Look at the text on page 426 for the answer.

Transcription

1 ur butterflies, but nly ne is real! The thers small, large, upright, and turned upside dwn are images that result frm reflectin and refractin in a single piece f glass. What must be the shape f the glass? Hw des the glass prduce all thse butterflies? Lk at the text n page 426 fr the answer.

2 CHAPTER 18 Mirrrs and Lenses It s an illusin any magician wuld be prud t claim: Prest! ur butterflies frm ne! What culd be mre amazing? Only ne f the butterflies is real! Mirrrs are part f everyday life. Yu use a flat mirrr t check yur hair in the mrning. When yu drive, yu use a differentshaped mirrr t check if there is anther car in the lane next t yu. In all, mirrrs are useful in everyday life. Lenses, hwever, are essential t ur lives. We are able t see because each f ur eyes has a lens. That lens prduces an image f the wrld arund us. In fact, all the ptical devices that are part f yur everyday life eyeglasses, cntact lenses, magnifying glasses, micrscpes, cameras, camcrders prduce images fllwing the same laws f reflectin and refractin. Light rays fllw a cmplex rute as they encunter mirrrs r pass thrugh a variety f lenses. As yu wrk thrugh this chapter, yu will learn hw t determine the paths taken by the rays f light that reflect frm an bject such as the real butterfly and then bend as they pass thrugh lenses f different shapes. This means nt just the lens shwn in the phtgraph, but als the lens f the camera that caught the image. As cmplex as a light ray s rute may be, yu can use the laws f ptics t trace its jurney and discver where it jins ther rays t frm an image. Yu will learn abut these laws as yu study this chapter. WHAT YOU LL LEARN Yu will lcate real and virtual images prduced by plane, cncave, and cnvex mirrrs. Yu will recgnize the causes f aberratins in lenses and mirrrs and hw these can be minimized. WHY IT S IMPORTANT The laws f reflectin and refractin that prduce images n the retinas f yur eyes are als the basis fr ptical instruments that allw scientists t see int uter space annt the wrld f subatmic particles. PHYSICS T find ut mre abut mirrrs and lenses, visit the Glence Science Web site at science.glence.cm 415

3 OBJECTIVES Explain hw cncave, cnvex, and plane mirrrs frm images. Lcate images using ray diagrams, and calculate image lcatin and size using equatins. Explain the cause f spherical aberratin and hw the effect may be vercme. Describe uses f parablic mirrrs. Clr Cnventins Light rays are red. Lenses and mirrrs are light blue. Objects are indig. Images are light vilet Mirrrs Mirrrs are the ldest ptical instruments. Undubtedly, prehistric humans saw their faces reflecten the quiet water f lakes r pnds. Almst 4000 years ag, Egyptians used plished metal mirrrs t view their images. But sharp, well-defined reflectemages were nt pssible until 1857, when Jean ucault, a rench scientist, develped a methd f cating glass with silver. Objects and Images in Plane Mirrrs If yu lked at yurself in a bathrm mirrr this mrning, yu saw yur image in a plane mirrr. A plane mirrr is a flat, smth surface frm which light is reflected by regular reflectin rather than by diffuse reflectin. This means that light rays are reflected with equal angles f incidence and reflectin. In describing mirrrs and lenses, the wrd bject is usen a new way. Yu were the bject when yu lkent the bathrm mirrr. An bject is a surce f spreading, r diverging, light rays. Every pint n an bject is a surce f diverging light rays. An bject may be luminus, such as a candle and a lamp. But mre ften, an bject, such as the mn r the page yu are reading is illuminated. An illuminated bject usually reflects light diffusely in all directins. igure 18 1 shws hw sme f the rays reflected ff pint O n the bill f a baseball cap strike a plane mirrr. The equal angles f incidence and reflectin are shwn fr three rays. Ntice that they diverge when they leave the pint f the cap, and they cntinue t diverge after they are reflected frm the mirrr. The persn sees thse rays that enter the pupil f his eye. The dashed lines are sight lines, the backward extensins f the rays leaving the mirrr. They cnverge at pint I. The eye and brain interpret the rays as having cme frm pint I. This pint is called the image f the bill f the cap. Because the rays d nt actually cnverge n that pint, this kind f image is called a virtual image. O I θ θ IGURE 18 1 The reflected rays that enter the eye appear t riginate at a pint behind the mirrr. Mirrr 416 Mirrrs and Lenses

4 h P Object d B M P Image h i IGURE 18 2 Light rays (tw are shwn) leave a pint n the bject. Sme strike the mirrr and are reflectent the eye. Sight lines, drawn as dashed lines, extend frm the lcatin n the mirrr where the reflectins ccurred back t where they cnverge. The image is lcated where the sight lines cnverge. By gemetry, d. Where is the image lcated? igure 18 2 shws tw f the rays that leave pint P n the bject. One ray strikes the mirrr at B, the ther at M. Bth rays are reflected with equal angles f incidence and reflectin. Ray PB, which strikes the mirrr at an angle f 90, is reflected back n itself. Ray PM is reflectent the bserver s eye. Sight lines, shwn in igure 18 2 as dashed lines, are extended back frm B and M, the psitins at which the tw rays are reflected frm the mirrr. The sight lines cnverge at pint P, which is the image f pint P. The distance between the bject and mirrr, the bject distance, is line PB, which has a length d. Similarly, the distance between the image and the mirrr is the length f line P B ans called the image distance,. The bject distance and the image distance, d and respectively, are crrespnding sides f the tw cngruent triangles PBM and P BM. Therefre, d. Hw large is the image? If yu drew the paths and the sight lines f tw rays riginating frm the bttm f the arrw, yu wuld find that they cnverge at the bttm f the image. Therefre, the bject and the image have the same size, r, as igure 18 2 shws, h h i. The image and the bject are pinting in the same directin, s the image is called an erect image. Is there a difference between yu and yur image in the mirrr? llw the rays and sight lines in igure 18 3a. The ray that diverges frm the right hand f the bject cnverges at what appears t be the left hand f the image. Yu might ask why the tp and bttm are nt als reversed. If yu lk at the figure carefully, yu ll see that the directin that is reverses the ne perpendicular t the surface f the mirrr. Left and right are reversed, but in the same way that a right-hand glve can be wrn n the left hand by turning it inside ut. Thus, it is mre crrect t say that the frnt and back f an image are reversed. Pcket Lab Where s the image? Suppse that yu are standing directly in frnt f a mirrr and see yur image. Exactly where is the image? Here is a way t find ut. ind a camera with a fcusing ring that has distances marked n it. Stand 1.0 m frm a mirrr and fcus n the edge f the mirrr. Check the reading n the fcusing ring. It shuld be 1.0 m. Nw fcus n yur image. What is the reading n the ring nw? Analyze and Cnclude Summarize yur results and write a brief cnclusin Mirrrs 417

5 Image Object Mirrr Mirrr O I a IGURE 18 3 The image frmed in a plane mirrr is the same size as the bject ans the same distance behind the mirrr as the bject is in frnt. If yu blink yur right eye, it lks as if yur left eye blinks. Pcket Lab Real r Virtual? Hld a small cncave mirrr at arm s length and lk at yur image. What d yu see? Is the image in frnt r behind the mirrr? What happens t the image as yu slwly bring the mirrr tward yur face? Analyze and Cnclude Briefly summarize yur bservatins and cnclusins. b Cncave Mirrrs Lk at yur reflectin in the inside surface f a spn. The spn acts as a cncave mirrr. A cncave mirrr reflects light frm its inner ( caven ) surface. In a spherical cncave mirrr, the mirrr is part f the inner surface f a hllw sphere, as shwn in igure The sphere f radius r has a gemetric center, C. Pint A is the center f the mirrr, and the line CA is the principal axis, that is, the straight line perpendicular t the surface f the mirrr at its center. Hw des light reflect frm a cncave mirrr? Think f a cncave mirrr as a large number f small plane mirrrs arranged arund the surface f a sphere, as shwn in igure 18 5a. Each mirrr is perpendicular t a radius f the sphere. When a ray strikes a mirrr, it is reflected with equal angles f incidence and reflectin. igure 18 4 shws that a ray parallel t the principal axis is reflected at P and crsses the principal axis at sme pint,. A parallel ray an equal distance belw the principal axis wuld, by symmetry, als crss the principal axis at. These parallel rays meet, r cnverge, at, which is called the fcal pint f the mirrr. The tw sides C and P f the triangle CP are equal in length. Thus, the fcal pint,, is half the distance between the mirrr and the center f curvature, C. Mirrr surface P Principal axis IGURE 18 4 The fcus f a spherical cncave mirrr is lcated halfway between the center f curvature and the mirrr surface. Rays entering parallel t the principal axis are reflected t cnverge at the fcal pint,. C r f A 418 Mirrrs and Lenses

6 a Hw can yu find the lcatin f the fcal pint f a cncave mirrr? irst yu need parallel light rays, because nly parallel rays will cnverge at the fcal pint. Because the sun is s far away, yu can cnsider it a surce f nearly parallel rays. If yu pint the principal axis f a cncave mirrr at the sun, all the rays will be reflected thrugh the fcal pint. Hld a piece f paper near the mirrr and mve the paper tward and away frm the mirrr until the smallest and sharpest spt is frmed. The spt must be at the fcal pint because, as was just discussed, the rays striking the mirrr are, fr all practical purpses, parallel. The distance frm the fcal pint t the mirrr alng the principal axis is the fcal length, f, f the mirrr. In igure 18 4, ntice that the fcal length is half the radius f curvature f the mirrr, r 2f r. Real versus virtual images The bright spt that yu see when yu psitin a piece f paper at the fcal pint f a cncave mirrr as it reflects rays frm the sun is an image f the sun. The image is a real image because rays actually cnverge and pass thrugh the image. A real image can be seen n a piece f paper r prjected nt a screen. In cntrast, the image prduced by a plane mirrr is behind the mirrr. The rays reflected frm a plane mirrr never actually cnverge but appear t diverge frm a pint behind the mirrr. A virtual image cannt be prjected nt a screen r captured n a piece f paper because light rays d nt cnverge at a virtual image. Real images frmed by cncave mirrrs T develp a graphical methd f finding the image prduced by a cncave mirrr, recall that every pint n an bject emits r reflects light rays in all pssible directins. It s impssible and unnecessary t fllw all thse rays, but yu can select just tw rays and, fr simplicity, draw them frm nly ne pint. Yu can als use a simplified mdel f the mirrr in which all rays are reflected frm a plane rather than frm the curved surface f the mirrr. That mdel will be explained shrtly. Here is a set f rules t use in finding images. b IGURE 18 5 The surface f a cncave mirrr reflects light t a given pint, as in (b). A slar furnace in the rench Alps, shwn in (a), reflects light in a similar way frm a grup f plane mirrrs arrangen a curve. Pcket Lab cal Pints Take a cncave mirrr int an area f direct sunlight. Use a piece f clay t hld the mirrr steady s that the cncave mirrr directly faces the sun. Mve yur finger tward r away frm the mirrr in the area f reflected light t find the brightest spt (fcal pint). Turn the mirrr s that the cnvex side faces the sun and repeat the experiment. Analyze and Cnclude Recrd and explain yur results Mirrrs 419

7 Lens/Mirrr Equatin Cnventins Applied t Mirrrs d is psitive fr real bjects. d is negative fr virtual bjects. is psitive fr real images. is negative fr virtual images. f is psitive fr cncave mirrrs. f is negative fr cnvex mirrrs. Pcket Lab Makeup D yu have a makeup mirrr in yur hme? Des this mirrr prduce images that are larger r smaller than yur face? What des this tell yu abut the curvature? eel the surface f the mirrr. Des this cnfirm yur predictin abut the curvature? Try t discver the fcal length f this mirrr. Analyze and Cnclude Recrd yur prcedure and briefly explain yur bservatins and results. Lcating Images in Mirrrs by Ray Tracing 1. Chse a scale fr yur drawing such that the drawing is apprximately the width f yur paper, abut 20 cm. a. If the bject is beynd, as shwn in igure 18 6, then the image will be n the bject side f the mirrr. Therefre, draw the mirrr at the right edge f yur paper. b. If the bject is beynd C, the image distance will be smaller, s draw the bject near the left edge f yur paper. c. If the bject is between C and, the image will be beynd C. The clser the bject is t, the farther away the image will be, s leave rm at the left side f yur paper. d. Chse a scale such that the larger distance, that f the image r the bject, is 15 t 20 cm n yur paper. Let 1 cm n the paper represent 1, 2, 4, 5, r 10 actual centimeters. 2. Draw the principal axis. Draw a vertical line where the principal axis tuches the mirrr. If the fcal pint is knwn, indicate that psitin n the principal axis. Label it. Lcate and label the center f curvature, C, at twice the fcal distance frm the mirrr. 3. Draw the bject and label its tp O 1. Chse a scale fr the bject that is different frm that f the verall drawing because therwise it may be t small t be seen. 4. Draw ray 1, the parallel ray. Ray 1 is parallel t the principal axis. All rays parallel t the principal axis are reflected thrugh the fcal pint,. 5. Draw ray 2, the fcus ray. It passes thrugh the fcal pint,, n its way t the mirrr ans reflected parallel t the principal axis. 6. The image is lcated where ray 1 and ray 2 crss after reflectin. Label the image I 1. Draw a vertical line frm I 1 t the principal axis t represent the image. Hw wuld yu describe the image in igure 18 6? It is a real image because the rays actually cnverge at the pint where the image is lcated. It is inverted. The bject O 1 is abve the axis, but the image pint I 1 is belw the axis. The image is reducen size; it is smaller than the bject. Thus, the image is real, inverted, and reduced. Where is the image? If the bject is beynd C, as it is in igure 18 6, the image is between C and. If the bject is mved utward frm C, the image mves inward tward and shrinks in size. If the bject is brught clser t C, the image mves utward frm the mirrr. If the bject is at C, the image will be there als, ant will be the same size as the bject. If the bject is mved even clser t, but nt inside it, the image will mve farther away and becme larger. 420 Mirrrs and Lenses

8 O 1 Ray 2 Ray 1 d IGURE 18 6 Nte that bth rays pass thrugh the fcal pint, ray 1 after it is reflected frm the mirrr and ray 2 n its way t the mirrr. The image is real, inverted, and reducen size. Image Object C All features f the image can be fund mathematically. Yu can use gemetry t relate the fcal length f the mirrr, f, t the distance frm the bject t the mirrr, d, and t the distance frm the image t the mirrr,. The equatin fr this is called the lens/mirrr equatin: Lens/Mirrr Equatin 1 f 1 1 d d This is the first equatin yu have seen that cntains the inverses f all quantities. Yu shuld first slve this equatin fr the quantity yu are seeking. r example, if yu are given the bject anmage distances and asked t find the fcal length, yu wuld first add the fractins n the right side f the equatin using the least cmmn denminatr, d. 1 f d d i d Then take the reciprcal f bth sides. d f i d d Anther useful equatin is the definitin f magnificatin. Magnificatin, m, is the rati f the size f the image, h i, t the size f the bject, h. Magnificatin i hi m h By using similar triangles in a ray diagram, yu btain the fllwing. Magnificatin Plane perpendicular t the principal axis m d Yu can write a single equatin fr the image height in terms f the bject height and the image and bject distances by equating the tw I 1 Math Handbk T review slving equatins, see the Math Handbk, Appendix A, page 740. HELP WANTED OPTICIAN Eye-care prfessinals are needed fr custmer assistance and behind-the-scenes psitins. Interpersnal skills and skills in precisin lab wrk are a must. Vcatinal/technical schl preparatin, including an assciate s degree, is desired but extensive apprenticeship experience may be substituted. Excellent finger dexterity, flexibility t wrk irregular shifts, and apprpriate certificatin are required. r infrmatin cntact: Opticians Assciatin f America 7023 Little River Turnpike Suite 207 Annandale, VA Mirrrs 421

9 preceding expressins. The right side f each equatin equals the magnificatin, m, and therefre, they are equal t each ther. Image Q Object C hi d, i r h h h di d 3 1 E 2 Q E Mirrr IGURE 18 7 T the eye at E, it appears that there is an bject at Q blcking the view f the mirrr. Hwever, if the eye mves t E and lks tward Q, the bject disappears because there is n light reflected frm Q t E. Describing a real image In the case f real images, and d are bth psitive, s h i will be negative. This means that the magnificatin is als negative. When the magnificatin is negative, the image is inverted. What is the magnificatin f a plane mirrr? Recall that in that case, and d have the same magnitude, but the image is behind the mirrr. Therefre, is negative and the magnificatin is 1, which means that the image and the bject are the same size. Hw can yu tell if an image is real? If an image is real, the rays will cnverge n it in a ray diagram. In the lens/mirrr equatin, will be psitive. If yu use an actual mirrr, yu can put a piece f paper at the lcatin f the image and yu ll see the image. Yu als can see the image flating in space if yu place yur eye s that the rays that frm the image fall n yur eye. But as igure 18 7 shws, yu must stare at the lcatin f the image and nt at the mirrr r bject. When slving prblems invlving mirrrs, yu may be asked t lcate the image by means f a scale drawing using the methds f the prblem slving strategy. At ther times, when yu are asked t find the image mathematically, yu shuld als make a careful sketch t enable yu t visualize the situatin and check the reasnableness f yur results. Example Prblem Calculating a Real Image rmed by a Cncave Mirrr A cncave mirrr has a radius f curvature f 20.0 cm. An bject, 2.0 cm high, is placed 30.0 cm frm the mirrr. a. Where is the image lcated? b. Hw high is the image? Sketch the Prblem Sketch the situatin; lcate the bject and mirrr. Draw tw principal rays. Calculate Yur Answer Knwn: Unknwn: h 2.0 cm? d 30.0 cm h i? r 20.0 cm 422 Mirrrs and Lenses h Object C d h i Image

10 Strategy: cal length is half the radius f curvature. Use lens/mirrr equatin t finmage lcatin. Use magnificatin relatins t find height f image. Check Yur Answer Are yur units crrect? All distances are in cm. D the signs make sense? Psitive lcatin and negative height agree with the drawing. Are the magnitudes realistic? The magnitudes agree with the drawing. Calculatins: f r/ cm 1 f 1 1 fd, s d d (d f) i 15.0 cm hi m d, i s h h di h d h i (10.0 cm)(30.0 cm) 30.0 cm 10.0 cm ( 15.0 cm)(2.0 cm) 30.0 cm 1.0 cm Virtual images frmed by cncave mirrrs Yu have seen that as the bject appraches the fcal pint,, f a cncave mirrr, the image mves farther away frm the mirrr. If the bject is at the fcal pint, all reflected rays are parallel. They never meet, and s the image is said t be at infinity. What happens if the bject is mved even clser t the mirrr, that is, between the fcal pint and the mirrr? The ray diagram is shwn in igure Again, tw rays are drawn t lcate the image f a pint n an bject. As befre, ray 1 is drawn parallel t the principal axis and reflected thrugh the fcal pint. T draw ray 2, first draw a dashed line frm the fcal pint t the pint n the bject. Then draw ray 2 as an extensin f the dashed line t the mirrr where it is reflected parallel t the principal axis. Nte that ray 1 and ray 2 diverge Ray 2 Ray 1 d Object Image IGURE 18 8 When an bject is lcated between the fcal pint and a spherical cncave mirrr, an enlarged, upright, virtual image is frmed behind the mirrr Mirrrs 423

11 IGURE 18 9 Objects placed between the fcal pint and the surface f a cncave mirrr frm enlarged, virtual images. as they leave the mirrr, s there can be n real image. Hwever, the dashed lines behind the mirrr are sight lines cming frm an apparent rigin behind the mirrr. These sight lines cnverge t frm a virtual image lcated behind the mirrr. When yu use the lens/mirrr equatin in slving prblems invlving cncave mirrrs, yu will find that is negative. The image is upright and enlarged like the statuette in igure An upright, enlargemage is a feature f shaving and makeup mirrrs, which are cncave mirrrs. When yu use a shaving r makeup mirrr, yu must hld the mirrr clse t yur face ann ding s, yu are placing yur face within the fcal length f the mirrr. Example Prblem A Cncave Mirrr as a Magnifier An bject, 2.0 cm high, is placed 5.0 cm in frnt f a cncave mirrr with a fcal length f 10.0 cm. Hw large is the image, and where is it lcated? Sketch the Prblem Sketch the situatin; lcate the bject and mirrr. Draw tw principal rays. Extend the rays behind the mirrr t lcate the image. Calculate Yur Answer Knwn: Strategy: h 2.0 cm d 5.0 cm f 10.0 cm Unknwn:? h i? Use lens/mirrr equatin t finmage lcatin. Slve magnificatin relatins t find height f image. Check Yur Answer Are yur units crrect? All are cm. D yur signs make sense? Negative lcatin means virtual image; psitive height means upright image. These agree with the ray diagram. Are the magnitudes realistic? Magnitudes agree with the diagram. h Object Calculatins: 1 f 1 1 fd, s d d d f i hi m d, i s h h di h d h i (10.0 cm)(5.0 cm) 5.0 cm 10.0 cm ( cm)(2.0 cm) 5.0 cm d Image h i cm, virtual 4.0 cm, upright 424 Mirrrs and Lenses

12 Practice Prblems Calculate a real image frmed by a cncave mirrr. 1. Use a ray diagram drawn t scale t slve the Example Prblem. 2. An bject 3.0 mm high is 10.0 cm in frnt f a cncave mirrr having a 6.0-cm fcal length. ind the image ants height by means f a. a ray diagram drawn t scale. b. the lens/mirrr and magnificatin equatins. 3. An bject is 4.0 cm in frnt f a cncave mirrr having a 12.0-cm radius. Lcate the image using the lens/mirrr equatin and a scale ray diagram. 4. A 4.0-cm-high candle is placed 10.0 cm frm a cncave mirrr having a fcal length f 16.0 cm. ind the lcatin and height f the image. 5. What is the radius f curvature f a cncave mirrr that magnifies by a factr f 3.0 an bject placed 25 cm frm the mirrr?.y.i. Sunlight can be cncentrated at the fcal pint f a large cncave mirrr. If a cking pt is placed at that pint, the temperatures prduced are high enugh t ck the fd. Image defects in cncave mirrrs In tracing rays, yu have reflected the rays frm a vertical line rather than the curved surface f the mirrr. The mirrr/lens equatin als assumes that all reflectins ccur frm a plane perpendicular t the principal axis that passes thrugh the mirrr. Real rays, hwever, are reflected ff the mirrr itself, s they will lk like the drawing in igure 18 10a. Ntice that nly parallel rays clse t the principal axis are reflected thrugh the fcal pint. Other rays cnverge at pints clser t the mirrr. The image frmed by parallel rays in a large spherical mirrr is a disk, nt a pint. This effect is called spherical aberratin. A mirrr grund t the shape f a parabla, igure 18 10b, suffers n spherical aberratin; all parallel rays are reflected t a single spt. r that reasn, parablic mirrrs have been usen telescpes. But many f the newest telescpes use spherical mirrrs and specially shaped secndary mirrrs r lenses t eliminate the aberratin. Pcket Lab Burned Up Cnvex (cnverging) lenses can be used as magnifying glasses. Use smene s eyeglasses t see if they magnify. Are the glasses cnverging? Can the lenses be usen sunlight t start a fire? Analyze and Cnclude Use yur answers t describe the lens. a Spherical mirrr b Parablic mirrr IGURE Sme rays reflected frm a cncave spherical mirrr cnverge at pints ther than the fcus, as shwn in (a). A parablic mirrr, such as the ne shwn in (b), fcuses all parallel rays at a pint Mirrrs 425

13 Cnvex Mirrrs A cnvex mirrr is a spherical mirrr that reflects light frm its uter surface. Rays reflected frm a cnvex mirrr always diverge. Thus, cnvex mirrrs d nt frm real images. When drawing ray diagrams, the fcal pint,, is placed behind the mirrr, at a distance halfway between the mirrr and the center f curvature. When using the lens/mirrr equatin, the fcal length, f, f a cnvex mirrr is a negative number, and is negative because the image is behind the mirrr. IGURE N real image is frmed by a cnvex mirrr. An erect, virtual image, reducen size, is frmed at the apparent intersectin f the extended rays. Cnvex mirrrs are ften used as wide-angle mirrrs fr safety and security. Ray 1 Ray 2 Object Image d ur butterflies, but nly ne is real! Answers questin frm page 414. The ray diagram in igure shws hw an image is frmen a cnvex mirrr. Ray 1 appraches the mirrr parallel t the principal axis. T draw the reflected ray, draw a dashed line frm the fcal pint,, t the pint where ray 1 strikes the mirrr. The reflected ray is in the same directin as the dashed line. Ray 2 appraches the mirrr n a path that, if extended behind the mirrr, wuld pass thrugh. The reflected part f ray 2 is parallel t the principal axis. The tw reflected rays diverge, as if cming frm a pint behind the mirrr. The image, lcated at the apparent intersectin f the extended rays behind the mirrr, is virtual, erect, and reducen size. Cnvex mirrrs frm images reducen size, and therefre, the images seem farther away. But cnvex mirrrs als reflect an enlarged field f view. Rearview mirrrs usen cars are ften cnvex mirrrs, as are mirrrs usen stres t bserve shppers. Ordinary glass als reflects sme light. If the glass is curved utward, it will act as a cnvex mirrr. Yu can frequently see reducemages f yurself if yu lk int smene s eyeglasses. The pht at the beginning f this chapter shws a glass lens that reflects sme light ff bth its frnt (cnvex) and rear (cncave) surfaces. What must be the shape f the glass? Hw des the glass prduce all thse butterflies? Bth reflectemages are reducen size; ne is upright and the ther is inverted. The upright image cmes frm the cnvex surface, the inverted ne frm the cncave surface. 426 Mirrrs and Lenses

14 Example Prblem Image in a Security Mirrr A cnvex security mirrr in a warehuse has a radius f curvature f 1.0 m. A 2.0-m-high frklift is 5.0 m frm the mirrr. What is the lcatin and size f the image? Sketch the Prblem Sketch the situatin; lcate the mirrr and the bject. h Draw tw principal rays. Calculate Yur Answer Knwn: Unknwn: h 2.0 m r 1.0 m? d 5.0 m h i? Strategy: The fcal length is negative fr cnvex mirrrs. Object Calculatins: f ( 1/2)r 1.0 m/ m d Image Use the lens/mirrr equatin t find the lcatin. Cmbine the magnificatin equatins t determine height. fd /(d f) ( 0.5 m)(5.0 m)/(5.0 m ( 0.50 m)) 0.45 m, virtual h i h /d h i ( 0.45 m)(2.0 m)/(5.0 m) 0.18 m, upright, reduced Check Yur Answer Are yur units crrect? All distances are in meters. D the signs make sense? Negative lcatin means virtual image; psitive height means upright image. These agree with the diagram. Are the magnitudes realistic? They agree with the diagram. Practice Prblems 6. An bject is 20.0 cm in frnt f a cnvex mirrr with a 15.0-cm fcal length. ind the lcatin f the image using a. a scale ray diagram. b. the lens/mirrr equatin. 7. A cnvex mirrr has a fcal length f 12 cm. A lightbulb with a diameter f 6.0 cm is placed 60.0 cm in frnt f the mirrr. Lcate the image f the lightbulb. What is its diameter? 8. A cnvex mirrr is needed t prduce an image three-furths the size f the bject and lcated 24 cm behind the mirrr. What fcal length shuld be specified?.y.i. In 1857, Jean ucault develped a technique fr silvering glass t make mirrrs fr telescpes. Silvered glass mirrrs are lighter and less likely t tarnish than metal mirrrs previusly used Mirrrs 427

15 The Hubble Space Telescpe Astrnmers have knwn fr decades that t see farther int space and time, telescpes must cllect mre light and this requires larger mirrrs. But massive mirrrs bend under their wn weight, distrting the images being bserved. Atmspheric distrtins, temperature effects, and light pllutin als limit the perfrmance f Earth-based telescpes. One apprach scientists are using t vercme these difficulties is t place telescpes in Earth rbit. The Hubble Space Telescpe, the first rbiting telescpe, was launchen Amng the revelatins prvided by the Hubble telescpe are views f galaxies s distant that they shw us what sme parts f the universe lked like just a few hundred millin years after its birth. Detailemages f the cmet Hale-Bpp, which visited ur regin f the slar system in 1997, enabled astrnmers t estimate the size f the cmet s nucleus and bserve vilent eruptins that tk place as different parts f the nucleus turned t face the sun. Hubble als has capturemages f giant plumes f gas and dust prduced by a vlcanic eruptin n I, ne f Jupiter s mns. In 1997, Hubble prduced spectacular images f jets f gas and dust blwn int space by a massive black hle at the center f the Egg Nebula, abut 3000 light-years frm Earth. Thinking Critically What are sme f the advantages and disadvantages f placing a telescpe in rbit? 18.1 Sectin Review 1. Draw a ray diagram shwing yur eye placed 12 cm frm a plane mirrr. Tw rays leave a pint n an eyelash and enter ppsite sides f the pupil f yur eye, 1 cm apart. Lcate the image f the eyelash. 2. If a beam f parallel light rays is sent int a spherical cncave mirrr, d all the rays cnverge at the fcal pint? 3. If a mirrr prduces an erect, virtual image, can yu immediately cnclude that it is a plane mirrr? Explain. 4. Critical Thinking A cncave mirrr is used t prduce a real image f a distant bject. A small plane mirrr is put between the mirrr and the image. The mirrr is put at a 45 angle t the principal axis f the cncave mirrr. a. Make a ray diagram. Is the image f the plane mirrr real r virtual? Explain. b. If the small mirrr were a cnvex mirrr, wuld the image be real r virtual? Explain. 428 Mirrrs and Lenses

16 Lenses Eyeglasses were made frm lenses as early as the thirteenth century. Arund 1610, Galile used tw lenses as a telescpe. With this instrument, he discvered the mns f Jupiter. Since Galile s time, lenses have been usen many ptical instruments such as micrscpes and cameras. Lenses are prbably the mst useful anmprtant f all ptical devices. Types f Lenses A lens is made f transparent material, such as glass r plastic, with a refractive index larger than that f air. Each f the lens s tw faces is part f a sphere and can be cnvex, cncave, r flat. A lens is called a cnvex lens if it is thicker at the center than at the edges. Cnvex lenses are cnverging lenses because they refract parallel light rays s that the light rays meet. A cncave lens is thinner in the middle than at the edges ans called a diverging lens because rays passing thrugh it spread ut. Use igure t cmpare the shapes f the tw types f lenses and the paths f light rays as they pass thrugh each lens OBJECTIVES Describe hw real and virtual images are frmed by cnvex and cncave lenses. Lcate the image with a ray diagram and find the image lcatin and size using a mathematical mdel. Define chrmatic aberratin and explain hw it can be reduced. Explain hw ptical instruments such as micrscpes and telescpes wrk. a b IGURE In (a), the refracted rays cnverge, while in (b) they diverge. Cnvex Lenses When light passes thrugh a lens, refractin ccurs at the tw lens surfaces. In Chapter 17, yu learned that Snell s law and gemetry can be used t predict the paths f rays passing thrugh a lens. T simplify yur drawings and calculatins, yu will use the same apprximatin yu used with mirrrs, that is, that all refractin ccurs n a plane, called the principal plane, that passes thrugh the center f the lens. This apprximatin, called the thin lens mdel, applies t all the lenses yu will learn abut in this bk. Real images frm cnvex lenses Have yu ever used a lens fr the purpse shwn in igure 18 13? By psitining the lens s that the rays f the sun cnverge n the leaf, the camper prduces the image f the sun n the leaf s surface. The image is real. Because the rays are cnverging n a small spt, enugh energy is being cncentrated there that it culd set the leaf ablaze. The rays f the sun are examples f light rays IGURE A cnverging lens can be used t start a fire in a pile f leaves Lenses 429

17 IGURE When an bject is placed well beynd the principal fcus f a cnvex lens, the image is real, inverted, and reducen size. If the bject were placed at the psitin f the image, yu culd lcate the new image by tracing the same rays in the ppsite directin. Object 2 Ray 1 Ray 2 Image 2 d = 30 cm = 15 cm Lens/Mirrr Equatin Cnventins Applied t Lenses f f is psitive fr cnvex lenses. is negative fr cncave lenses. d is psitive n the bject side f the lens. is psitive n the ther side (image side) f the lens, where images are real. is negative n the bject side f the lens where images are virtual. that are almst exactly parallel t the principal axis because they have cme frm such a distant surce. After being refracten the lens, the rays cnverge at a pint called the fcal pint,, f the lens. igure shws tw fcal pints, ne n each side f the lens. This is because the lens is symmetrical and light can pass thrugh it in bth directins. The tw fcal pints are imprtant in drawing rays, as yu will see. The distance frm the lens t a fcal pint is the fcal length, f. The fcal length depends upn the shape f the lens and the refractive index f the lens material. In igure 18 14, yu can trace rays frm an bject lcated far frm a cnvex lens. Ray 1 is parallel t the principal axis. It refracts and passes thrugh n the ther side f the lens. Ray 2 passes thrugh n its way t the lens. After refractin, its path is parallel t the principal axis. The tw rays intersect at a pint beynd and lcate the image. Rays selected frm ther pints n the bject wuld cnverge at crrespnding pints n the image. Nte that the image is real, inverted, and smaller than the bject. Where is the image f an bject that is clser t the lens than the bject in igure is? Yu can find the lcatin f the image withut drawing anther ray diagram. If yu imagine the bject in the psitin f the image in igure 18 14, yu can easily lcate the new bject by using a basic principle f ptics that states that if a reflected r refracted ray is reversen directin, it will fllw its riginal path in the reverse directin. This means that the image and bject may be interchanged by changing the directin f the rays. Imagine that the path f light thrugh the lens in igure is reversed and the bject is at a distance f 15 cm frm the right side f the lens. The new image, lcated at 30 cm frm the left side f the lens, is again real annverted, but it is nw larger than the bject. If the bject were placed at a distance twice the fcal length frm the lens, that is, at the pint 2 n igure 18 14, the image als wuld be fund at 2. Because f symmetry, the image and bject wuld have the same size. Thus, yu can cnclude that if an bject is mre than twice the fcal length frm the lens, the image is reducen size. If the bject is between and 2, then the image is enlarged. 430 Mirrrs and Lenses

18 The lens/mirrr equatin can be used t find the lcatin f an image, and the magnificatin equatin can be used t fints size. 1 f 1 1 d d i hi m d i h d Recall that yu used the lens/mirrr equatin, as well as the equatin fr magnificatin, in slving prblems invlving mirrrs. The fllwing Example Prblem will shw yu hw t apply these equatins t prblems invlving lenses. Example Prblem An Image rmed by a Cnvex Lens An bject is placed 32.0 cm frm a cnvex lens that has a fcal length f 8.0 cm. a. Where is the image? Object b. If the bject is 3.0 cm high, hw high is the image? c. Is the image inverted r upright? h Sketch the Prblem Sketch the situatin, lcating the bject and lens. Draw tw principal rays. Calculate Yur Answer Knwn: Strategy: d 32.0 cm h 3.0 cm f 8.0 cm Unknwn:? h i? Use lens/mirrr equatin t determine. Slve magnificatin relatins t finmage height. Check Yur Answer Are the units crrect? All are in cm. D the signs make sense? Lcatin is psitive (real); height is negative (inverted). These are in agreement with the diagram. Are the magnitudes realistic? Lcatin and height agree with the drawing. 2 d Calculatins: 1 f 1 1 fd, s d d i d f (8.0 cm)(32.0 cm) 32.0 cm 8.0 cm 11 cm, real hi m d, i s h h di h d h i (11 cm)(3.0 cm) 32.0 cm Image h i cm, inverted 18.2 Lenses 431

19 Practice Prblems 9. Use a ray diagram t find the image psitin f an bject 30 cm t the left f a cnvex lens with a 10-cm fcal length. (Let 1 cm n the drawing represent 20 cm.) 10. An bject, 2.25 mm high, is 8.5 cm t the left f a cnvex lens f 5.5-cm fcal length. ind the image lcatin and height. 11. An bject is placed t the left f a 25-mm fcal length cnvex lens s that its image is the same size as the bject. What are the image and bject lcatins? Pcket Lab ish-eye Lens Hw can fish fcus light with their eyes? The light frm an bject in the water ges frm the water int the fish eye, which is als mstly water. Obtain a cnverging lens and bserve that it can be used as a magnifying glass. Nw hld the lens under water in an aquarium. Des the lens still magnify? Analyze and Cnclude Cmpare the magnifying ability f the glass lens when used under water ann air. Wuld a mre curved lens bend the light mre? Wuld yu predict that the index f refractin f the material in a fish eye is the same as water? Defend yur predictin. Why use a large lens? r simplicity, yu have drawn ray diagrams as if nly tw rays frmed the image. But, in reality, all the rays that leave a pint n the bject and pass thrugh the lens cnverge and frm an image at the same spt. igure 18 15a shws mre f the rays invlved. Ntice that nly the rays that hit the lens are imaged at the same spt. If yu put a piece f paper at the image lcatin, the size f the spt will be smallest at that pint. If yu mve the paper in either directin alng the principal axis, the size f the spt gets bigger but fuzzier. Yu wuld say that the image is ut f fcus. What wuld happen if yu used a lens f larger diameter? Mre f the rays that miss the lens wuld nw g thrugh it, as yu can see in igure 18 15b. With mre rays cnverging n the image, it wuld be brighter. Wuld the reverse be true if yu used a smaller lens? ewer rays wuld pass thrugh the smaller lens and fcus n the image, s the image wuld be dimmer. Cameras use this principle t allw the aperture t be adjusted fr dimmer r brighter days. Virtual images If an bject is placed at the fcal pint f a cnvex lens, the refracted rays will emerge in a parallel beam. If the bject is brught clser t the lens, the rays d nt cnverge n the ppsite side f the lens. Instead, the image appears n the same side f the lens as the bject. This image is virtual, erect, and enlarged. IGURE All the rays that pass thrugh the lens fcus at the same pint. A larger lens allws mre rays t pass thrugh and thus prduces a brighter image. a b b 432 Mirrrs and Lenses

20 Seeing Is Believing Prblem Hw can yu lcate the image f a lens? Materials large-diameter cnvex lens large-diameter cncave lens 2 small balls f clay 2 rulers 2- r 3-cm-lng nail 2 pieces f paper Prcedure 1. Assemble the equipment as shwn in the pht using the cncave lens. 2. Lk thrugh the lens t make sure that yu can see bth ends f the nail. Mve the nail clser r farther frm the lens until bth ends are visible. Data and Observatins 1. Mark the paper t shw the tip f the nail, the head f the nail, and als the lens line. 2. Line up yur straight edge t pint t the head f the nail. Have yur lab partner verify that the edge is accurate. 3. Draw the line f sight. 4. Mve t anther psitin and draw a secnd line f sight t the head f the nail. 5. Repeat steps 2 4, this time drawing tw lines f sight t the tip f the nail. 6. Use a new sheet f paper and repeat steps 1 5 using the cnvex lens. 7. When yu are finished, put away any materials that can be reused. Analyze and Cnclude 1. Analyzing Data The image can be lcated by extending the lines f sight until they intersect. Extend the tw lines f sight that pint t the image head. Extend the tw lines f sight that pint t the image tip. Describe the results. 2. Analyzing Data Repeat the analysis fr the cnvex lens, and describe the results. 3. Cmparing Data Recrd yur bservatins anmage descriptins in a table. Data and Observatins Image Image Image Lcatin Size Type (with respect (with respect (upright r t bject Lens t bject) upside dwn) and lens) cncave cnvex 4. Extending Results Hw wuld the image size and lcatin change if yu mved the bject clser t the lens? D the answers depend n whether the lens is cncave r cnvex? Apply 1. Describe an applicatin f a similar arrangement fr a cnvex lens Lenses 433

21 igure shws hw a cnvex lens frms a virtual image. The bject is between and the lens. Ray l, as usual, appraches the lens parallel t the principal axis ans refracted thrugh the fcal pint,. Ray 2 travels frm the tip f the bject, in the directin it wuld have if it had started at n the bject side f the lens. The dashed line frm t the bject shws yu hw t draw ray 2. Ray 2 leaves the lens parallel t the principal axis. Rays 1 and 2 diverge as they leave the lens. Thus, n real image is pssible. Drawing sight lines fr the tw rays back t their apparent intersectin lcates the virtual image. It is n the same side f the lens as the bject, erect, and larger than the bject. Example Prblem A Magnifying Glass A cnvex lens with a fcal length f 6.0 cm is held 4.0 cm frm an insect that is 0.50 cm lng. a. Where is the image lcated? b. Hw large des the insect appear t be? Sketch the Prblem Sketch the situatin, lcating the lens and the bject. Draw tw principal rays. Calculate Yur Answer Knwn: Unknwn: d 4.0 cm? h 0.50 cm h i? f 6.0 cm Strategy: Use lens/mirrr equatin t determine. Slve magnificatin relatins t finmage height. Calculatins: Check Yur Answer Are yur units crrect? All are in cm. D the signs make sense? Negative means virtual image; psitive h i means upright image, as the diagram shws. Are the magnitudes realistic? They agree with the diagram. h i Image 1 f 1 1 fd, s d d d f i hi m d, i s h h di h d h i (6.0 cm)(4.0 cm) 4.0 cm 6.0 cm ( 12 cm)(0.50 cm) 4.0 cm h Object d 12 cm, virtual 1.5 cm, upright 434 Mirrrs and Lenses

22 Virtual image Ray 2 Ray 1 Object d IGURE The tw principal rays shw that an upright, enlarged, virtual image, frmed by a cnvex lens when the bject is lcated between the lens and the principal fcus. Drawing principal rays allws yu t lcate and cnstruct the image f an bject. These rays d nt necessarily pass thrugh the lens itself. Practice Prblems 12.A newspaper is held 6.0 cm frm a cnvex lens f 20.0-cm fcal length. ind the image distance f the newsprint image. 13.A magnifying glass has a fcal length f 12.0 cm. A cin, 2.0 cm in diameter, is placed 3.4 cm frm the lens. Lcate the image f the cin. What is the diameter f the image? 14.A stamp cllectr wants t magnify an image by 4.0 when the stamp is 3.5 cm frm the lens. What fcal length is needed fr the lens? Cncave Lenses In igure 18 17, yu can see hw an image is frmed by a cncave lens. A cncave lens causes all rays t diverge. Ray 1 leaves O 1 and appraches the lens parallel t the principal axis. It leaves the lens in the directin it wuld have if it had passed thrugh the fcal pint. Ray 2 passes directly thrugh the center f the lens withut bending. Rays 1 and 2 diverge after passing thrugh the lens. Their apparent intersectin is i, n the same side f the lens as the bject. The image is virtual, erect, and reducen size. This is true n matter hw far frm the lens the bject is lcated. The fcal length f a cncave lens is negative. Pcket Lab Bright Ideas Stick the edge f a cnverging lens int a ball f clay and place the lens n a tabletp. Use a small lightbulb n ne side and a screen n the ther side t get a sharp image f the bulb. Predict what will happen t the image if yu place yur hand ver the tp half f the lens. Try it. Analyze and Cnclude What happened? Hw much f the lens is needed fr a cmplete image? O 1 Ray 1 Ray 2 Object Virtual image d IGURE Cncave lenses are usen eyeglasses t crrect nearsightedness ann cmbinatin with cnvex lenses in cameras and telescpes Lenses 435

23 White light a White light b Lens Achrmatic lens IGURE Chrmatic aberratin is depicten a, which shws light f different wavelengths fcused at different pints. The achrmatic lens in b is a cmbinatin f a cnvex and a cncave lens, which minimizes the chrmatic defect. Defects f lenses The mdel yu have used fr drawing rays thrugh lenses suggests that all rays that pass thrugh all parts f a lens fcus at the same lcatin. Hwever, this is nly an apprximatin. In real lenses, rays that pass thrugh the extreme edges f the lens are fcused at a lcatin different frm rays that pass thrugh the center. This inability f the lens t fcus all parallel rays t a single pint is called spherical aberratin. Lenses as well as mirrrs have spherical aberratin. Spherical aberratin is eliminaten inexpensive cameras by using nly the centers f lenses. In mre expensive instruments, many lenses, ften five r mre, are used t frm a sharp, well-definemage. Lenses have a secnd defect that mirrrs d nt. The edges f a lens resemble a prism, and different wavelengths f light are bent at slightly different angles, as yu can see in igure 18 18a. Thus, the light that passes thrugh a lens, especially near the edges, is slightly dispersed. An bject viewed thrugh a lens appears ringed with clr. This effect is called chrmatic aberratin. The term chrmatic cmes frm the Greek chrm, which means related t clr. Chrmatic aberratin is always present when a single lens is used, but this defect can be greatly reduced by jining a cnvex lens with a cncave lens that has a different index f refractin. Such a cmbinatin f lenses is shwn in igure 18 18b. Bth lenses disperse light, but the dispersin caused by the cnverging lens is almst canceled by that caused by the diverging lens. The index f refractin f the diverging lens is chsen s that the cmbinatin lens still cnverges the light. A lens cnstructen this way is called an achrmatic lens. All precisin ptical instruments use achrmatic lenses. Crnea Vitreus humr Retina Optic nerve Lens Pupil Iris Iris Tp View Retina Pupil IGURE The curved surfaces f the crnea and lens refract light rays that enter the eye thrugh the pupil t frm an image n the retina. Crnea Lens Vitreus humr Optic nerve 436 Mirrrs and Lenses

24 a c b Optical Instruments that Use Lenses Althugh the eye itself is a remarkable ptical device, its abilities can be greatly extended by a wide variety f instruments cmpsed f lenses and mirrrs. The eye is a fluid-filled, almst spherical vessel that frms the image f an bject n the retina, as shwn in igure Mst f the refractin ccurs at the curved surface f the crnea. The eye lens is made f flexible material with a refractive index different frm that f the fluid. Muscles can change the shape f the lens, thereby changing its fcal length. When the muscles are relaxed, the image f distant bjects is fcused n the retina. When the muscles cntract, the fcal length is shrtened, permitting images f bjects 25 cm r clser t be fcused n the retina. The eyes f many peple d nt fcus sharp images n the retina. Instead, images are fund either in frnt f the retina r behint. External lenses, in the frm f eyeglasses r cntact lenses, are needed t adjust the fcal length and mve the image t the retina. igure shws that the nearsighted, r mypic, eye has t shrt a fcal length. Images f distant bjects are frmen frnt f the retina. Cncave lenses crrect this defect by diverging the light rays, thus increasing the image distance, and placing the image n the retina. Yu als can see in igure that farsightedness, r hyperpia, is the result f t lng a fcal length, which results in the image falling behind the retina. A similar result is caused by the increasing rigidity f the lenses in the eyes f peple mre than abut 45 years ld. Their muscles cannt shrten the fcal length enugh t fcus images f clse bjects n the retina. r either defect, cnvex lenses prduce a virtual image farther frm the eye than the bject. This image then becmes the bject fr the eye lens and can be fcused n the retina, thereby crrecting the defect. Sme peple have lenses r eye shapes that are nt spherical. This defect is called astigmatism, and the result is that vertical lines f images can be in fcus while hrizntal lines are nt. Eyeglasses having a nnspherical shape can crrect astigmatism. d IGURE A nearsighted persn cannt see distant bjects because the image is fcusen frnt f the retina as shwn in a. The cncave lens in b crrects this defect. A farsighted persn cannt see clse bjects because the image is fcused behind the retina as shwn in c. The cnvex lens in d crrects this defect. BIOLOGY CONNECTION.Y.I. The earliest eyeglasses were made f thick, cnvex lenses. These lenses reminded their makers f lentils. Hence the term lens, frm the Latin fr lentil beans Lenses 437

25 Tear fluid Cntact lens Crnea Eye IGURE A cntact lens rests n a layer f tears between it and the surface f the crnea. Cntact lenses prduce the same results as eyeglasses. These very thin lenses are placed directly n the crnea, as shwn in igure A thin layer f tears between the crnea and lens keeps the lens in place. Mst f the refractin ccurs at the air-lens surface, where the change in refractive index is greatest. Micrscpes and telescpes Micrscpes allw the eye t see extremely small bjects. Mst micrscpes use at least tw cnvex lenses. An bject is placed very clse t a lens with a very shrt fcal length, the bjective lens. This lens prduces a real image lcated between the secnd lens, the cular r eyepiece lens, ants fcal pint. The cular prduces a greatly magnified virtual image f the image frmed by the bjective lens. An astrnmical refracting telescpe uses tw cnvex lenses. The bjective lens f a telescpe has a lng fcal length. The parallel rays frm a star r ther distant bject fcus in a plane at the fcal pint f this lens. The eyepiece lens, with a shrt fcal length, then refracts the rays int anther parallel beam. The viewer sees a virtual, enlarged, invertemage. The primary purpse f a telescpe is nt t magnify the image. It is t increase the angle between the rays frm tw different stars and t cllect mre light than wuld strike the unaided eye Sectin Review 1. What wave behavir allws lenses t wrk? Describe hw a lens fcuses light. 2. Which f the lenses whse crss sectins are shwn in igure are cnvex r cnverging lenses? Which are cncave r diverging lenses? a b c d IGURE Suppse yur camera was fcused n a persn 2 m away. Yu nw want t fcus it n a tree that is farther away. Shuld the lens be mved clser t the film r farther away? 4. Yu first fcus white light thrugh a single lens s that res fcused t the smallest pint n a sheet f paper. Which directin shuld yu mve the paper t best fcus blue? 5. Critical Thinking An air lens cnstructed f tw watch glasses is placen a tank f water. Cpy igure and draw the effect f this lens n parallel light rays incident n the lens. Water Light rays IGURE Air Water 438 Mirrrs and Lenses

26 CHAPTER 18 REVIEW Key Terms 18.1 plane mirrr bject image virtual image erect image cncave mirrr principal axis fcal pint fcal length real image lens/mirrr equatin magnificatin spherical aberratin cnvex mirrr 18.2 lens cnvex lens cncave lens chrmatic aberratin achrmatic lens Summary 18.1 Mirrrs An bject is a surce f diverging light rays. Sme mirrrs reflect light rays that appear t diverge frm a pint n the ther side f a mirrr. The pint frm which they appear t diverge is called the virtual image. The image in a plane mirrr is the same size as the bject. It is as far behind the mirrr as the bject is in frnt f the mirrr. The image is virtual and erect. The fcal pint f a cnvex r cncave mirrr is halfway between the center f curvature f the mirrr and the mirrr. Parallel rays striking a cncave mirrr cnverge at the fcal pint. Parallel rays striking a cnvex mirrr appear t diverge frm the fcal pint behind the mirrr. Cncave mirrrs frm real, inverted images if the bject is farther frm the mirrr than the fcal pint, and virtual, upright images if the bject is between the mirrr and the fcal pint. Cnvex mirrrs always prduce virtual, upright, reducemages. Parallel light rays that are far frm the principal axis are nt reflected by spherical mirrrs t cnverge at the Reviewing Cncepts Sectin Describe the physical prperties f the image seen in a plane mirrr. 2. Where is the image f an bject in a plane mirrr? 3. Describe the physical prperties f a virtual image. 4. A student believes that very sensitive phtgraphic film can detect a virtual image. The student puts phtgraphic fcal pint. This defect is called spherical aberratin Lenses Cnvex lenses are thinner at their uter edges than at their centers. Cncave lenses are thicker at their uter edges than at their centers. Cnvex lenses prduce real, inverted images if the bject is farther frm the lens than the fcal pint. If the bject is clser than the fcal pint, a virtual, upright, enlargemage is frmed. Cncave lenses prduce virtual, upright, reducemages. Lenses have spherical aberratins because parallel rays striking a lens near its edge d nt fcus at ne spt. Lenses als fcus light f different wavelength (clr) at different lcatins. This is called chrmatic aberratin. Key Equatins f 1 1 di d hi m h m d film at the lcatin f the image. Des this attempt succeed? Explain. 5. Hw can yu prve t smene that an image is a real image? 6. What is the fcal length f a plane mirrr? Des the lens/mirrr equatin wrk fr plane mirrrs? Explain. 7. An bject prduces a virtual image in a cncave mirrr. Where is the bject lcated? Chapter 18 Review 439

27 CHAPTER 18 REVIEW 8. Why are cnvex mirrrs used as rearview mirrrs? 9. What causes the defect that all cncave spherical mirrrs have? Sectin Lcate and describe the physical prperties f the image prduced by a cnvex lens if an bject is placed sme distance beynd What factr, ther than the curvature f the surfaces f a lens, determines the lcatin f the fcal pint f the lens? 12. T prject an image frm a mvie prjectr nt a screen, the film is placed between and 2 f a cnverging lens. This arrangement prduces an invertemage. Why d the actrs appear t be erect when the film is viewed? Applying Cncepts 13. Lcate and describe the physical prperties f the image prduced by a cncave mirrr when the bject is lcated at the center f curvature. 14. An bject is lcated beynd the center f curvature f a spherical cncave mirrr. Lcate and describe the physical prperties f the image. 15. An bject is lcated between the center f curvature and the fcus f a cncave mirrr. Lcate and describe the physical prperties f the image f the bject. 16. Yu have t rder a large cncave mirrr fr a piece f high-quality equipment. Shuld yu rder a spherical mirrr r a parablic mirrr? Explain. 17. Describe the physical prperties f the image seen in a cnvex mirrr. 18. List all the pssible arrangements in which yu can use a spherical mirrr, either cncave r cnvex, t frm a real image. 19. List all pssible arrangements in which yu can use a spherical mirrr, either cncave r cnvex, t frm an image reducen size. 20. The utside rearview mirrrs f cars ften carry the warning Objects in the mirrr are clser than they appear. What kind f mirrr is this and what advantage des it have? 21. What physical characteristic f a lens distinguishes a cnverging lens frm a diverging lens? 22. If yu try t use a magnifying glass underwater, will its prperties change? Explain. 23. Suppse igure were redrawn with a lens f the same fcal length but a larger diameter. Hw wuld the lcatin f the image change? 24. Why is there chrmatic aberratin fr light that ges thrugh a lens but there is nt chrmatic aberratin fr light that reflects frm a mirrr? Prblems Sectin Penny wishes t take a picture f her image in a plane mirrr. If the camera is 1.2 m in frnt f the mirrr, at what distance shuld the camera lens be fcused? 26. A cncave mirrr has a fcal length f 10.0 cm. What is its radius f curvature? 27. Light frm a star is cllected by a cncave mirrr. Hw far frm the mirrr is the image f the star if the radius f curvature is 150 cm? 28. An bject is 30.0 cm frm a cncave mirrr f 15-cm fcal length. The bject is 1.8 cm high. Use the lens/mirrr equatin t find the image. Hw high is the image? 29. A jeweler inspects a watch with a diameter f 3.0 cm by placing it 8.0 cm in frnt f a cncave mirrr f 12.0-cm fcal length. a. Where will the image f the watch appear? b. What will be the diameter f the image? 30. A dentist uses a small mirrr f radius 40 mm t lcate a cavity in a patient s tth. If the mirrr is cncave ans held 16 mm frm the tth, what is the magnificatin f the image? 31. Draw a ray diagram f a plane mirrr t shw that if yu want t see yurself frm yur feet t the tp f yur head, the mirrr must be at least half yur height. 32. Sunlight falls n a cncave mirrr and frms an image 3.0 cm frm the mirrr. If an bject 24 mm high is placed 12.0 cm frm the mirrr, where will its image be frmed? a. Use a ray diagram. b. Use the lens/mirrr equatin. c. Hw high is the image? 33. A prductin line inspectr wants a mirrr that prduces an upright image with magnificatin f 7.5 when it is lcated 14.0 mm frm a machine part. a. What kind f mirrr wuld d this jb? b. What is its radius f curvature? 440 Mirrrs and Lenses

28 CHAPTER 18 REVIEW 34. Shiny lawn spheres placed n pedestals are cnvex mirrrs. One such sphere has a diameter f 40.0 cm. A 12-cm rbin sits in a tree 1.5 m frm the sphere. Where is the image f the rbin and hw lng is the image? Sectin The fcal length f a cnvex lens is 17 cm. A candle is placed 34 cm in frnt f the lens. Make a ray diagram t lcate the image. 36. The cnvex lens f a cpy machine has a fcal length f 25.0 cm. A letter t be cpies placed 40.0 cm frm the lens. a. Hw far frm the lens is the cpy paper? b. The machine was adjusted t give an enlarged cpy f the letter. Hw much larger will the cpy be? 37. Camera lenses are describen terms f their fcal length. A 50.0-mm lens has a fcal length f 50.0 mm. a. A camera with a 50.0-mm lens is fcused n an bject 3.0 m away. Lcate the image. b. A mm lens is fcused n an bject 125 m away. Lcate the image. 38. A cnvex lens is needed t prduce an image that is 0.75 times the size f the bject and lcated 24 cm behind the lens. What fcal length shuld be specified? 39. In rder t clearly read a bk 25 cm away, a farsighted persn needs an image distance f 45 cm frm the eye. What fcal length is needed fr the lens? 40. A slide f an nin cell is placed 12 mm frm the bjective lens f a micrscpe. The fcal length f the bjective lens is 10.0 mm. a. Hw far frm the lens is the image frmed? b. What is the magnificatin f this image? c. The real image frmes lcated 10.0 mm beneath the eyepiece lens. If the fcal length f the eyepiece is 20.0 mm, where des the final image appear? d. What is the final magnificatin f this cmpund system? Extra Practice r mre practice slving prblems, g t Extra Practice Prblems, Appendix B. Critical Thinking Prblems 41. Yur lab partner used a cnvex lens t prduce an image with 25 cm and h i 4.0 cm. Yu are examining a cncave lens with a fcal length f 15 cm. Yu place the cncave lens between the cnvex lens and the riginal image, 10 cm frm the image. T yur surprise, yu see a real, enlargemage n the wall. Yu are tld that the image frm the cnvex lens is nw the bject fr the cncave lens, and because it is n the ppsite side f the cncave lens, it is a virtual bject. Use these hints t find the lcatin and size f the new image and t predict whether the cncave lens changed the rientatin f the riginal image. 42. What is respnsible fr the rainbw-clred fringe cmmnly seen at the edges f a spt f white light frm a slide r verhead prjectr? 43. A lens is used t prject the image f an bject nt a screen. Suppse yu cver the right half f the lens. What will happen t the image? Ging urther Applying Calculatrs Yu are examining a 5-cm butterfly under a magnifying glass with a fcal length f 15 cm. The equatin fr calculating hw large the butterfly appears is h i ( h f)/(d f). Graph this equatin n a graphing calculatr with h i n the y-axis (with a range f 50 cm t 50 cm) and d n the x-axis (with a range f 0 cm t 50 cm). Hw large des the butterfly appear at 5 cm? At 10 cm? 13 cm? 17 cm? 20 cm? 30 cm? 50 cm? r what distances is the image upright? Team Prject Research annterpret the rle f refractin and/r reflectin in the fllwing industries: cntact lenses, cameras, telescpes, sunglasses, and windws. PHYSICS T review cntent, d the interactive quizzes n the Glence Science Web site at science.glence.cm Chapter 18 Review 441