What would be the appearance of the Moo8xyym f jr1tunc/f(i:. lo:(zn if it had
(a) a rough surface;
(b) a polished mirrorlike surface?

Archimedes is said to have burned the whole Roman fleet in the harbor yiwoqm*4 o jh mxs82t374zag+of Syracuse by focusing the rays of the Sun with *w48 got+ys3q o4z 7mi a2hmxja huge spherical mirror. Is this reasonable?

Although a plane mirror ao/u:j/h1a ect hus ybi0- p,.nppears to reverse left and right, it doesn’t reverse up and down.h .:hujna-eo/u0/ s,b i y1ctp Explain.

If a concave mirror produces a real image, is thr89x0rk. p du8:x;wbdg8 vjpse image necessarily inverted? Explas.9 rwp0pk 8:xrdx8d; uvgb8 jin.

An object is placed along tg aipt.;tl*g0g*l-uil mz/b- he principal axis of a spherical mirror. The magnification of the object is -3.0 Is the image real or virtual, inverted or upright? Is the mirror concave or convex? On which l/aig*gl*iz;- mtlb0 -.pg tuside of the mirror is the image located?

Using the rules for the three rays discussed with refereny hozf;n lye09. 87 pq/fjm:knce to (Fig. Below a), draw ray 2 oef0k8 ;.yhn zlfmj:9qp 7 y/nfor (Fig. Below b).
(a)
(b)

What is the focal length of a plane mirror? What is the magnification of;q ropw:qvx+w 2ekc4 58pbx/y a plane mirr5w e; vp8ow 2rp y+/cb:xkx4qqor?

When you look at the Moon’s reflection from a rippl-w-*og 7xb dzn2r 2urty sea, it appears elongated . Exdbrr-x * oz-2gwut 2n7plain.

What is the angle of refraction when a light6(ygr0+v pi(wwpgd-v i(mi 5z ray meets the boundary between two mamii6dg-5rv+ g(p wp w y((0izvterials perpendicularly?

How might you determine the speed of light in a solid, re76o/ (x:+ozpcs)iq d;n b emgcctangular, transparent object?no:e)7g/ xbzm6(p+ ci d qoc;s

When you look down into a swimming pool or a lakf; we)subo4 r62lr yl3e, are you likely to underestimate or overestimate its depth? Explain. How does the apparent depth vary with the viewing angle? (Use r2o lu r4lrb;w f)s3ye6ay diagrams.)

Draw a ray diagram to show why a stick looklod79wiy*7s6st- gho,) o5z6ql wpfv s bent when part of it is under water (Fi*,5yoh6o7w)dtl o9f psgzlqw6vs i 7-g. Below).

Your eye looks into an aquarium and views a fish inside. One ray of ligh7 6oq4fe mezpabyu3e;1-es( u t 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. Br3 be1y;a4ms e-u6u e(zfop qe7iefly justify your answer.

How can you “see” a round drop of water on a table even though the water is trave m 8;z5u2 dy6rzw+xsnsparent andmzrx+8 ued;yv6 z w5s2 colorless?

When you look up at an object in airaqqvxa/r ;,4m from beneath the surface in a swimming pool, does the object appear to be the same size as when yourqqa m4xav;, / see it directly in air? Explain.

How can a spherical mirror have a negative object dob y+ )r8ly9 bxfp7irvw (n6c:istance?

Light rays from stars (including our Sun) alw9c6ooc2aqph0v cu*.q x9g* uvays bend toward the vertical direction as they pass through the Earth’s atmosphere.xvh og60upq c.o *cc 9qva9*2u
(a) Why does this make sense?
(b) What can you conclude about the apparent positions of stars as viewed from Earth?

Where must the film be placed if a camera lens is to make a sharpl7wlirhy lx3)r hq.*d 0 4j/ts image of an object ve)y/ht wdqjill*4h0r . x37rlsry far away?

What type of mirror is shown in (Fig. Below)? Exp;*8 bm y is glylp-,h u/flsxp7oqj yu.108p.llain.

A photographer moves closer to his sd aspmlni+5t -*qx i*5ubject and then refocuses. Does the camera lens momt-5qx* in l+ d*i5spave farther from or closer to the film? Explain.

Can a diverging lens form a real image under anlb 1ryu*;f;j fy circumstances? Explain.

Use ray diagrams to shownvtk,3lc+6;fuq wvnv;hyxb0um /h 5 / that a real image formed by a thin lens is always inverted, whereas a vir0 5k 6/ +u v,nvv/hlmxqutn ;bf3hywc;tual image is always upright if the object is real.

Light rays are said to be “reversible.” Is this consis al3rnr 0c-7xem-(au dtent with the thin lens equation? Expla 0aun-(mrxe-cr d3l7 ain.

Can real images be projected on a screen? Can virtual images? Can either be pholg-7igwpu-qqsh.7//sa,d ql 9th 9vi tographed? Discuss carefulp-ih- /,7lgt.laqu s99wiqqdg v 7/shly.

A thin converging lens is moved closer to a nearby objd- 2.cpkvh. +(-en 5i8,hhedg f wyvtyect. Does the real image formed cha.,dhf nkh8h-v2ecd+yvp e- .(ywti 5gnge
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a material with an index of refractiqq*mf be+a+3 iyp.-g g t/dr)kon n = 1.30 In air, it is a converging lens. Will it still be a converging lens if placed in watek3 -pa gq/+f +erm .dyt*)bgqir? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the air stands facing a convergi/trg m5up 3i6 nrbf;s0ng lens. If the nose and the tail are each focused on a screen in turn, which will have the greater ft ig5sbu30 p;n/r6m rmagnification? ----待选择----nosetail 

A cat with its tail in the air stands facin). pojnx9 pmv;g a converging lens. Under what circumstances (if any) would the image of the nose be virt p .o;m)vxnj9pual 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 converg8 n2q*+(84cugd1ydngtfwyk h ing lens have a shorter focal length than the diverging lens if the latter’s focal length is tcdk g 1gu4(*w2+tyndn8h yf q8o be determined by combining them?

Explain how you could have a virtual o*nr (g7h4vn/ b6slr3eo01 gk jmomq4object.

  An unsymmetrical lens (say, planoconvex) forms an image of a nearby g w9sh 5izb9f6k;c 3eo0 (qvkpjbujioj;(x4 2 object. Does the image point change if the lens is turned around9(2xb3z po;w4fi50jshk6i 9; q kguj(ce jbvo? ----待选择----yesno 

The thicker a double convex lens is in the center as compared to its edgesi)r* eitv8lx8yog lemc()h 13, the shorter its focal length for a given lens diameter. Explaincov x ime)rtil1388)h * eyg(l.

Consider two converging lenses separated by som+n+gk :8 a yo-v2o;icczmd ef u:+iu*ee 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: 2c8 ;d +zu+i g*eyk+ui ocavnem-:fo not, why not?

  Suppose that you want to take a photograp9:g/ilhpbxq4 o2*cqx-2t-v k a o8fkth of yourself as you look at your image in a flat mirror 2.5 m away. For what distance should the camera lens be focused? hoxfpq gcbxa-qi/ 4to t298 k l2*-k:v   m

When you look at yourself in a 60-cm-tallas.p ( fyg ,ym+.o3uyo plane mirror, you see the same amount of your body whether you are close to the mirror or far away. (Trg(s yo3 m +ua,pf.yo.yy it and see.) Use ray diagrams to show why this should be true.

  Two mirrors meet at a 1qwj6.ga/ zcpml q * 1p2weu6l)35$^{\circ}\,$ angle, (Fig. Below). If light rays strike one mirror at 40$^{\circ}\,$ as shown, at what angle $\phi$ do they leave the second mirror?    $^{\circ}\,$

  A person whose eyes are 1.68 m above the floor stands 2.sth zu))3n-36arzz ekw t f+p1h/a 2n) qi3thf20 m in front of a vertical plane mirror whose bottom edge is 43e nraz)h)3t6sa+qf 2w zpz-/ 3tkh3 1tunf) ih cm above the floor, (Fig. Below). What is the horizontal distance x to the base of the wall supporting the mirror of the nearest point on the floor that can be seen reflected in the mirror?    cm

  Suppose you are 90 cm o,lmhfh-a-+9-l+ bx2c knso hfrom a plane mirror. What area of the mirror is used to reflect the rays entering one eye fr- hhll akh-+ -osc,fn+92xmboom 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 m t -icj(x/x,ulp*-naweet 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, real.( zt kv +fn1gd. jz;nevmmnbb9q+;5 mly a concave mirror pointed at the Sun, focuses the Sun’s rays 18.0 cm in front of the mirror. What is the radius of the spherical surface from which the mirror w bbgz1+.;k m.mev5 n +(v d9f;nznmqtjas made?    cm

  How far from a concave mirror (radius 23.0 cm) must an object be placed i pl+38rdxllz 6f its image is to be at infinity?l6 8pl3rldz x+    cm

  If you look at yourself in a shiny Christmasd6wy .mm 84mtb tree ball with a diameter of 9.0 cm when 6m.wt4 8dbmym your face is 30.0 cm away from it, where is your image? Is it real or virtual? Is it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusement pa0qtxeqb i;iwx)ol:; be fq e58ps2j(, rk shows an upright image of any person who stands 1.4 m in front of it. If the image is three times the person’s height, what is the radius of curv l t)eqj;e0e(sqxbii:qb2 5wp8f x,;o ature?    cm

  A dentist wants a small mirror that, when 2.20 cm from a toosma/ ,bn 8fm8a82tpb nth, 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 arex.2qeaa6tq5gc lx5 7i smaller than they would be ifgxq5ci eaq 7x6t al2.5 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 size?
 ----待选择----convexconcave 
r =    m

  A luminous object 3.0 mm high is placed 20.0 cm from a convex mirw k1kr p97 29e16nwwtxbv3beu ror of radius of curverb1k9u6k7 2nww13 9xw pevtbature 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 from70r- shv h;pat a convex security mirror in a store. You estimate the height of your image to be half of your actual height-70a;h hvr spt. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object be placed in front of a concave mirr v 1lvh-h61xunor so that it produces an i1v1h xnhv-ul6 mage 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 virtual 7spl t t/9qn/zand very small when viewed in a curved mirror. The image appears to bezntpts9/q/ l 7 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 techniq4uahtycff*p v b.zp6.5d , l0iues,
(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 magnificatiohlq+ ec2+p*w gn 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 thq lei3qm.v5g: at the mirror equation, Eq. 23–2, is valid for a convev5l.mq: qie3gx mirror as long as f is considered negative.

  The magnification of a colm uocdu5 )-qv/ c5m(envex 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 on kg--uzux8i3 ct7* jff a spherical mirror. It is desired to produce a virtual image that is upfkgcu-x-tz nj 7 *3i8uright 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 designedo*xedw4 28xeb to magnify your face by a factor of 1.33 when your face is placed 20.0 cm in front oxxbd*eo84 e2wf it.
(a) What type of mirror is it?  ----待选择----convex mirrorconcave mirror 
(b) Describe the type of image that it makes of your face.
(c) Calculate the required radius of curvature for the mirror. r =    cm

  What is the speed of wizx+diga 5ojwo8d3/7 :cmv9 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 qg4n imt+xj xm9p(b6:w-j dn(ice 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 its value in wa/fv/ 1, at qhxnkjk34eter. What is the index of refractiaq3f4nx1,v/hjt/e kkon of this substance? n =   

  A flashlight beam strikes the surface of a pane of glass (n = qyxba jio2x6p )fjfm ):1*t;s1.58) at a 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashlight upward from beneath the water yd( :ueuibcqq 6fr9-gh6r9 j4at 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 p70 b7jo5 btumexits the water at an angle of 66.007 tp5mou bj7b$^{\circ}\,$ 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 maky *mx38+urh.ir+x3a g:sx xh se a 31.0$^{\circ}\,$ angle to the vertical beneath the water. At what angle above the horizon is the Sun?    $^{\circ}\,$

  An aquarium filled with water has flat glass sides who3:lhe0dg* m6keua 50 usvkjy; se index of refraction is 1.52. A beam of light from outside the aquarium strikes the glass at a 43.5° angle to the perpenmkj:sh;50vyu*ek0e ad l 6ug3dicular (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 hc d0ka)t /bb6shines 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 spot of light hit the bottom of the pool, measured from the wall beneath his foot, if d ha6tk0 /)bcbthe pool is 2.1 m deep?    m

  Light is incident on an6w9z.onb: qpd j8 7q ibmpmlu(g ;;0xt equilateral 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 glaa(aj j2re- s+43zyz h2t(zqwbss (n = 1.52) and is partially reflected and partially refracted. Find the aw(2tjsazq4-h+ 2b (zaezj 3yrngle of incidence if the angle of reflection is twice the angle of refraction.    $^{\circ}\,$

Prove in general that fo1g1oszvpx:k8k : vvj6r a light beam incident on a uniform layer of transparent material, as in (Fig. Below), the direction of the emerging beam is parallel to the incident beam, independent of the incident angle g:8:vsjo 1vz p 6xk1kv$\theta$. Assume air on both sides of the glass.

A light ray is incident on a flat piece of glass c767f d u(s81axdhnjjwith index of refraction n as in (Fig. Belowc(7jxndu1687ha s d fj). Show that if the incident angle $\theta$ is small, the emerging ray is displaced a distance $d=t\theta(n-1)/n$ from the incident ray, where t is the thickness of the glass and $\theta$ is in radians. [Hint: for small $\theta,\sin\theta\approx\tan\theta\approx\theta$ in radians.]

  What is the critical angle for thqjd1clmd 1u25 e interface between water and Lucite? To be totally internally reflected, the ligjcl du5qm1 d21ht must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a cerq;z6hxb* 0jtutain liquid–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 q utbdxl9qj+ ig h/2krh(o-s4t-74yr depth of 62.0 cm. Where must it strike the air–water interface, relative to the spot dirj2b4ky4lq9it/+xo q r-7 ghhu-t dr(sectly above it, in order that the light does not exit the water?    cm

  A beam of light is emitted 8.0 cm beneath the surface of k8:hwi dg-mpv 9,p+;rin sn(8eiaoj9 a liquid and strikes the surimvhe8ikr;g8:ja i+ w(9 ps9-dn, pon face 7.0 cm from the point directly above the source. If total internal reflection occurs, what can you say about the index of refraction of the liquid? $n_{liquid} \geq$   

  Suppose a ray strikes the left face of the prism in (Fig.q h fsdkii/ +6l928h/uskhxk/ 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). Shf;j*gvj:con +lff9 .qow 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 back into the material at point a.;fclj .9n vfo+:qgfj*

  (a) What is the minimum indexobwd7:w (k,vvr2l n g+ of refraction for a glass or plastic prism to be used in binoculars (Fig. Below) so that total internal reflection occurb+g:7vrod2 ln, (wkvws 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-mmp odj-qs(0 2wb-focal-length converging lens. Fi p(qowdb sj-20nd the object distance
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to wa9haw . /g;gwryhm;1 focus at 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 ob4ugwug886mfoaau )b s5),lsl ject 2.75 m away as an image 48.3 cm on the other side of the lens. What type of lens is it and w)suob 8uggl48lu,f a 56am) wshat 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-focm3 h0 m8ftws-,byf u;aal-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 lengthmm:n): f* h rpw.b/bgu9r; wuv 24 cm to view a stamp 18 cm in front of the)m:uw :npr/wb9f;ru g*.hm bv lens.
(a) Where is the image located?    cm behind the lens (virtual)
(b) What is the magnification? m =   

  A -5.5-D lens is held 14.0 cm from an object 4.0 mm high. What m 1z7f*v,rgc(xhr0-f+t nsx x are the position, type, and height or, *1mvc0- xnstfz( xrx 7hg+ff the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to focus an ma,y j;3+lo icv nz:6yimage on the film of a camera. The maximum distance allowed between the lens and the +aizn6oyy:j vm ;,c3lfilm 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 readingn,f fyv;sbi+y )lw(.0ww .pjg material by a factor of 2.5× when a book is placed 8.0 cm be,;w+0fg n(yf. swp blv. jwy)ihind a lens.
(a) Draw a ray diagram and describe the type of image this would be.  ----待选择----realvirtual 
(b) What type of lens is needed?  ----待选择----converging lensdiverging lens 
(c) What is the power of the lens in diopters? P =    D

  An object is located 1.5 m from an 8.0-D lens. By how much does the imageix4a,m*s2c+x ;cu u fl move i m;xu,u*il+4cafc xs2 f 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 sci/ taxb09 x)u.1:8qdjqjpsnhould an object be placed to produce a real image which is the same size asjx )npjs t :q. /bai1udcx809q the object?    cm

  (a) How far from a 50.0-mm-focal-sf)ob4-4lfdner0bw m1wf3* 46p fm1 p.h lygalength lens must an object be placed if its image is to be magnified 2.00× and be real?gyl p-efow1m. 4)fw04nspr ffbalh3 6*mb 1d4    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 m 5wb-soc s99iax4dd1 iust an object be placed if its image is to be magnified 2.00× and be rdsds4wc ba19 x5i-9oieal?    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 1.2 8 kkasw:0x9qd0 m from a 135-mm-focal-length lens. Where is the xawd9kqk 08s: image, 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. 3fqp zz(w.l)jxeuv 0 formed by a 75-cm-focal-length converging lens ( qxu).e zpzv3fwj0.lif 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 acik f7 ,9h/fg1v b;4 guscm8g66.0 cm. At what location(s) v9a ifb f,4sugmghgc71/;k8c 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 be placed    cm or    cm from the object

  Two 28.0-cm-focal-lendk8()dybk*bo4 iy, tf3,t d eqgth converging lenses are placed 16.5 cm apart. An object is placed 36.0 cm in front of one lens. Where will the final image formed by the second lens be located? What is the total magnifi3y (8b* tqifb ,yd4etod ,k)kdcation?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens with3fpe hn7d 8w.r $f=-31.5\mathrm{~cm}$ 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( 9tvlc5d1ot )t4daai behind a diverging lens. Parallel light strikes the addt(i5la94tcovt )1 diverging lens. After passing through the converging lens, the light is again parallel. What is the focal length of the diverging lens? [Hint: first draw a ray diagram.]    cm

  The two converging lenses of Example 23–12 are now plai,*4*ll6hhst bk *lw vced only 20.0 cm apart. The object is still 60.0 cm iwb46v* lth * l*hs,lkin front of the first lens as in (Fig. Below). In this case, determine
(a) the position of the final image,    cm
(b) the overall magnification.    cm
(c) Sketch the ray diagram for this system.

  Two converging lenses are placed 30.0 cm apart. The focal length of thr yt9 u)pj3 v/4hf6wjwe lens on the rightwf43 h jup)v6 w/jry9t 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. 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 plyq9h va.-:bj3uf79p y-ptqp gaced 12 cm to the right of a converging lens with a focal length of 18 cm. An object is placed 33 cm to the left of the co ap9yqh3-q9jpyt fg b:v7u- p.nverging 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 ;qxn0( jrxa/v 20.0 cm and one diverging with focal length are placed 25.0 cm apart. An object is placed 60.0 cm in front of the converging lens. Dejx0nvx(;r q a/termine
(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 convergin++ges47mop bobe 7m0 6o(3 4hsrnk3fkaq c,fvg lens of focal length $f_C$ as in (Fig. Below). If $f_T$ represents the focal length of the combination, show that the focal length of the diverging lens, $f_D$, is given by
$\frac{1}{f_\mathrm{D}}=\frac{1}{f_\mathrm{T}}-\frac{1}{f_\mathrm{C}}.$

  A double concave lens has surface radii of 34.2 cm and 23.zi elexxi3hq,jejyv17 2l : my*9 r3z08 cm. What is the focal length i97 qhm lr2yxv*:3e1j ,i zzjye3 x0elif n = 1.52?    cm

  Both surfaces of a doublto/w,ygjgqe*69+:rrg vc : e pe convex lens have radii of 31.0 cm. If the focal length is 28.9 cm, what is the index of refraction of the lens materia/ry*p :e:6+ gj gqoev9 wtrgc,l?    cm

  A planoconcave lens (n=1.50) has a focal length of -23.4cm. What is the ra(4sipw)oblryrg s(a :bu7w+3 dius of the c luw(3s:gb+abs(r7ri4op y w)oncave surface?    cm

  A Lucite planoconcave a avx3kr3js 3*lens (see Fig. Below) has one flat surface and the other has R = -18.4 cm. What is the focal length? 3 rvk3* ja3xas    cm

  A symmetric double convex lens with a focal la nb1cs9z 3k8-ee t;(b1wagtxength of 25.0 cm is to be made from glass with an iz;tt( an3bk9e8 -c1 swbx1eagndex of refraction of 1.52. What should be the radius of curvature for each surface?    cm

  A prescription for a corre,s j+x93 inwn3rrudi;snk- g(wg, *n vctive lens calls for +1.50D. The lensmaker grinds the lens from a “blank” with n=1.56 and a preformed convex fros3 w9sj+ndgn iigvrr -n;wx ,*(,3uknnt 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 m9i0ve r4 xh6mx apart as in (Fig. Below). You stand 1.5 m ae4h6xv0ir9xm way from one of these mirrors and 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 watene hcz aplzd+f 9 sx7 0..kur56,5adpxr. We measure the width (x=5.50m) and thenp.xru6 d 55sa z ef+7p cnxz,9.hal0kd note that the bottom edge of the pool is just visible at an angle of 14.0$^{\circ}\,$ above the horizontal as shown in (Fig. Below). Calculate the depth of the pool.    m

  The critical angle of a certain piece of plas tn .i)lfubq6x x5 xd4sgs2(k.od7.kwtic 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 consider , z31tprls0lued a limiting case of a spherical mirror. Specify 0u,rtlz1s pl 3what this limit is.
(b) Determine an equation that relates the image and object distances in this limit of a plane mirror.
(c) Determine the magnification of a plane mirror in this same limit.
(d) Are your results in parts (b) and (c) consistent with the discussion of Section 23–2 on plane mirrors?

Stand up two plane mirrors 0o ms2r; h-lpgpy muas(:4 9qqso they form a 90$^{\circ}\,$ angle as in (Fig. Below). When you look into this double mirror, you see yourself as others see you, instead of reversed as in a single mirror. Make a careful ray diagram to show how this occurs.

Show analytically that a diverging lens caxwflz ktntr tl;44x36 6.hx/ln never form a real image of a real object. Can you describe a situation in which a diverging lel ;6t 4nr36fwtl/.4 ht xxzkxlns can form a real image?

  Each student in a phyptm ev9dv+b 51sics lab is assigned to find 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 assignmp 5 bvt1mve+d9ent at different times using identical equipment, but when they compare notes later, they discover that their answers for the object distance are not the same. Explain why they do not necessarily need to repeat the lab, and justify your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of a prblszmr.e7 lej --t57cism 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 cylindrivbec0j rsln9a;vg6z iru j78l qbw:3ptz-;68 cal 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 off -.x* lhsx: )u,moasl a converging lens of focal length $f_1=15\mathrm{~cm},$ which in turn is 55 cm in front of another converging lens of focal length $f_1=15\mathrm{~cm},$ (see Fig. Below).
(a) Draw a ray diagram and estimate the location and the relative size of the final image.
(b) Calculate the position and relative size of the final image.

A bright object is placed on one side of a converging lens o 0v7vzy8 ayf1a-kttq3f focal length f, and a white screen for viewing 0vz7va-t3 yqak1y8ft 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 the object whose image is projeu8xogb 6k4dv1cted on a screen (Fig. Below). If a 105-mm-focal-length lens is to proov xubk6dg48 1ject 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) is to be projected on a scrtia*-xb0-e 08wnsir ceen 1.a8- ei0xt0 bnrs -*iwc80 m by 2.70 m placed 7.50 m from the projector. What focal-length lens should be used if the image is to cover the screen?    cm

Show analytically that the image formed by a converg;df8w*s,g b4gb lei;5n bhebl-0s br-9t7m guing lens is real and inverted if the objeen5i-b0 g; s9bu, *m;hg 8b- w slgr7fet4lbbdct 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 reporterw v9ng az3;6dm shooting pictures of her at home. She claims the reporter was trespassing. To prove her point, she gives as evidence the film she sn9 av w;6mdz3geized. 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 in a cambui)kxu l9bv08reb 88h js8x.bz cj0,era 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 imaged 8x i(ba r/: l,fserq4w4dec -/y.20 cm in front of that lens (on the same side as the object). What type of lens is this, and wbq-lwr4f/ x/y:rda4ce(, seihat 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 plac+ ) ;:ufmy njslk*n2awed 60.0 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 frm;lf as nw+y):j2u*nkom the lens. Find the focal length of this lens.    cm