What would be the appearanc/ f7bg7dp2ey5icmhj*k xg9u1 e 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 the harbor of Syracmk /dzha9fbqn:ps4u vyh 6e( 9s0d3 y(use by focusing the rays of the Sun with a huge spherical mid0u9f36:z(h/pndsh 9e qy ( ybksm v4arror. Is this reasonable?

Although a plane mirror ggb8, /jm jiogr5qtvknn huc,l2c0rv,q55 , )appears to reverse left and right, it doesn’t reverse up and down. Explain.q5q), jvo 2m5,0jr, nrl,c8hn5g gvugb/tc ik

If a concave mirror produces a real image, is the image j/c m(yh+y su0/j yi8gnecessarily inverted? Expla myyciy(j8j0h g+u/s/in.

An object is placed along the principal axis of a spherical mirioak1,fy0ro +qigt-;ror. The magnification of the object is -3.0 Is the image real or virtual, inverted or upright? Is the mirror concave or convex? On whi; kf 1ot+riy-iqg 0ao,ch side of the mirror is the image located?

Using the rules for the three rays discussed with reference to (Fig. Below a), p 0 (2 q8b8 l1ym2bjgelgohvw3draw ray 2 for (Fig. Bel2vhqg pom0el8g 3blj b 2(81wyow b).
(a)
(b)

What is the focal length of a plane mirror? Whatmv3v u(wx*u1 0kd7 qss is the magnification of a plane mirrv*x 7 0 s(uwm1uvsdq3kor?

When you look at the Moon’s reflection from a ripply sea, it appears elo63le 8bx6y rcnngated . Explain.8b63 rxnly ec6

What is the angle of refraction wh*g nxdb s-4v8qq aid+yohh/91en a light ray meets the boundary between two materials pohd d *-1aqs+b 4ny/qh 9ig8vxerpendicularly?

How might you determin*xyj lutc*8w3(j4uj7mp me o +e the speed of light in a solid, rectangular, transparent objl8m*tjp (4e ux*7 cwm3u+jojyect?

When you look down intzvd*wzx.( 3wziw1v:e o a swimming pool or a lake, are you likely to underestimate or overestimate its depth? Explain. 3wwzzv*x1i e zwv:.d(How does the apparent depth vary with the viewing angle? (Use ray diagrams.)

Draw a ray diagram to show why a stick looks bent when pv:;gmw.k6 b v .7+r2dbduq.hzj- akilart of it is under water (Fig. Belok6h vqrg.+ b2b. .: 7mjidu- zlk;dwavw).

Your eye looks into an aquarium and views a fjp.m5fm wri8hk-/ 0q7epc, jh ish inside. One ray of light that emerges from the tank is shown in (Fig. Below), as well as the apparent position of the fish. In the drawing, indicate the approximate pqm7jp.h-c ,e0jrhi /kwf8 m p5osition of the actual fish. Briefly justify your answer.

How can you “see” a round drop of water onkb)*5 v91ew i9sxy7 l khvi,qb a table even though the water is transparent and q )vb9kiy*klh9 v7s5x,1i bew colorless?

When you look up at an object in air fx +.tv n- ; xctlu yjc(e7qyfo:/)js:qrom beneath the surface in a swimming pool, does the object appear to be the same size as when you se(fn.c yeuq jjv+7 ts:o/q:xt-xlc y );e it directly in air? Explain.

How can a spherical mirror hav /gy1 bc,t8dtoe a negative object distance?

Light rays from stars (ii0 7fyji,hrh 3hb/ xo4w/jn)yncluding our Sun) always bend toward the vertical direction as they pass thr/nb4 w)xfyr0h7 jhhi /3ji o,yough the Earth’s atmosphere.
(a) Why does this make sense?
(b) What can you conclude about the apparent positions of stars as viewed from Earth?

Where must the film be placed if a camera lens is to maked )mbc9tf 4tsi 4na9jkb4m ua)a (c-5i a sharp image of an object very far awa) 4 9jumta 4iikmscb9-tc(df4) 5aanb y?

What type of mirror is shown in (Fig. Below)5dsbbhi 267,e i.qsacyfs; b.? Explain.

A photographer moves closer to his subject and then refocuses. Does tjh ,zj(stxj9cr:d; ,qhe camera leh9 tdjqx cs(,jrj:;,zns move farther from or closer to the film? Explain.

Can a diverging lens form a real image under +:d;t;m /g ioa7gvfsq1gn/as any circumstances? Explain.

Use ray diagrams to show that s+rwj+,)ghddtnc 6ozg(,y, - qlyu0 aa real image formed by a thin lens is always inverted, whereas a virtual image is always upright if the object ijgdy( +rzc,-0,nsq od,a+6lu g whyt)s real.

Light rays are said to be “reversible.” Is this consistent with the thin lens eqf u61pz ku7 d6)nlz9o4f6yqt huattly6p 47u1q6d) zzhf9 onkf6uion? Explain.

Can real images be projected on a screen? Can virtual images? Can eithe fceukv-4v23 lpa jyogi31 a.:r be photographed? Discuss k.y 2:i4-g ao1l cjf eau3vpv3carefully.

A thin converging lens is moved closer to a n3;e l4fapr hp.earby object. Does the real image fo ;r.aep3h4f lprmed change
(a) in position,
(b) in size? If yes, describe how.

  A lens is made of a materialz/dzxh (jx24u2hcv 3 x with an index of refraction n = 1.30 In air, it is a converging lens. Will it still be a converging lens if place v /xdh3x4xzu2j2h (zcd in water? ----待选择----yesno  Explain, using a ray diagram.

  A dog with its tail in the airit 91kn2xrtc+hzp)2w stands facing a converging lens. If the nose and the tail are eacip +wx2k)2r9n 1thctzh focused on a screen in turn, which will have the greater magnification? ----待选择----nosetail 

A cat with its tail in the air stanc2m 01 86*hmyiw2 opa twoew1pds facing a converging lens. Under what circumstances (if any) would the image of the nose be virtual and the image of the tail p8w i2t m wo0eo 6yc1mw*1h2apbe real? Where would the image of the rest of the cat be?

Why, in Example 13, must the converging lens haveasc1:vx6q r) i a shorter focal length than the diverging lens if the latter’s focal length is to be determined by combining thv ia )6rscx:1qem?

Explain how you could have at rvfj(x)(3pw virtual object.

  An unsymmetrical lens (say, planoconvex) forms an image of a nearby object..( jgkoh5 ;ugu Does the image og ;5hg .k(ujupoint change if the lens is turned around? ----待选择----yesno 

The thicker a double conv s uvn)8qoat;3qk4bu1 ex lens is in the center as compared to its edges, the shorter its fotq;vboas8q1n )uk 43ucal length for a given lens diameter. Explain.

Consider two converging lenses separated by some zk rvjosys0m)y. o+x.uj,v5rl( ,;kcdistance. An object is placed so that the image rk0 ur,zysx+c.,vksv jo;o(y5 ) j .lmfrom the first lens lies exactly at the focal point of the second lens. Will this combination produce an image? If so, where? If not, why not?

  Suppose that you want to take a photograph of yourself as you look at your im.pbnwq we-i)l,: hkeun.h c-9 age in a flat mirror 2.5 m away. For what distance should the camera lens be fol.eih-9w cb hnk,:wup.q- e) ncused?    m

When you look at yourself in a 60-cm-tall plane mirror, you ,y+fue*(e k gmsee 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 should be tr ue+mk,fy(*ge ue.

  Two mirrors meet at a 13gk.ct5 dvs*os 442wn bw(vhgv )ge73k5$^{\circ}\,$ 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 in front ovk l(-x+frv x8f a vertical plane mirror whose bottom edge is 43 cm above the floor, (Fig. Below). What is the horizontal distance x to the base of the wall supporting the mirror of the nearelv8vkxx +r(f -st point on the floor that can be seen reflected in the mirror?    cm

  Suppose you are 90 c-xpjdaqd py 8ft4x39 ,m from a plane mirror. What area of the mirror is used to reflect xxj q4ypa9-3pft dd8,the rays entering one eye from a point on the tip of your nose if your pupil diameter is 5.5 mm?   $\times10^{-6}\,m^2$

Show that if two plane mirrors meet at anp tia- dz6q;2h 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 concap.6fz1+-v4c ztqjc r xve mirror pointed at the Sun, focuses the Sun’s rays 18.0 cm in front of v+x6 t qj1zrpz4f.-ccthe 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 an op()3xsju,wi8ul g c d0bject be placed if its image s,d )i gpux(80ucl3wjis to be at infinity?    cm

  If you look at yourself in a shiny Christmas tree ball with a diameter of 9.07n 1ck3ld.5r 0jp27fr ttbstcnh +b5 s5s jec2 cm when your face is 30.0 cm away from it, where is your image? Is it real or virtual? 7.jk 5 t+ s0t3tc2 jr55r7fsesn2 dl1hbnccpbIs it upright or inverted?
   cm behind the surface, virtual
 ----待选择----invertedupright 

  A mirror at an amusemen9zhr nbbp)7;z, lvw8tt park 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 curvaturvw8lhpzn b9,)z; r b7te?    cm

  A dentist wants a small mirror that, when 2.20 cm from a tooth, will produ szl rj8jpj).1mqe7k t:*8rkdce 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 ofqi zqv5b- -o8 s,k:ivs cars behind 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 ofsk bv-8isiov 5-,zq:q 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 fr9 o n+lzv-8ossd: hu2 ste:qe:om a convex mirror of radius of curvature 20.0u2h do :e onq-+szs8sve:l9:t 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.c4w 7w g 33srlnm,ut a9qh6f/v You estimate the hei3cl79h/3w4rfstg 6q vunmaw ,ght of your image to be half of your actual height. Estimate the radius of curvature of the mirror.    m

  (a) Where should an object be placed in front of a concave mr6v p 5* *bdi9frorp8eirror so that it produces an image at the same location as *ro*vpe5r9 r8p fbd6ithe 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 when v6bz jlc) yei1t- sio0pc0+xn;iewed in a curved mirror. The image appears tot)bzn+0i cxslc;0i-61ej yo p 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 techniques,vzm2h wz 6tp rsva91ge7yl5e.xs5x; ,
(a) a ray diagram,
(b) the mirror equation, to show that the magnitude of the magnification of a concave mirror is less than 1 if the object is beyond the center of curvature $C\left(d_0>r\right),$ and is greater than 1 if the object is within $ C (d_0 < r) $.

Show, using a ray diagram, that the magnification m of a convex mirr86jh ;/m:ovsf3 juwst or 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 vasf zi- z3f4*u9 zdwioy2t5m h3lid for a convex mirror as long as f is considered negmiz y 3two*-di3z9szf52u 4hfative.

  The magnification of j;spf,avmi- 6a convex mirror is $+0.65\times$ for objects 2.2 m from the mirror. What is the focal length of this mirror? $\theta_2$ =    $^{\circ}\,$

  A 4.5-cm-tall object is placed 28 cm in front of qe/i7b:rah+rw/ o 0 i6tufu 8la spherical mirror. It is desired to produce a virtual image that fuuhb o 0a/r8q7: l6 t+i/rweiis 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 *fphpp. 3p*d td6u:i c59gbxl is designed to magnify your face by a factor of 1.33 when your face is placed 20.c*ddt6pppu3bi .:9g5*xph fl0 cm in front of it.
(a) What type of mirror is it?  ----待选择----convex mirrorconcave mirror 
(b) Describe the type of image that it makes of your face.
(c) Calculate the required radius of curvature for the mirror. r =    cm

  What is the speed of light3st3 1p6pnotk gcr*: k 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 ic;xma85 2dffn:rni6v9 oiyk z) e 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 valuo/b, 2b; fb.5oo aagkhe in water. What is the index of refraction oa2o . fooah5;bb/,bgkf this substance? n =   

  A flashlight beam strikes the surface of a pane of glass z 2*rpm7lln, /mg+kl uju n/n/(n = 1.58) at a 63$^{\circ}\,$ angle to the normal. What is the angle of refraction? $\theta_2$ =    $^{\circ}\,$

  A diver shines a flashlig0 eeo+pr.tn ovb0,*a mht upward from 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 au;f +y /v9uvp4y+sti,agx0uu n angle of uxuu yfsi,p0v a;t+uyv/4g9 +66.0$^{\circ}\,$ 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. moj rx*tuay90 2j8vp 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 g 6ud1thxgqjo. y5e/w)m t /f6dlass sides whose index of refraction is 1.52. Aw6odqm)/.6jt x/u 5f1e thy gd 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 t;vx1;b , jvxl7b1gy-r6 hmria narrow beam of light from his i1hm xxtr y1vbv7gl;-;bj,6 r 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 the pool is 2.1 m deep?    m

  Light is incident on an equilateral glass prism at6,1ipgv5ja2lc vg m0x d -yog.,x ;rkb 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 j kf)d f0:qdi73w*(dkn5tetiglass (n = 1.52) and is partially reflected and partially refracted. Find the angle of incidence if the angle of reflection is twice the angle of refract3e f0i( )tj7*f5k:nqwtddikd ion.    $^{\circ}\,$

Prove in general that for a light beam incident on a unifxmb.zl,q,pmu 7 man, ;orm layer of transparent material, as in (Fig. Below), the direction of the emerging beammxbu ,nm;l., zma7,qp is parallel to the incident beam, independent of the incident angle $\theta$. Assume air on both sides of the glass.

A light ray is incident on a flat piece of mrix+pefl(d3f;1; wi glass with index of refraction n as in (Fig. Below). ip xefl;+(w1dim;3rf 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 thd+2 j55o1(xoshh izaspbhmd6 ji*v- -e interface between water and Lucite? To be totally internally reflected, o m6sz b ji s5-5oh+2(*djh1hdip- xvathe light must start in which material?
$\theta$ =    $^{\circ}\,$
{water|Lucite|}

  The critical angle for a certain liqu5wt rsx:k* 6s1 k5cpkeid–air surface is 47.7$^{\circ}\,$. What is the index of refraction of the liquid? $n_{liquid}$ =   

  A beam of light is emitted *2uec9io 16g yn3z:q aufr,o hin a pool of water from a depth of 62.0 cm. Where must it strike the air–water interface, relative to the spot directly above it, in order that the light does not exit the water? rgyhe2if* o qzuo3 19:ucn,a6   cm

  A beam of light is emitted 8.0 cm beneath the surface of a liquid and strikes 5 0i2dg*;) vjh6 dmcrpuxujy4 the surface 7.0 cm from the point directldgx5h0m j2 6 udy )j;*pr4ivcuy 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,rqk; h.c1tyd 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 wiah+olx u7:8cx/:u 6.i scr(v, ycaxoptic 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 back into the material at point av:w:yxh,ix7.ac crs8(cu+xlio 6 a u /.

  (a) What is the minimum index o:p(x 5qib/7 tg*ib6a asbcf8 wf refraction for a glass or plastic prism to be used in binoculars (Fig. Below) so that totf:bw*t b(c68b ia 5i7qg apxs/al 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 6trfvh +cpu,la3fd4 79: 5iioz5.0-mm-focal-length converging lens. Find the object distance ft79 3:5+zparh , vludfco 4ii
(a) using a ray diagram,    mm
(b) by calculation.    cm

  Sunlight is observed to focus at a point 18.5 cm behind a lens. ,:xilol 7cl y6ad+ai:
(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 as an imazd)w ug )3we*sge 48.3 cm on the other side of the lens. What type of lens ie)w3 gsd)*wuzs 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 ,ep/ ivrj(:zg( r)lglwp dr0420.5-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 tobpo*1)it tz,e view a stamp 18 cm in front of the lens.ti z*1p,b)eot
(a) Where is the image located?    cm behind the lens (virtual)
(b) What is the magnification? m =   

  A -5.5-D lens is held 1+d yy5+ 9rhe+en :*n f6sxpfay)lb-vv4.0 cm from an object 4.0 mm high. What are the position, type, andned+y) x 9a6+y-fsy +epb5 v hlnf:r*v height of the image?
   cm (virtual image behind the lens)
$h_1$    mm (upraight)

  An 80-mm-focal-length lens is used to fof1mt.s u- y* 3w0ran21 qlvelycus an image on the film of a camera. The maximum distancee-y2f1 a1s lmynwq 0l3t. r*vu allowed between the lens and the film plane is 120 mm.
(a) How far ahead of the film should the lens be if the object to be photographed is 10.0 m away?    mm
(b) 3.0 m away?    mm
(c) 1.0 m away?    mm
(d) What is the closest object this lens could photograph sharply?    mm

  It is desired to magnify reading material b a2 li9kg k(6kpyxmrs2q8yk1 0y a factor of 2.5× when a book is placed 8.0 cm behind a leky r myk8pk1sk09i6lx aq2(2g ns.
(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 ho*1/f uxo- kjft ilet3;w much does the image move if the objectt iulx*f/k-f te;o3j1 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 s.vll z k(l3wss0kmv0/hould an object be placed to produce a real image which is the s3kms 0l0w zkv/ll.s(vame size as the object?    cm

  (a) How far from a 50.0-mm k*ndq98m kg 49m2vpecaeh2 c.-focal-length lens must an object be placed if its image is to be magnihm8cg *2kq2k9a eemnv dc9.p4 fied 2.00× 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 lens must an object be pl8dot/ lr b7.ey7gu+geu;xi 4naced if its image is to be magnified 2.00× and be re e+go t8e7i.;7yu 4ldnr u/bgxal?    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 mw0 4du4pewov 1 from a 135-mm-focal-length lens. Where is the image, how high is it, and what tdwvuop4e w1 40ype 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 fmys/p, yuxe5ga93ep ,te *5gcormed by a 75-cm-focal-length converging lens if the image *,,s5eyaue/5 gpy3g 9cptmex is 2.5× larger than the object and is real?    m

  A bright object and a viewing screen are separatey+:xgg 9r n0x.fsq9dv d 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 sh dy+qg9x:0f.9vsxnr gould be placed    cm or    cm from the object

  Two 28.0-cm-focal-length conc/yz u7;:7;wie (ihr 8nixg;ghl(mipverging 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 h( x8gn 7um;(iliycw7;;r gp/z:eiih the total magnification?
 ----待选择----realvirtual ,
   cm beyond second lens.
m =    (inverted)

  A diverging lens with9:i;kr b5t9o jlfy)mkl ey-7 32wzkee $f=-31.5\mathrm{~cm}$ is placed 14.0 cm behind a converging lens with $f=20.0\mathrm{~cm.}$ Where will an object at infinity be focused?  ----待选择----realvirtual ,    cm beyond second lens.

  A 31.0-cm-focal-length converging lens is 21.0 cm behind a divergi*f*eslj(n t0v ng lens. Parallel light strikes the diverging lens. After passing through the converging lens, the light is again parallel. j lv fn(0s**etWhat 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 3/gz)3z tfosbplaced only 20.0 cm apart. The object is still 60.0 cm in front of the first lt /3z 3gbs)fozens 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 85xxrcuy.ii ow2/ d:ithe 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. How far to the left of the 15.0-cm-focal-length lens is the origxw xioi/2uri5:y8 . dcinal object?    cm

  A diverging lens wit(aqeb +7h jg,4)2ri nnnxp6ku h a focal length of is placed 12 cm to the right of a conve nrqa ,+7huxpn 4b )k6nieg(j2rging 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 and one diver,ju;.t pf./fke36eexnbki r (ging with focal length are placed 25.0 cm apart. An object is placed 60.0 cm in front of the converging lens. Detb f . .pjtfe(e/e6knxiu3k;,r ermine
(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 z- ,:b /a.8augt ,mbi 7kqfwlxof 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 surfagxenx:;w 9y(aiom3* ou,h* j z2;bagrce radii of 34.2 cm and 23.8 cm. What is the focal length iex w x ma 3(n:2;y zi*;ggrb,9o*uojahf n = 1.52?    cm

  Both surfaces of a double convex lens have radii of 31.0 cxu1 x/ndi4rjw : kv-c kdzod4m(48g7sm. If the focal length is 28.9 cm, what is the index of refraction of the lens mj7ddv-o 4wdn/zxuk 41mgx4ski8r: ( caterial?    cm

  A planoconcave lens (n=1.50) has a foca)2ig+ d7m7quw6lhhn el length of -23.4cm. What is the radius of the concave surface? w+7gh6i mqlh7d) eu2n   cm

  A Lucite planoconcave lens (see (4q0yo vy g /nxf6dtvk,8hi(bFig. Below) has one flat surface and the other has R 6fi 4b yh(vqx80o(/yt ,kvdgn= -18.4 cm. What is the focal length?    cm

  A symmetric double convex lens with a focal length of 25.0 cm is to be made ff/0khn. xonwhd*bj o k6.-j5orom glass with an index of 0 /okbjoofknh 5d .xhw-6*.jn refraction of 1.52. What should be the radius of curvature for each surface?    cm

  A prescription for a corrective lens calls for +1.50D. The lensmaker grinbe-y j+)au. rh ms x*e:jd.*ldds the lens from a “blank” with n=1.56 and a preformed convex front surface of radius of curvature mj +hed..-uld sbj:*)era*yx of 40.0 cm. What should be the radius of curvature of the other surface?    m (convex)

  Two plane mirrors face each other 2.0 m apart as in (Fig. Below). You sta -6ferb*yl5. cvqv*rjnd 1.5 m away from one of these mirrors and look into it. You will see multiple images of youveyr *.jfrl c5q b*-6vrself.
(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 water. We m 5n*xlix17k viy3;mizeasure the width (x=5.50m) and then note that the bottom edge of the pool is *57kizlivn x 1;3yxm ijust 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 plastic in al*rqly;q7se . ir 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 consq1lxt)im;e w2gac8*dpc e o/9idered a limiting case of a spherical mirror. Specify what this limit is./m9teade ;)xo1clg8wq* icp2
(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 miqmui+ls6.kv.w g*dd . rrors so they form a 90$^{\circ}\,$ angle as in (Fig. Below). When you look into this double mirror, you see yourself as others see you, instead of reversed as in a single mirror. Make a careful ray diagram to show how this occurs.

Show analytically that a diverging lens can neej5md/hh7: j ib l/s;iver form a real image of a real object. dj7h:/lmijs; heb/5iCan you describe a situation in which a diverging lens can form a real image?

  Each student in a physics lab is assiqr-o 6knx*x b.gned 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 comp-*q.xbrn kx6olete the assignment at different times using identical equipment, but when they compare notes later, they discover that their answers for the object distance are not the same. Explain why they do not necessarily need to repeat the lab, and justify your response with a calculation.
$d_o$ =    cm    cm

  If the apex angle of ;jaxl ls4 okc1bde *41a prism is $\phi=72^\circ$ see (Fig. Below), what is the minimum incident angle for a ray if it is to emerge from the opposite side (i.e., not be totally internally reflected), given $\mathrm{n=1.50~?}$ $\theta_1$$\geq$    $^{\circ}\,$

The end faces of a cylindrical glass rodezpia t 0s;rs: 6r34ox $(n=1.54)$ 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 llbn;va3vl ( 1eength $f_1=15\mathrm{~cm},$ 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 leeoe4d8yvr7;9dt )w iv ns of focal length f, and a white screen for viewing the image is on the op t;dvyoe rv7)9wdi4e8posite 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 ptdh9(5u,s mjby pxboy4 .h.7the object whose image is projected on a screen (Fig.xdupyb. t ,ob54y mph7h.( s9j 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) is to be p6 afnk79f bvv4dy(,mhrojected on a screen 1.80 m by 2.70 m placed 7.50 m from the projector. What focal-len 7hfky46,vv9(nmdab fgth lens should be used if the image is to cover the screen?    cm

Show analytically that the image formed by a converging lens is real3ib b x2akm6/n and inverted if the object is beyondim 2n6x /b3bka 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 hoyrm: pw46l7eh a hg8:fme. She claims the reporter was trespassing. To prove her point, she gives as evidence the film she seized. Her 1.75-m height is 8.25 mm high on the film, and the fo lp:h74af m6g:rh ywe8cal 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 camerauc77 kg+i .gzu 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 c-7:hz oz ;gn6 wnu. 7pxvc*jmtertain lens is imaged 8.20 cm in front of that lens (on the same side as the object). What type of lens is; *:wcnjvp6zxguhn z -m7ot.7 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)