What would be the appearance ofab-5z o yw+t2f the Moon if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to hav.pvui 5nn4a,ka ng*imwdo , 1k/ ;0kooe burned the whole Roman fleet in the harbor of Syracuse by focusing the rays of the Sun with a huge spherical mirror. Is this reasonablek * anoi0 oio1m/dkkpnw,;.gu5an4,v ?

Although a plane mirror appears to reverse left and right, it doesn’t mwftyx7h c:4: reverse up and down. Explaif y:h:tc7x 4mwn.

If a concave mirror produces a real image, is the image necessarily inverted? w(x6 w:czhvc 9Explaincvz w:(h6wc9x .

An object is placed along the principal axis of a sbvnmoz: h t2 50kb2c2;lzx, adpherical mirror. The magnification of the object is -3.0 I2 zl xd 5nm,oc2tz2;bka:bh v0s 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 three rays discussed with remn0fc q kw8)0pference to (Fig. Below a), draw ray 2 for (Fig.) kq0wfnm cp80 Below b).
(a)
(b)

What is the focal length of a plane mirror? What is the magnification of ,tzrtff 1 b-a4tb38jy a planetay,t-fb8b f3 tj4zr1 mirror?

When you look at the Moon’s re5mdv39e2l kgamvbu,q1 y 26j lflection from a ripply sea, it appears elongated . Explain.6bu5mgk 2 9l mq 31ajdvveyl2,

What is the angle of refraction when (ryhh0r5 hbv0a light ray meets the boundary between two my00r bvh h5(rhaterials perpendicularly?

How might you determine the speed of light in a solid, rectangular, transpar0 d/t ahcdkf* 57)rgzsent s0*7hrf)kat/5 dzgcd object?

When you look down into a swimming pool or0i)f epyc5k 9t2 sz+(gkxtfy ;xuc62 a a lake, are you likely to underestimate or overestimate its depth? Explain. How does the apparent depth vary with yuzs )x02k + gc6 9iftx2 aep;fct(5ykthe viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks bent when partdxqowl gi06- : of it is under water (Fig. Below wl6xqo0g d:-i).

Your eye looks into an aquarium and views a fish inside. Onegw i9q6cnjfn hx4hf4t(( ite. x21n 8p ray of light that emerges from the tank is shown in (Fig. Below), as well as the apparent position of the fis w 8g 1nnc4hijh(4(f x26pteqix.9tnfh. In the drawing, indicate the approximate position of the actual fish. Briefly justify your answer.

How can you “see” a round drop of water on a table even though the water is 4vl1;xf ijvq-u //eviy( a7ab transparent and colorlee vu7b;xv4f(y/i1lq/v jaa-i ss?

When you look up at an object in air from beneath the surface in a swimming poolenr rc)/q jv (:ii)x(w, does the object appear to be the same size as when you see/ )i) vcjq i(en:rxr(w it directly in air? Explain.

How can a spherical mirror have a n5yp8k6 4 ynxztd3tk8jinyb/ + egative object distance?

Light rays from stars (including our Sun) .e) ) o-cizgryalways bend toward the vertical direction as they pass through the Earth’s atmosphere. -z)ry oce)i.g
(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 plu:qseius:a 4 7aced if a camera lens is to make a sharp image of an objecte7:uua qi:4ss very far away?

What type of mirror is shown in (Fig.j g(jz- :,93gwg5yit buup m.l Below)? Explain.

A photographer moves closem j 596qkmgesh0k9a o;d5*kl dr to his subject and then refocuses. Does the camera lens move farther from or 9d0 jehg55osk6daq * km;mkl9 closer to the film? Explain.

Can a diverging lens form a real image under any circumstances? Exati17 ) kkh/b;xh*n5y(tl jhjplain.

Use ray diagrams to show that a real image formed by a th; *o. gqdt pecyo,5.xmin lens is always inverttp;q 5*y.xdoeo. m,gced, whereas a virtual image is always upright if the object is real.

Light rays are said to be “reversible.” Is fw bq*+ghv/yg-du)q+ this consistent with the thin lens equation? Expla u*w/g-)d+ bgfqvhqy+in.

Can real images be projected on a screen? Can virtual images? Can either be 9spab5jf5.ae ;sgs .ophotographed? Discuss car .j; as 5soapgf9es.b5efully.

A thin converging lens is moved closer *0unk ;yuq svqb h:n15yk7h.oto a nearby object. Does the real image formed changqs1 k5:hhqu.n y7b0onkuy ;v*e
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of refraction n 2rh.9v8)hj.a9 tubj yjf t -t6p. hmgx= 1.30 In air, it is a converging lens. Will it still be a converging lens if placyrt) a. t8.v htf.jhjh92g9 mbuj-xp6ed in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands facing a converging lens. If the nose afr u; y,dazz4dtf:v*a s*1x -b mnq,:lnd the tail are each focused on a screen in-fxdly*r z ausb;,*af z1:md4 v: tq,n turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stands facing a converging lens. Under what td/3uinsg e 00circumstances (if any) w3n tdgse/ u00iould 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, mustsfswhax 05a 9)ng;pe7 the converging lens have a shorter focal length than the diverging lens if the latter’s5;s0 n ax p)7he9afswg focal length is to be determined by combining them?

Explain how you could have a vir;xbw)o:wzpjb6h(,cnm5 dp (v tual object.

  An unsymmetrical lens (say, planoconvex) formvhsf9w3 .mrs-8j205eck tsrgs an image of a nearby object. Does the image3ekw8gs 5h9jrrvt -m . 2sf0sc point change if the lens is turned around? ----待选择----yesno 

The thicker a double convex lens is in the ceiruv+uh(+.y qzqnso (of47 b2 nter as compared to its edges, the shorter its focal length for a given lens diameter. Explainy z.r ((vnoi+oh b2 qqusu+74f.

Consider two converging lenses separated by jyc)wwzot s -c j8k8 *j7lk+/rsome 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, wherek7lj )yz/k j8o cj -w8tr*wsc+? If not, why not?

  Suppose that you want to take a photograph of youhvz1)ol+ d5mg rself as you look at your image in a flat mirror 2.5 m away. For what distance shoulv5+oz)lg h1 mdd the camera lens be focused?    m

When you look at yourself in a 60-cm-tall plane mirro8hix,sjfs4v/7 dir* b r, you see the same amount of your body whether you are close to the mirror or far away. (Try it and see.) Use ray diagrams to show why this sho8sxih/sf7* bji, dv 4ruld be true.

  Two mirrors meet at al-t(v6qp w(cj a)d3 vk 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 are 1.68 m above the floor stands 2.20 m inb(((8yrbg- lwm r1 uyz front of a vertical plane mirror whose bottom edge is 43 cm above the floor, (Fig. Below). What is the h(lzwry8bgb(r- ( 1myuorizontal distance x to the base of the wall supporting the mirror of the nearest point on the floor that can be seen reflected in the mirror?    cm

  Suppose you are 90 cm from a plane mirror. What arg j1t7nn0f u2 (e(zizyea of the mirror is used to reflect the rays entering one eye from a j1nnz( 2ziu(gft y e70point on the tip of your nose if your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors mi vya/v5 v+hg:eet at an angle $\phi$. a single ray reflected successively from both mirrors is deflected through an angle of $2\phi$ independent of the incident angle. Assume $\phi<90^{\circ}$ and that only two reflections, one from each mirror, take place.

  A solar cooker, really a concave mirror pointed at the 1sgkw )(5 jxx 7zb-l2bl+ uyhhSun, focuses the Sun’s rays 18.0 cm i5xk1s ( b)lxw7y -u2zjlgh+hb n front of the mirror. What is the radius of the spherical surface from which the mirror was made?    cm

  How far from a concave g x-quii3v2fm)ty6(t mirror (radius 23.0 cm) must an object be placed if its imagify u -2it)xgm(6vq3te is to be at infinity?    cm

  If you look at yourself in a shiny Christmas tree ball with a diameter of 6:v(ex ,ylsw e9.0 cm when your face is 30.0 cm away from it, where is your image? Is it real or virtuays6:e vew x,l(l? 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 stands 1.ww5b+pjv1:p k 4 m in front of it. If the image is three times the :jwbw+15p pkvperson’s height, what is the radius of curvature?    cm

  A dentist wants a small msoq3qgpdz8 w16hy8; eirror 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 be -06*xyy6qe 1ywpquka hind 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 e0 6qu-yw1pxa6q* kyysize?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is placed 20.0 cm fri(t8wi8zuw1o r di8cd z;2:odjux j 8)om a convex mirror of radius of curvature88(ouiw 2)o;1uxddi:ij d ct8rzj8 w z 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 mire*,d g s)l;dkcror in a store. You estimate the height of your image to ;esg*cdk), l dbe half of your actual height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object be placed in frob 8v(eb pd0hc+:p ut+tnt of a concave mirror so that it produces an image at the same location as th t0b +c p+d8:bpveu(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 and very small wy*l: mk/ mko-s2bu.dg hen viewed in a curved mirror. The image appears to be 18.0 cm behind thbk/s2m-md* .y:ukl go e mirror. What kind of mirror is it, and what is its radius of curvature?
 ----待选择----convexconcave 
r =    cm

Use two different techni virrqk;1+9miques,
(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 o abzgru u60v sbd. 81 fi.j*nnidw8.,yf 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 equi+xqr: ze-(kmizrn xttghn 7p .a7.04ation, Eq. 23–2, is valid for a convex mirror as long as f is considered negatrax+ rgt0 x(t:4iqh nn .zzm.-ip e7k7ive.

  The magnification of a convex mirror t z,a f3cde51;,vma di (jb2yhis $+0.65\times$ 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 pl, 4s n925xmxfwajd( c; z.yn blq8do8jaced 28 cm in front of a spherical mirror. It is desired to produce a virtual imaged2q ;xfw8ljc,8 yzn(s.49 5abnmoxdj 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 designe0/*r 0yjxyuh ed to magnify your face by a factor of 1.33 when your face is placed 20.0 cm in front of it.e 0y*xh/r0 ujy
(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 ofk5) h)o3kb6kkkzz1 ny 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 i*3ib t1nxpn+ tce is $2.29\times10^8\mathrm{~m/s}.$ What is the index of refraction of ice? n =   

  The speed of light in a certain substance is 89% of it,0ah ndz*xr4)iu4 x yms value in water. What is the index of refraction of this substance? n dxauim 4h,r*)40x z ny=   

  A flashlight beam strikes the surface of a pane of glass 832gu9d cjcyrwb s+6ls,b g5l(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 fd4e dw/wu 7+tfrx0w1jrom beneath the water at a 42.5$^{\circ}\,$ angle to the vertical. At what angle does the light leave the water? $\theta_2$ =    $^{\circ}\,$

  A light beam coming from an underwater spotlight exits the water at an angle oj/pgqbsy+w, sgrk(jk lu.y.(hdb(0r+h )w 7 hf 66 ds0bh7jgq(.k+ r/ (+) gy hwhru,jp(k.wl ysb.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 3s sl8 clfzdw;:8w kn-make a 31.0$^{\circ}\,$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?    $^{\circ}\,$

  An aquarium filled with water mzg6 ;v/g nmnea1h9 :rw7ken9has flat glass sides whose index of refraction is 1.52. neg:nm;vh9agk /r9ze n 7w16mA 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 jk:.*fj8gg.4 5rgry u j,6eik8rnypr 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 spot of light hit the bottom of the pool, measurygkr rgj k58i:4,u* 6 ryj enfj.r.8gped from the wall beneath his foot, if the pool is 2.1 m deep?    m

  Light is incident on an equilateral glass prism ai hx7 21qzgh7w41:sbdc2s yao t 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 ocyn jg1;zj r19mc+.csy idu3+f glass (n = 1.52) and is partially reflected and partially refracted. Find the angle of incideics+1 jd3cyzc+19ugr.;n mjy nce 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 transparen6ce zv1i1p;c et material, as in (Fig. Beloe1ce izc6v ;1pw), 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 qr3crz,wsqh9v72 v9 r piece of glass with index of refraction n as in (Fig. Below). Showqzsc q,vv 9h9wr2r37r that if the incident angle $\theta$ is small, the emerging ray is displaced a distance $d=t\theta(n-1)/n$ from the incident ray, where t is the thickness of the glass and $\theta$ is in radians. [Hint: for small $\theta,\sin\theta\approx\tan\theta\approx\theta$ in radians.]

  What is the critical angle for the in+z soagb(9f 861q9jyyo9i ocl/w*ybq terface between water and Lucite? To be totally internally reflected, the light must start in wi8*o916a oyo /sqb q wy(9+g9fjczblyhich material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain lrgch1 20vm izs28)lzmiquid–air surface is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted in a pool of water from a depth of 62.0 cm. Where musbvlfpsyi 5 h o94szt/a./69aut it strike the air–water interface, relative to the spot dire9uf s/i/b sala6t9yp.z o4v5hctly above it, in order that the light does not exit the water?    cm

  A beam of light is emitted w(0ts l 3:xp8zdimom88.0 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 w3sozd x0(8i p:mltm8 about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face of the prism in (Fiyra2nkzp 69l c*jj,j-+-g xe pg. 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);hao5izy/6 qb . Show that we can guarantee total internalq5/ayo;iz hb6 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 back into the material at point a.

  (a) What is the minimum inde -p*qpw( 34/ ru mqb-wzi/gk7z3kxa7oukmkt4 x of refraction for a glass or plastic prism to be used in binocularsp p/3 bk z7-uma w3 twku-q*4k4kg/i q7m(rxoz (Fig. 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-foc :wpuvq2rc5vmhh 0,t2 al-length converging lens. Fi22vr q0phcut:, m5 whvnd the object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at aq+ md0+cfvvwvk. ol31 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 as9qn s. j9 ltxpw4mdp1+ an image 48.3 cm on the other side of the jwn9 pm+9q 1txdsp4.llens. What type of lens is it and what is its focal length? Is the image real or virtual?  ----待选择----converging lensdiverging lens  $f$ =    cm the image is  ----待选择----realvirtual 

  (a) What is the power of a 20.5-cm-focal-lengtimb )f76b7an qc07lgfe+3p eeh 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(e5f bdfzwk8yk9py- :6l8cb u cm to view a stamp 18 cm in front of thecuke d-kfl98b8 py 6wzf( :b5y 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. Whafnhac gy0/ in-m1s- 5zndbd6xwp71k5t are the position, type,7/0ni nmkdbn 1- wahf 65g-1ypsc5 dzx and height of the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length nxw0 /t xg++p(wj0eztlens is used to focus an image on the film of a camera. The maximum distance allowed between the lens andtwj0 e(zn/xw0+ +x gtp 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,rhm6yq d(ihb ii .22u by a factor of 2.5× when a book is placed 8.0 cm be,h2yih2uim i(.r d qb6hind 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 aj 9 :ax(woze6dn 8.0-D lens. By how much does the image move if the object is moveez( djax69o:wd
(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 focl c e6)d -c)dwn-uvphf747rd ial length of 25 cm should an object be placed to produce a real image which is the same size as the u d)f7c74n)d hcl rv6e-w- dipobject?    cm

  (a) How far from a 50.0-mm-focal-length lens must an ol( -8kcb - bw5zel c+6qb;uqq/bz0oh rbject be placed if its image is to be magnified 2.0q;0kr8q5lchz bbbzu(- b+c ql -oew/60× and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm

  (a) How far from a 50.0-mm-focal-length le2vam 6ld-dp3 2afj 7jlns must an object be placed if its image63jdaa l- jdpl2vfm27 is to be magnified 2.00× and be real?    mm
(b) What if the image is to be virtual and magnified 2.00×?    mm (formed by some other piece of optics).]

  (a) A 2.00-cm-high insect is 1.20 m from a 1 9,nbaw:3eaq d35-mm-focal-length lens. Where is the image,9wde3 qb,n:a a how high is it, and what type is it?
$d_i$ =    mm (real,behind the lens) $h_1$ =    cm (inverted)
(b) What if $f=-135\mathrm{~mm}$?
$d_i$ =    mm (virtual,in front of the lens)
$h_1$ =    cm (upright)

  How far apart are an object and an image formed by a 75-cm-focal- bq3+9yjp n9aulength converging lens if theu9qb 3 +ypa9nj image is 2.5× larger than the object and is real?    m

  A bright object and a viewing screen are separated by +eb35la opg r(hr79czf2l j,t a distance of 66.0 cm. At what location(s) between the object and the screen shobg a7e,59rlo (cp2 z trfjh+3luld 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 be placed    cm or    cm from the object

  Two 28.0-cm-focal-length converging lenses are playv6av xj ,fy8+w 03gopced 16.5 cm apart. An object is placed 36.0 cm in front of one lens. Where will the final image formed by the second lens be located? What is the tota f6v0 y,x+wgj8ovyp3al magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens with*-puxpavx7z2rut2 o- sa ms:, $f=-31.5\mathrm{~cm}$ 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-lengmz5q jow8 5/rcife *w0th converging lens is 21.0 cm behind a diverging lens. Parallel light strikes the diverging lens. After58 jwqizro/ cf0wme*5 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 Exxp1g q9hhs+ g: xc0k/4bm r5eclyckzq*7y -f7ample 23–12 are now placed only 20.0 cm apart. Theqf* meh lk9 z/x7s+yhgcxqc c07yk 54: r-gpb1 object is still 60.0 cm in front of the first lens as in (Fig. Below). In this case, determine
(a) the position of the final image,    cm
(b) the overall magnification.    cm
(c) Sketch the ray diagram for this system.

  Two converging lenses are placed 30.0 cm+xc5h4 /5bhnpq ;qtx5; svjkf apart. The focal length of the 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 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. Hqc5fsj4hkhn ; t+ ;x5 5bxpqv/ow far to the left of the 15.0-cm-focal-length lens is the original object?    cm

  A diverging lens with a focal length ofa2pkdlz;4 j/ dd(7 llw is placed 12 cm to the right of a converging/jzldddk ap7;l2( wl4 lens with a focal length of 18 cm. An object is placed 33 cm to the left of the converging lens.
(a) Where will the final image be located?    cm to the left of the converging lens
(b) Where will the image be if the diverging lens is 38 cm from the converging lens?    cm to the right of the diverging lens

  Two lenses, one converging with focal length 20.0 cm;gmzrzq9f 96joi)h/k91uyfc and one diverging with focal length are placed 25.0 cm apart. An object is placed 60.0 cm izy 6/oucm91;q )z9 fhjfkrg 9in 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 lens o 3f.k/cgz cya4 ren,zl8n.ul*8w c2gth $f_C$ 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 lqnh)vscn: 5;/xwiu;jnv 7b2 radii of 34.2 cm and 23.8 cm. What is the focal length if n = nhnjv;u:25sbicvnlx;q7) w/ 1.52?    cm

  Both surfaces of a double convex le)zc kn,e jg0s0z rh+0vns have radii of 31.0 cm. If the focal length is 28.9 cm, what is the index of refraction of the lens matecz0 j+e,zgrs0)0n hv krial?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4p *j1 nai0qv4wcm. What is the radius of the concave surface4qp wjvan i*01?    cm

  A Lucite planoconcave lens (see Fig. st73 z3uty8ytv s/9pn Below) has one flat surface and the other has R = -18.4 n8t7 339/zytsutpys vcm. What is the focal length?    cm

  A symmetric double convex lens with a focal length of 25.0 cm773c:det)8kzu lzbfq is to be made from glass with an index of refraction of 1.52. What should be the radius of curvature for each surface? :c8)k3f euqbdtzl7z 7    cm

  A prescription for a corrective lens cap 0 ud20p*+;py ssmlimlls for +1.50D. The lensmaker grinds the lens from a “blank” with n=1 l smm0*yp2dsi0 +u;pp.56 and a preformed convex front surface of radius of curvature of 40.0 cm. What should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fig. z -jzf7)foi r/Below). You stand 1.5 m away from one of these mirrors anozj/f rf7i)z-d look into it. You will 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 p 1/0 u ir+zrd+xdyj/swater. We measure the width (x=5.50m) and then note that the bottom edge of the poor1 /duj p0y/ dsi+xzr+l 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 c:e;sy5/i idho: kv6gm ertain 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 consingta-z/fx, oqm 7x: p)dered a limiting case of a spherical mirror. Specify what thisnz xf)/pg: mq7xo t,-a 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 yd5zpl 19eh4by2spj fbcl*( /a 90$^{\circ}\,$ angle as in (Fig. Below). When you look into this double mirror, you see yourself as others see you, instead of reversed as in a single mirror. Make a careful ray diagram to show how this occurs.

Show analytically that a diverging lens cadmzc 6 .i.vsee/ei hmy+7i r.3n never form a real image of a real object. Can you describe a situation in which a diverging lens can form ai +3 .i/he6 i ..crve7emsmydz real image?

  Each student in a physics lab is assigned to find the location where a brightk5ik9ajru 4x6 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 ansi94k j56a xrkuwers for the object distance are not the same. Explain why they do not necessarily need to repeat the lab, and justify your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of a pri;-h ab4q9k/ v 5;miqzexxn9pasm 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 gwz2lt cch/f8olh)5+iidc7 2 blass 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 :qesu*;qa i:tlength $f_1=15\mathrm{~cm},$ 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 converginf61ic v d24.s2 l*rroh,jswhr g lens of focal length f, and*wlrf.ri 4hv,co sj2s6h2 1dr a white 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 o7e* exzu g-0l-nxc3kthe object whose image is projected on a screen (Fig. Below). If a 105-mm-focal-length lens is to project an image n 7x3lucze-xe 0kg -*oon 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 mplz7;jzou ,ur zo,h3 h;d7(ratl3 dq1 m) is to be projected on a screen 1.80 m by 2.70 m placed 7.50 m from the p llrh hzqo3u zr73dup,ojtd( ;;1z7a,rojector. What focal-length lens should be used if the image is to cover the screen?    cm

Show analytically that the image formed by a converging lens is xm-/ilhtgr2 jyl89 6dreal and invertej8mrt- /96xdy2il lghd if the object is beyond the focal point $(d_0>f),$ and is virtual and upright if the object is within the focal point $(d_0>f),$ Describe the image if the object is itself an image, formed by another lens, so its position is beyond the lens, for which $-d_0>f$, and for which $0$<$-d_0$<$f$.

  A movie star catches a reporter shooting pictures of her at hq57tja tbz14 ,sq* unoome. She claims the reporter was trespassing. To prove her point,t 5 zqnq,ao4btu 7sj1* 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 imageve zpbi9*xryqscr;nr0 x*3 hu.4 /y+x of the Sun on film used in a camera with
(a) a 28-mm-focal-length lens,    mm
(b) a 50-mm-focal-length lens,    mm
(c) a 135-mm-focal-length lens?    mm
(d) If the 50-mm lens is considered normal for this camera, what relative magnification does each of the other two lenses provide? The Sun has diameter $1.4\times10^6\mathrm{~km},$ and it is $1.5\times10^8\mathrm{~km}$ away.    for the 28 mm lens    for the 135 mm lens.

  (a) An object 34.5 cm in froc7u6u zzlj/v6ypd -g:6m3 tx fnt of a certain lens is imaged 8.20 cm in front of that lens (on the same side as the object). What type of6:3 -guzcztj/y p7 f6muxvl6d 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.ruz 6) m5+fa*(neqmv1ule i2f 0 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 the lens. Find the focal lenf+*qi2em( e f6l) 5 1muzuarnvgth of this lens.    cm