vo4
(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 nguv e o+l63b1u30 m/x7eqsgoin
(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 36 . fk1xvc ywmt.ieb)8+w cwp$2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light ini*w.rf6 0-nl dlm3vys a certain substance is 89% of its value in water. What is the insv3i l0y6*d- mf.wrl ndex of refraction of this substance? n =   

  A flashlight beam strikes the surface of a pane of glass (n =jap 4mm)yc6s;1;xa ma 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 froml*uh93 h7ww cdan6vq q k21*oj beneath the water at a 42.5$^{\circ}\,$ angle to the vertical. At what angle does the light leave the water? $\theta_2$ =    $^{\circ}\,$

  A light beam coming from8v8sxhtfdl7 xm-0vvqcf 1 b8 8 an underwater spotlight exits the water at an angle of 66v 7 xh8l1xsqv0vmfc8ft- b8d8.0$^{\circ}\,$ to the vertical. At what angle of incidence does it hit the air–water interface from below the surface? $\theta_1$ =    $^{\circ}\,$

  Rays of the Sun are seen to make a 3oiu+ *xo0afk)g k*g, d1.0$^{\circ}\,$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?    $^{\circ}\,$

  An aquarium filled with watek lmn.e(:wf flrp5g3 -r 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 thip(f.l kgwnml- e5fr3 :s 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 scwwwqp7fh/ 8 )jkd+-,q r2ggu hines a narrow beam of light from his flashlight, 1.3 m above the water level, onto the surface of the water at a point 2.7 m from the edge of the pool (Fig. Below). Where does the sq- 8u7wwrfh,/2gjpw )+c qdgkpot 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 equilat:,r+8dnmu 8xlebz cb)5 k svpzgb:, i1eral glass prism at a 45.0$^{\circ}\,$ angle to one face, (Fig. Below). Calculate the angle at which light emerges from the opposite face. Assume that n = 1.58.    $^{\circ}\,$ from the normal

  A beam of light in air strikes a slab of g851p8cwadmxr lass (n = 1.52) and is partially reflected aa8mr5pxc d18w nd partially refracted. Find the angle of incidence if the angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that for a light beam incident on a uniform layer of transpareseq ;e0hc)-dq8u (a lrnt material, as in (Fig. Below), the direction of the emerging beam is parallel to the incide;eqr q a()ds8c-he0 ulnt beam, independent of the incident angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on a flat piecexrvzx54x; zo9 of glass with index of refraction n as in (Fig. Below). Show t9zro4x5 x;vx zhat 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 f-aqa9ee) h fxqv ).e 6b*br5xeor the interface between water and Lucite? To be totally internally reflected, the ligh.reqe)bqfxb) e * 6xa5- evha9t must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liquid–aw q f yvs-sbap7tb/*awh 7+h8mp r;:20sdkb(sir surface is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in a gh3fais ( 66u5ylbcy-9k *4zua dcf/mpool of water from a depth of 62.0 cm. Where must it strike the air–water interface, relative to the spot dirmflia6 d( sbf6uhcu39zayc54k y -g*/ ectly above it, in order that the light does not exit the water?    cm

  A beam of light is emitted 8.0 cm beneath the surfa mjvo wzw(ha:2c sb:j+ya-f5*ce of a liquid and strikes the surface 7.0 cm from the point directly above the source. If 2o(w:5ahvaw f jzcmsb- +yj: *total internal reflection occurs, what can you say about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes theo9 a :thl0hqm08aid9w 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 opzy gvwy :dy85kp8 6*z5ua(ucqtic fiber as shown in (Fig. Below). Show that we can guarantee total internal reflection at the side surface of the material (at point a), if the index of refraction is greater than about 1.42. In other words, regardless of the angle the light beam reflects bacyawgyu qkcz(*6:y85v8d zpu5 k into the material at point a.

  (a) What is the minimum index of refraction for a glass or plastic prism to be uqo7t6+n rqgz-sed in binoculars (Fig. Be 6zotrq+n q-7glow) 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 sn h:2;- kl(bg s a-zojf76jsibehind a 65.0-mm-focal-length converging lens. Fo;i2(a- js7zh6 gb-fs snjk:lind the object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus ajm t9z tt.d3c: su38xat a point 18.5 cm behind a lens.
(a) What kind of lens is it?  ----待选择----converging lensdiverging lens 
(b) What is its power in diopters? P =    D

  A certain lens focuses light from an object 2.75 m away asu p5v(kpz1x5:u.5l nbkpz8h j an image 48.3 cm on the other side of the lens. Wha5 hpk (u1k8nl:xpbvuzj5 p.5 zt type of lens is it and what is its focal length? Is the image real or virtual?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the power of a 2jf h+acuox cks+g m g)9,0/xw39o0 ouj0.5-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 focal length 24 cm to view a stamp/,rv i1 zuj/e)eiunb, w7 wa9i 18 cm in front of the lens.971u n ru)ii ,,bv/j ezei/wwa
(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.cm72w nqjm.,n lt79r- dysat. ppa (,x What are the position, type, ylsp,nq7jtcwpmrm.2t( n9,- 7x a.d aand height 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 thef-kur b oks38dq2y 6;b4rv-a f film of a camera. The maximum distance allof4--v3qbbarsuk6;o2y d 8r fk wed 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 reading868y*ezb;kheipqz5 1ktpk- n material by a factor of 2.5× when a book is plac* zie;- zt8ph 8pnq5ekb1y6kked 8.0 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 fj0k6aebx xi2v285hg:l;dg b lens. By how much does the image move if the object isigxe x0a5;hbdb2l:f vk8gj62 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 converyav 18gux) 9(a1h;( exfmxwkvging lens with a focal length of 25 cm should an object be placed to producg;w 1(x)(kva8xxfma u hv9e 1ye a real image which is the same size as the object?    cm

  (a) How far from a 50.rovnfe,b* tg9w3/a p70-mm-focal-length lens must an object be placed if its image is to be magnified 2.00× and be real vgwbfrt/ poean3,*9 7?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm

  (a) How far from a 50.0-mm-focal-length lens must an object be pld(j,) ll k7n9h gp4d/ym; imrxaced if its image is to be magnified 2.07 ,yhd9r/jnl dl( xm);g4kpmi 0× 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 led4og cd(h3r 8 f*1tvxdvtj /,uns. Where is the image, how high is it,x4d/t *d ofr,dtvujvg h83( c1 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 tuj-/k+3gen s di9 w/3uwfwo*o ,7xbp converging lens if the image is 2.5× larger than ww-3i +9wg3f oxd/us/epot j* 7 un,bkthe object and is real?    m

  A bright object and qle4q v8bct pnv-*+ 5igpi4w6 a viewing screen are separated by a distance of 66.0 cm. At what location(s) between the object and the screen should a lens of focal length 12.5 cm be placed in order to produce a crisp image on the screen? [Hint: first draw a diagram.] lens should i vtq+5q4 bpw6pi l4-8n vcge*be placed    cm or    cm from the object

  Two 28.0-cm-focal-length conv/h ek31eh y(bherging lenses are placed 16.5 cm apart. An object is placed 36.0 cm in front of one lens. Where will the final imagehb/e1yk( eh3 h 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 with rhx :sm +n90pu$f=-31.5\mathrm{~cm}$ 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 i6wkx +w f6+kkjs 21.0 cm behind a diverging lens. Parallel light strikes the diverging lens. After passing through the converging lw+kxkw6+k6 j fens, 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 arz2yut5b-gs , ne now placed only 20.0 cm apart. The object is still 60.0 cm in front of the first lens as in (Fig. Below). In this case, determine u-gy sn2,5z tb
(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 thlv+,jnmfj (.v e lens on the right is 20.0 cm, and the focal length of the lens on the left is 15.0 cm. An object is placed to tvvmf.+,j n (ljhe 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 placed 12 cm to the right of a ,)z: ive1aajt s6yx ,7*xbukiconverging lens with a focal length of 18 cm. An object is placed 33 xvi:b )ata,7*u,se61 i j ykzxcm 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 focaiy4; m9ggg il+l length 20.0 cm and one diverging with focal len 4;g+ggyili m9gth are placed 25.0 cm apart. An object is placed 60.0 cm in front of the converging lens. Determine
(a) the position    cm to the right of the diverging lens
(b) the magnification of the final image formed.   
(c) Sketch a ray diagram for this system.

A diverging lens is placed gtia;/z ie.48*zsx;1r oomcwyk*sh) *6dm qb 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 hasl62nba ,, xr*nyrmxnce 29s g1 surface radii of 34.2 cm and 23.8 cm. What is the focal2,xc2yx, na6r r1bleg9*nmn s length if n = 1.52?    cm

  Both surfaces of a double convex lens have radii of 31.0 cm. If the focapv9m-hr*fg*yh nv8 6)i6pkqbbm0 y p ;l length is 28.9 cm, wyp) mp6gnpm9y*kr v-;iqb hb* v 86h0fhat is the index of refraction of the lens material?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm. W16l wggsm375lino 9 rjhat is the radius of the concave surfac7 9nj3lsgi ro w1ml5g6e?    cm

  A Lucite planoconcave lens (see Fig. Below) has one flat surface an4xs6lrb5 (jc sv;,two d the other has R = -18.4 cm. What is the focal ;vt 4xb 5rlojc(sws6,length?    cm

  A symmetric double convex lens with a focal lecwchl:vzbm: ww; )66wngth 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 eachb:)cv hm6w6z;wl:w cw surface?    cm

  A prescription for a corrective lens calls forw/x/(a/mfua)ff l7 ek +1.50D. The lensmaker grinds the lens from a “blank” with n=1.56 and a preformed fe(w la/)/7 fmaxfku /convex 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 (Figl q n1u* y swc;yen-cm;*x,6yg. Below). You stand 1.5 m away from one of these mirrors and look into it. You will see multiple img c;*lnx6 1y,mqyy w c*;e-sunages 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 dep7d wu ek;9jb*pth of a swimming pool filled with water. We measure the width (x=5.50m) and then note u*ekdwj7 9 pb;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 uj:bohh-, sf5,yob 7(8q yavr certain 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 o/ rkcb o/5v/x(qod8t nf a spherical mirror. Specify what this limit ib kq/cn/v( 5xt/ odr8os.
(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 soq)r+gr6 fuc).y t4rwq 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 ax5p ;.wf 9tu tdk.i5fa diverging lens can never form a real image of a real object. Can you describe a situation in which a divergingti95w fpx. tau;5. kdf lens can form a real image?

  Each student in a physics lab is assigned to fi z .(iq,+oryre/5eqzjnd the location 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 ejr,eqi5zq(o/yz+. r 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 ofvdzb5( q (fb1/:c-of4p3u gwok 6 zoga a 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 cyl-r*k be 6; v+iyf39hna fir,czindrical 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 ordxe c78s4 kgp 5t-nd4f 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 converk2xdf(u c uf.(ging lens of focal length f, and a white screen for viewing the image is o xcf du.(2u(fkn 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 -1c ;k if ff ghewmpo;7 ur,o8l7w/a7macts as the object whose image is projected on a scg8 okpl7 af;f;imhw7o/ue,cm7 1r -wfreen (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 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)dosvg fb5 -,.d is to be projected on a screen 1.80 m by 2.70 m placed 7.50 m from the projector. What focal-length.fddbg o 5,vs- lens should be used if the image is to cover the screen?    cm

Show analytically that the image forw1oa: 2du it:vmed by a converging lens is real and inverted if the object is beyond thto::v w1a2diu e 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 hedl h:x3o/3he j.5hhx8 qfnj 3kr at home. She claims the reporter was trespassing. To prove her poinhq f3xldj o8:3 h/jhknx.5h3et, she gives as evidence the film she seized. Her 1.75-m height is 8.25 mm high on the film, and the focal length of the camera lens was 210 mm. How far away from the subject was the reporter standing?    m

  How large is the image of the Sun on film used jcc- dlf56f+kmv6fax)eu i.+ 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 cq6tg 7i1)zcreertain lens is imaged 8.20 cm in front of that lens (on the same side as the object). What type of lens is this, 7cgt6 1)rze qiand 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 60.0 cm from a certa5 yh7xs5rskk7xf4;c lod-fb 2 in converging lens, it forms a real image. When the object is moved to 40.0 cm from the lens, the image moves 10.0 5 o 2f ks-5s7xhc f7dxlbkyr;4cm farther from the lens. Find the focal length of this lens.    cm