CHAPTER 17 Reflection And Mirrors

Chapter 17 continued41. If you know the image position and objectposition relative to a curved mirror, how canyou determine the mirror’s magnification?(17.2)The magnification is equal to thenegative of the image distance dividedby the object distance.42. Why are convex mirrors used as rearviewmirrors? (17.2)Convex mirrors are used as rearviewmirrors because they allow for a widerange of view, allowing the driver to seea much larger area than is afforded byordinary mirrors.43. Why is it impossible for a convex mirror toform a real image? (17.2)The light rays always diverge.Applying ConceptsCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.pages 478–47944. Wet Road A dry road is more of adiffuse reflector than a wet road. Basedon Figure 17-16, explain why a wetroad appears blacker to a driver thana dry road does.46. Locate and describe the physical propertiesof the image produced by a concave mirrorwhen the object is located at the center ofcurvature.The image will be at C, the center ofcurvature, inverted, real, and the samesize as the object.47. An object is located beyond the center ofcurvature of a spherical concave mirror.Locate and describe the physical propertiesof the image.The image will be between C and F, andwill be inverted, real, and smaller thanthe object.48. Telescope You have to order a largeconcave mirror for a telescope thatproduces high-quality images. Should youorder a spherical mirror or a parabolicmirror? Explain.You should order a parabolic mirror toeliminate spherical aberrations.49. Describe the properties of the image seen inthe single convex mirror in Figure 17-17.Wet asphaltDry asphalt Figure 17-16Less light is reflected back to the carfrom a wet road.45. Book Pages Why is it desirable that thepages of a book be rough rather thansmooth and glossy?The smoother and glossier the pagesare, the lesser the diffuse reflection oflight and the greater the glare fromthe pages.Physics: Principles and Problems Figure 17-17The image in a single convex mirror isalways virtual, erect, smaller than theobject, and located closer to the mirrorthan the object.Solutions Manual363

Chapter 17 continued50. List all the possible arrangements in whichyou could use a spherical mirror, eitherconcave or convex, to form a real image.You can use only a concave mirror withthe object beyond the focal point. A convex mirror will not form a real image.51. List all possible arrangements in which youcould use a spherical mirror, either concaveor convex, to form an image that is smallercompared to the object.You may use a concave mirror with theobject beyond the center of curvatureor a convex mirror with the objectanywhere.52. Rearview Mirrors The outside rearviewmirrors of cars often carry the warning“Objects in the mirror are closer than theyappear.” What kind of mirrors are these andwhat advantage do they have?55. A ray of light incident upon a mirror makesan angle of 36 with the mirror. What is theangle between the incident ray and thereflected ray?!i ! 90 " 36 ! 54 !r ! !i! 54 ! ! !i # !r! 54 # 54 ! 108 Level 256. Picture in a Mirror Penny wishes to take apicture of her image in a plane mirror, asshown in Figure 17-18. If the camera is1.2 m in front of the mirror, at what distance should the camera lens be focused?Convex mirror; it provides a wider fieldof view.Mastering Problems!r ! !i! 38 54. A ray of light strikes a mirror at an angle of53 to the normal.a. What is the angle of reflection?!r ! !i Figure 17-18The image is 1.2 m behind the mirror, sothe camera lens should be set to 2.4 m.! 53 b. What is the angle between the incidentray and the reflected ray?! ! !i # !r57. Two adjacent plane mirrors form a rightangle, as shown in Figure 17-19. A light rayis incident upon one of the mirrors at anangle of 30 to the normal.! 53 # 53 ! 106 364Solutions ManualPhysics: Principles and ProblemsCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.17.1 Reflection from Plane Mirrorspage 479Level 153. A ray of light strikes a mirror at an angle of38 to the normal. What is the angle thatthe reflected angle makes with the normal?

Chapter 17 continuedthe feet hits the mirror halfway betweenthe eyes and the feet. The distancebetween the point the two rays hit themirror is half the total height.30 Figure 17-19a. What is the angle at which the light rayis reflected from the other mirror?Reflection from the first mirror:!r1 ! !i1 ! 30 Reflection from the second mirror:!i2 ! 90 " !r1! 90 " 30 ! 60 !r2 ! !i2! 60 Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.b. A retroreflector is a device that reflectsincoming light rays back in a directionopposite to that of the incident rays.Draw a diagram showing the angle ofincidence on the first mirror for whichthe mirror system acts as a retroreflector.Level 359. Two plane mirrors are connected at theirsides so that they form a 45 angle betweenthem. A light ray strikes one mirror at anangle of 30 to the normal and then reflectsoff the second mirror. Calculate the angle ofreflection of the light ray off the secondmirror.Reflection from the first mirror is!r, 1 ! !i, 1 ! 30 . The angle the rayforms with the mirror is thus 90 " 30 !60 . Because the two mirrors form a 45 angle, the angle the ray reflecting offthe first mirror forms with the secondmirror is 180 " 60 " 45 ! 75 . Theangle the ray forms with the secondmirror is thus !i, 2 ! 90 " 75 ! 15 .The angle of reflection from the secondmirror is !r, 2 ! !i, 2 ! 15 .60. A ray of light strikes a mirror at an angle of60 to the normal. The mirror is then rotated18 clockwise, as shown in Figure 17-20.What is the angle that the reflected raymakes with the mirror?Incident light45 18 58. Draw a ray diagram of a plane mirror toshow that if you want to see yourself fromyour feet to the top of your head, the mirrormust be at least half your height.EyelevelMirrorNormal60 ImageMirrorFeetThe ray from the top of the head hitsthe mirror halfway between the eyesand the top of the head. The ray fromPhysics: Principles and Problems Figure 17-20!i ! !i, old " 18 ! 60 " 18 ! 42 Solutions Manual365

Chapter 17 continued!r ! !i! 42 !r, mirror ! 90 " !r! 90 " 42 ! 48 17.2 Curved Mirrorspage 480Level 161. A concave mirror has a focal length of10.0 cm. What is its radius of curvature?r ! 2f ! 2(10.0 cm) ! 20.0 cm62. An object located 18 cm from a convexmirror produces a virtual image 9 cm fromthe mirror. What is the magnification of theimage?"diCF Figure 17-21real; inverted; largerLevel 265. Star Image Light from a star is collected bya concave mirror. How far from the mirroris the image of the star if the radius ofcurvature is 150 cm?! !!Stars are far enough away that thelight coming into the mirror can beconsidered to be parallel and parallellight will converge at the focal point.! 0.5Since r ! 2f,m ! !!do"("9 cm)18 cm13r2150 cm2f ! !! ! !! ! 75 cm66. Find the image position and height for theobject shown in Figure 17-22.mirror is !!, what is the boy’s height?him ! !!hohiho ! !!m!3.8 cmF16 cm0.60 m "!13!#31 cm! 1.8 m64. Describe the image produced by the objectin Figure 17-21 as real or virtual, invertedor upright, and smaller or larger than theobject. Figure 17-22111!! ! !! # !!fdodid fdo " fdi ! !o!(31 cm)(16 cm)31 cm " 16 cm! !!366Solutions ManualPhysics: Principles and ProblemsCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.63. Fun House A boy is standing near aconvex mirror in a fun house at a fair. Henotices that his image appears to be0.60 m tall. If the magnification of the

Chapter 17 continuedwhat is the magnification of the image?! 33 cmhi"dihodom ! !! ! !!"dihohi ! !!do"(33 cm)(3.8 cm)! !!!31 cm! "4.1 cm67. Rearview Mirror How far does the imageof a car appear behind a convex mirror,with a focal length of "6.0 m, when the caris 10.0 m from the mirror?111!! ! !! # !!dodifd fdo " fdi ! !o!(10.0 m)("6.0 m)10.0 m " ("6.0 m)! !!!Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.! "3.8 m68. An object is 30.0 cm from a concave mirrorof 15.0 cm focal length. The object is1.8 cm tall. Use the mirror equation tofind the image position. What is the imageheight?(40 mm)2r2f ! !! ! !! ! 20 mm111!! # !! ! !!dodifd fdo " f(16 mm)(20 mm)16 mm " 20 mmdi ! !o! ! !! ! "80 mm"di"("80 mm)16 mmm ! !! ! !! ! 5do70. A 3.0-cm-tall object is 22.4 cm from aconcave mirror. If the mirror has a radius ofcurvature of 34.0 cm, what are the imageposition and height?r2f ! !!34.0 cm2! !!! 17.0 cm111!! ! !! # !!dodifd fdo " fdi ! !o!(22.4 cm)(17.0 cm)22.4 cm " 17.0 cm! !!!! 70.5 cm111!! # !! ! !!dodifm ! !! ! !!d fdi ! !o!do " fhi ! !!(30.0 cm)(15.0 cm)! !!!30.0 cm " 15.0 cm! 30.0 cmhi"dim ! !! ! !!hodo"dihohi ! !!do"(30.0 cm)(1.8 cm)(30.0 cm)! !!!! "1.8 cm69. Dental Mirror A dentist uses a small mirror with a radius of 40 mm to locate acavity in a patient’s tooth. If the mirror isconcave and is held 16 mm from the tooth,Physics: Principles and Problemshi"dihodo"dihodo"(70.5 cm)(3.0 cm)22.4 cm! !!!! "9.4 cmLevel 371. Jeweler’s Mirror A jeweler inspects awatch with a diameter of 3.0 cm by placingit 8.0 cm in front of a concave mirror of12.0-cm focal length.a. Where will the image of the watchappear?111!! # !! ! !!dodifSolutions Manual367

Chapter 17 continuedd fdo " f(8.0 cm)(12.0 cm)8.0 cm " 12.0 cmdi ! !o! ! !!!111!! # !! ! !!dodiffdo! "24 cmb. What will be the diameter of the image?hi"di!! ! !!hododi ! !!do " f("10.0 cm)(150 cm)150 cm " ("10.0 cm)! !!! ! "9.4 cm"diho"("24 cm)(3.0 cm)8.0 cmhi ! !! ! !!!do"di"("9.4 cm)150 cmm ! !! ! !! ! #0.063dohi ! mho ! (0.063)(12 cm) ! 0.75 cm! 9.0 cm72. Sunlight falls on a concave mirror andforms an image that is 3.0 cm from themirror. An object that is 24 mm tall isplaced 12.0 cm from the mirror.a. Sketch the ray diagram to show thelocation of the image.O1 Ray 1Ray 2C FHorizontal scale:1 block ! 1.0 cmVertical scale:1 block ! 4 mmI1Mixed Reviewpages 480–481Level 174. A light ray strikes a plane mirror at an angleof 28 to the normal. If the light source ismoved so that the angle of incidenceincreases by 34 , what is the new angle ofreflection?!i ! !i, initial # 34 ! 28 # 34 ! 62 !r ! !i! 62 b. Use the mirror equation to calculate theimage position.fddo " f(3.0 cm)(12.0 cm)12.0 cm " 3.0 cmodi ! !! !!!! 4.0 cmc. How tall is the image?"di"4.0 cmm ! !! ! !! ! "0.33do12.0 cm3.0 cm8.0 cmF4.0 cmhi ! mho ! ("0.33)(24 mm)! "8.0 mm73. Shiny spheres that are placed on pedestalson a lawn are convex mirrors. One suchsphere has a diameter of 40.0 cm.A 12-cm-tall robin sits in a tree that is1.5 m from the sphere. Where is the imageof the robin and how tall is the image? Figure 17-23r ! 20.0 cm, f ! "10.0 cm368Solutions ManualPhysics: Principles and ProblemsCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.111!! # !! ! !!dodif75. Copy Figure 17-23 on a sheet of paper.Draw rays on the diagram to determine theheight and location of the image.

Chapter 17 continuedb. What is the image height?O1I1Horizontal scale:1 block ! 1.0 cmVertical scale:2 blocks ! 1.0 cmhi ! 1.0 cmdi ! "2.7 cmhim ! !!hoF"dihohi ! !!do"(22.9 cm)(2.4 cm)30.0 cm! !!!The image height is 1.0 cm, and itslocation is 2.7 cm from the mirror.Level 276. An object is located 4.4 cm in front of aconcave mirror with a 24.0-cm radius.Locate the image using the mirror equation.78. What is the radius of curvature of a concavemirror that magnifies an object by a factorof #3.2 when the object is placed 20.0 cmfrom the mirror?him ! !!rf ! !!2ho24.0 cm2! !!! 12.0 cm111!! ! !! # !!dodifd fdo " fdi ! !o!(4.4 cm)(12.0 cm)4.4 cm " 12.0 cm! !!!! "6.9 cmCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.! "1.8 cmdi ! "mdo! "(3.2)(20.0 cm)! "64 cm111!! ! !! # !!dodifd ddo # diif ! !o!(20.0 cm)("64 cm)20.0 cm # ("64 cm)! !!!! 29 cm77. A concave mirror has a radius of curvatureof 26.0 cm. An object that is 2.4 cm tall isplaced 30.0 cm from the mirror.a. Where is the image position?r2f ! !!26.0 cm2! !!r ! 2f! (2)(29 cm)! 58 cm79. A convex mirror is needed to produce animage one-half the size of an object andlocated 36 cm behind the mirror. Whatfocal length should the mirror have?! 13.0 cm111!! ! !! # !!dodifd fdi ! !o!do " fhi"dihodom ! !! ! !!"dihodo ! !!hi"("36 cm)ho ho"!2!#(30.0 cm)(13.0 cm)! !!!30.0 cm " 13.0 cm!! 22.9 cm! 72 cm111!! ! !! # !!dodifPhysics: Principles and ProblemsSolutions Manual369

Chapter 17 continueda. What kind of mirror would do this job?dodif ! !!do # diAn enlarged, upright image resultsonly from a concave mirror, with theobject inside the focal length.(72 cm)("36 cm)72 cm # ("36 cm)! !!!b. What is its radius of curvature?! "72 cm"dim ! !!80. Surveillance Mirror A convenience storeuses a surveillance mirror to monitor thestore’s aisles. Each mirror has a radius ofcurvature of 3.8 m.dodi ! "mdo ! "(7.5)(14.0 mm)! "105 mma. What is the image position of a customerwho stands 6.5 m in front of the mirror?111!! # !! ! !!dodifA mirror that is used for surveillanceis a convex mirror. So the focallength is the negative of half theradius of curvature.dodi(14.0 mm)("105 mm)14.0 mm # ("105 mm)f ! !! ! !!!di # do! 16 mmr ! 2f ! (2)(16mm)! 32 mm"r2f ! !!"3.8 m2! !!! "1.9 m111!! ! !! # !!dodif82. The object in Figure 17-24 moves fromposition 1 to position 2. Copy the diagramonto a sheet of paper. Draw rays showinghow the image changes.d fdo " fdi ! !o!1C2F! "1.5 m1.0 mb. What is the image height of a customerwho is 1.7 m tall?hi"dihodo1.5 m2.0 m2.5 mm ! !! ! !! "dihohi ! !!doO1"("1.5 m)(1.7 m)6.5 mLevel 381. Inspection Mirror A production-lineinspector wants a mirror that produces animage that is upright with a magnificationof 7.5 when it is located 14.0 mm from amachine part.370Solutions ManualO21Ray 1Ray 2Ray 2! !!!! 0.38 mRay 1Figure 17-242CFI1I2Horizontal scale:1 block ! 10 cm83. A ball is positioned 22 cm in front of a spherical mirror and forms a virtual image. If thespherical mirror is replaced with a plane mirror, the image appears 12 cm closer to the mirror. What kind of spherical mirror was used?Physics: Principles and ProblemsCopyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.(6.5 m)("1.9 m)6.5 m " ("1.9 m)! !!!

Chapter 17 continuedThe object position for both mirrors is22 cm. So, the image position for theplane mirror is "22 cm.Because the spherical mirror forms avirtual image, the image is locatedbehind the mirror. Thus, the image position for the spherical mirror is negative.! "34 cm111!! ! !! # !!dodifd ddo # diif ! !o!(22 cm)("34 cm)22 cm # ("34 cm)hi ! 2.4 mdi ! 14 mCFI1The image is 2.4 m tall, and it is 14 mfrom the mirror.86. A 4.0-cm-tall object is placed 12.0 cm from aconvex mirror. If the image of the object is2.0 cm tall, and the image is located at"6.0 cm, what is the focal length of the mirror? Draw a ray diagram to answer the question. Use the mirror equation and the magnification equation to verify your answer.! !!!O1 Ray 1! 62 cmI1Ray 2The focal length is positive, so thespherical mirror is a concave mirror.hi"dihodod ddo # diif ! !o!"hidodi ! !!ho(12.0 cm)("6.0 cm)12.0 cm # ("6.0 cm)! !!!"(0.28 m)(3.2 m)1.6 m! !!!111!! ! !! # !!dodifd ddo # diif ! !o!(3.2 m)("0.56 m)3.2 m # ("0.56 m)! !!!f ! "12 cm111!! ! !! # !!fdodim ! !! ! !!! "0.56 mFHorizontal scale:1 block ! 1.0 cmVertical scale:3 blocks ! 2.0 cm84. A 1.6-m-tall girl stands 3.2 m from a convexmirror. What is the focal length of the mirrorif her image appears to be 0.28 m tall?Copyright Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.Horizontal scale:1 block ! 1.0 mVertical scale:2 blocks ! 1.0 mRay 2di ! di, plane " 12 cm! "22 cm " 12 cmRay 1O1! "12 cmThinking Criticallypages 481–48287. Apply Concepts The ball in Figure 17-25slowly rolls toward the concave mirror on theright. Describe how the size of the ball’s imagechanges as it rolls along.! "0.68 m85. Magic Trick A magician uses a concavemirror with a focal length of 8.0 m to make a3.0-m-tall hidden object, located 18.0 m fromthe mirror, appear as a real image that is seenby his audience. Draw a scale ray diagram tofind the height and location of the image.Physics: Principles and ProblemsC FFigure 17-25Solutions Manual371

Chapter 17 continuedmirror, what is the focal length of the concave mirror?Beyond C, the image is smaller than theball. As the ball rolls toward the mirror,the image size increases. The image isthe same size as the ball when the ballis at C. The image size continues toincrease until there is no image whenthe ball is at F. Past F, the size of theimage decreases until it equals theball’s size when the ball touches themirror.di, initial ! do, initial! 6.0 cmdi ! di, initial # ("8.0 cm)! "6.0 cm # ("8.0 cm)! "14.0 cm111!! ! !! # !!dodif88. Analyze and Conclude The object inFigure 17-26 is located 22 cm from aconcave mirror. What is the focal lengthof the mirror?d ddo # diif ! !o!(6.0 cm)("14.0 cm)6.0 cm # ("14.0 cm)f ! !!!f ! 1.0&101 cm22 cm 91. Analyze and Conclude The layout of thetwo-mirror system shown in Figure 17-11 isthat of a Gregorian telescope. For thisquestion, the larger concave mirror has aradius of curvature of 1.0 m, and thesmaller mirror is located 0.75 m away. Whyis the secondary mirror concave?r2f ! !!do! !!222 cm2! !!! 11 cm89. Use Equations Show that as the radius ofcurvature of a concave mirror increases toinfinity, the mirror equation reduces to therelationship between the object positionand the image position for a plane mirror.92. Analyze and Conclude An optical arrangement used in some telescopes is theCassegrain focus, shown in Figure 17-27.This telescope uses a convex secondarymirror that is positioned between theprimary mirror and the focal point ofthe primary mirror.Convexsecondary mirrorAs f %, 1/f 0. The mirror equationthen becomes 1/do ! "1/di, or do ! "di.90. Analyze and Conclude An object is located6.0 cm from a plane mirror. If the pla

Physics: Principles and . 17 Reflection and Mirrors CHAPTER Practice Problems 17.1 Reflection from Plane Mirrors pages 457–463 page 460 1. Explain why the reflection of light off ground glass changes from diffuse to specular if you spill water on it. .