17 Reflection and Mirrors

Transcription

1 CHAPTER 17 Reflectin an Mirrrs Cpyright Glence/McGraw-Hill, a ivisin f The McGraw-Hill Cmpanies, Inc. Practice Prblems 17.1 Reflectin frm Plane Mirrrs pages page Explain why the reflectin f light ff grun glass changes frm iffuse t specular if yu spill water n it. Water fills in the rugh areas an makes the surface smther.. If the angle f incience f a ray f light is 4, what is each f the fllwing? a. the angle f reflectin r i 4 b. the angle the incient ray makes with the mirrr i, mirrr 90 i c. the angle between the incient ray an the reflecte ray i r i If a light ray reflects ff a plane mirrr at an angle f 35 t the nrmal, what was the angle f incience f the ray? i r Light frm a laser strikes a plane mirrr at an angle f 38 t the nrmal. If the laser is mve s that the angle f incience increases by 13, what is the new angle f reflectin? i i, initial r i Tw plane mirrrs are psitine at right angles t ne anther. A ray f light strikes ne mirrr at an angle f 30 t the nrmal. It then reflects twar the secn mirrr. What is the angle f reflectin f the light ray ff the secn mirrr? r1 i1 30 i 90 r Sectin Review 17.1 Reflectin frm Plane Mirrrs pages page Reflectin A light ray strikes a flat, smth, reflecting surface at an angle f 80 t the nrmal. What is the angle that the reflecte ray makes with the surface f the mirrr? r i 80 r, mirrr 90 r Law f Reflectin Explain hw the law f reflectin applies t iffuse reflectin. The law f reflectin applies t iniviual rays f light. Rugh surfaces make the light rays reflect in many ifferent irectins. 8. Reflecting Surfaces Categrize each f the fllwing as a specular r a iffuse reflecting surface: paper, plishe metal, winw glass, rugh metal, plastic milk jug, smth water surface, an grun glass. Specular: winw glass, smth water, plishe metal. Diffuse: paper, rugh metal, grun glass, plastic milk jug. 9. Image Prperties A 50-cm-tall g stans 3 m frm a plane mirrr an lks at its image. What is the image psitin, height, an type? 3 m Physics: Principles an Prblems Slutins Manual 357

2 Chapter 17 cntinue h 50 cm The image is virtual. 10. Image Diagram A car is fllwing anther car wn a straight ra. The first car has a rear winw tilte 45. Draw a ray iagram shwing the psitin f the Sun that wul cause sunlight t reflect int the eyes f the river f the secn car. Driver f secn car The Sun s psitin irectly verhea wul likely reflect light int the river s eyes, accring t the law f reflectin. 11. Critical Tnking Explain hw iffuse reflectin f light ff an bject enables yu t see an bject frm any angle. The incming light reflects ff the surface f the bject in all irectins. Ts enables yu t view the bject frm any lcatin. Practice Prblems 17. Curve Mirrrs pages page Use a ray iagram, rawn t scale, t slve Example Prblem. Hrizntal scale: 1 blck 1.0 cm Vertical scale: 3 blcks 1.0 cm The Sun C Ray 1 Ray I 1 Rear winw f first car Ra grae 13. An bject is 36.0 cm in frnt f a cncave mirrr with a 16.0-cm fcal length. Determine the image psitin. 1 f 1 1 f f 8.8 cm 14. A 3.0-cm-tall bject is 0.0 cm frm a 16.0-cm-raius cncave mirrr. Determine the image psitin anmage height. 1 f 1 1 f f m i h ih.0 cm 13.3 cm 15. A cncave mirrr has a 7.0-cm fcal length. A.4-cm-tall bject is 16.0 cm frm the mirrr. Determine the image height. 1 f 1 1 f f 1.4 cm m i h (36.0 cm)(16.0 cm) 36.0 cm 16.0 cm (16.0 cm)(7.0 cm) 16.0 cm 7.0 cm (0.0 cm) 16.0 cm 0.0 cm 16.0 cm h (1.4 cm)(.4 cm) 16.0 cm 1.9 cm (13.3 cm)(3.0 cm) 0.0 cm Cpyright Glence/McGraw-Hill, a ivisin f The McGraw-Hill Cmpanies, Inc. 358 Slutins Manual Physics: Principles an Prblems

3 Chapter 17 cntinue 16. An bject is near a cncave mirrr f 10.0-cm fcal length. The image is 3.0 cm tall, inverte, an 16.0 cm frm the mirrr. What are the bject psitin an bject height? 1 f 1 1 i f i f 6.7 cm m i h h (16.0 cm)(10.0 cm) 16.0 cm 10.0 cm 5.0 cm i (6.7 cm)(3.0 cm) 16.0 cm page An bject is lcate 0.0 cm in frnt f a cnvex mirrr with a 15.0-cm fcal length. in the image psitin using bth a scale iagram an the mirrr equatin. f f 10.7 cm m i h m ( 10.7 cm) cm mh (0.178)(6.0 cm) 1.1 cm 19. A cnvex mirrr is neee t pruce an image that is three-furths the size f an bject an lcate 4 cm ben the mirrr. What fcal length shul be specifie? 1 f 1 1 i f (60.0 cm)(13.0 cm) 60.0 cm (13.0 cm) s m an m i 4 cm an m 0.75, s Cpyright Glence/McGraw-Hill, a ivisin f The McGraw-Hill Cmpanies, Inc f s f f Ray 1 Ray Hrizntal scale: 1 blck 1.0 cm 8.57 cm 18. A cnvex mirrr has a fcal length f 13.0 cm. A lightbulb with a iameter f 6.0 cm is place 60.0 cm frm the mirrr. What is the lightbulb s image psitin an iameter? f (0.0 cm)(15.0 cm) 0.0 cm (15.0 cm) I cm ( 4 cm) cm Physics: Principles an Prblems Slutins Manual 359 f 96 cm 0. A 7.6-cm-iameter ball is lcate.0 cm frm a cnvex mirrr with a raius f curvature f 60.0 cm. What are the ball s image psitin an iameter? 1 f 1 1 f f (3 cm)(4 cm) 3 cm (4 cm) (.0 cm)(30.0 cm).0 cm (30.0 cm) 1.7 cm

4 Chapter 17 cntinue m i h ih 4.4 cm 1. A 1.8-m-tall girl stans.4 m frm a stre s security mirrr. Her image appears t be 0.36 m tall. What is the fcal length f the mirrr? m i h h 0.48 m 1 f 1 1 i f i (1.7 cm)(7.6 cm).0 cm (.4 m)(0.36 m) 1.8 m (0.48 m)(.4 m) 0.48 m.4 m 0.60 m Sectin Review 17. Curve Mirrrs pages page 473. Image Prperties If yu knw the fcal length f a cncave mirrr, where shul yu place an bject s that its image is upright an larger cmpare t the bject? Will ts pruce a real r virtual image? Yu shul place the bject between the mirrr an the fcal pint. The image will be virtual. 3. Magnificatin An bject is place 0.0 cm in frnt f a cncave mirrr with a fcal length f 9.0 cm. What is the magnificatin f the image? 1 f 1 1 f f 16.4 cm m i 16.4 cm 0.0 cm Object Psitin The placement f an bject in frnt f a cncave mirrr with a fcal length f 1.0 cm frms a real image that is.3 cm frm the mirrr. What is the bject psitin? 1 f 1 1 i f i f (0.0 cm)(9.0 cm) 0.0 cm 9.0 cm (.3 cm)(1.0 cm).3 cm 1.0 cm 6.0 cm 5. Image Psitin an Height A 3.0-cm-tall bject is place.0 cm in frnt f a cncave mirrr having a fcal length f 1.0 cm. in the image psitin an height by rawing a ray iagram t scale. Verify yur answer using the mirrr an magnificatin equatins. 3.6 cm 6.4 cm 1 f 1 1 f f I 1 C Ray 1 Ray Hrizntal scale: 1 blck 1.0 cm Vertical scale: 1 blck 1.0 cm Cpyright Glence/McGraw-Hill, a ivisin f The McGraw-Hill Cmpanies, Inc. 360 Slutins Manual Physics: Principles an Prblems

5 Chapter 17 cntinue 6.4 cm m i h ih (.0 cm)(1.0 cm).0 cm 1.0 cm (6.4 cm)(3.0 cm).0 cm 3.6 cm m i h h (16.4 cm)(.8 cm) 6.0 cm 7.7 cm 1 f 1 1 f Cpyright Glence/McGraw-Hill, a ivisin f The McGraw-Hill Cmpanies, Inc. 6. Ray Diagram A 4.0-cm-tall bject is lcate 14.0 cm frm a cnvex mirrr with a fcal length f 1.0 cm. Draw a scale ray iagram shwing the image psitin an height. Verify yur answer using the mirrr an magnificatin equatins. 1 f 1 f f 6.46 cm m i h ih Ray 1 Ray Hrizntal scale: 1 blck 1.0 cm Vertical scale: 3 blcks.0 cm 1 i 1.8 cm 7. Raius f Curvature A 6.0-cm-tall bject is place 16.4 cm frm a cnvex mirrr. If the image f the bject is.8 cm tall, what is the raius f curvature f the mirrr? I 1 (14.0 cm)(1.0 cm) 14.0 cm (1.0 cm) (6.46 cm)(4.0 cm) 14.0 cm 1.8 cm 6.5 cm Physics: Principles an Prblems Slutins Manual cm r f ()( 14.5 cm ) 9 cm 8. cal Length A cnvex mirrr is use t pruce an image that is tw-trs the size f an bject an lcate 1 cm ben the mirrr. What is the fcal length f the mirrr? m i h m 18 cm 1 f 1 1 f (7.7 cm)(16.4 cm) 7.7 cm 16.4 cm 36 cm (1 cm) 3 (1 cm)(18 cm) 1 cm 18 cm 9. Critical Tnking Wul spherical aberratin be less fr a mirrr whse height, cmpare t its raius f curvature, is small r large? Explain. It wul be less fr a mirrr whse height is relatively small cmpare t

6 Chapter 17 cntinue its raius f curvature; iverging light rays frm an bject that strike the mirrr are mre paraxial s they cnverge mre clsely t create an image that is nt blurre. Chapter Assessment Cncept Mapping page Cmplete the fllwing cncept map using the fllwing terms: cnvex, upright, inverte, real, virtual. plane Mirrrs cncave cnvex virtual real virtual virtual upright inverte upright upright 34. Describe the prperties f a plane mirrr. (17.1) A plane mirrr is a flat, smth surface frm wch light is reflecte by specular reflectin. The images create by plane mirrrs are virtual, upright, an as far ben the mirrr as the bject is in frnt f it. 35. A stuent believes that very sensitive phtgrapc film can etect a virtual image. The stuent puts phtgrapc film at the lcatin f a virtual image. Des ts attempt succee? Explain. (17.1) N, the rays nt cnverge at a virtual image. N image frms an the stuent wul nt get a picture. Sme virtual images are ben the mirrr. 36. Hw can yu prve t smene that an image is a real image? (17.1) Place a sheet f plain paper r phtgrapc film at the image lcatin an yu shul be able t fin the image. Mastering Cncepts page Hw es specular reflectin iffer frm iffuse reflectin? (17.1) When parallel light is reflecte frm a smth surface, the rays are reflecte parallel t each ther. The result is an image f the rigin f the rays. When light is reflecte frm a rugh surface, it is reflecten many ifferent irectins. The rays are iffuse r scattere. N image f the surce results. 3. What is meant by the phrase nrmal t the surface? (17.1) any line that is perpenicular t the surface at any pint 33. Where is the image pruce by a plane mirrr lcate? (17.1) The image is n a line that is perpenicular t the mirrr an the same istance ben the mirrr as the bject is in frnt f the mirrr. 37. An bject pruces a virtual image in a cncave mirrr. Where is the bject lcate? (17.) Object must be lcate between an the mirrr. 38. What is the efect that all cncave spherical mirrrs have an what causes it? (17.) Rays parallel t the axis that strike the eges f a cncave spherical mirrr are nt reflecte thrugh the fcal pint. Ts effect is calle spherical aberratin. 39. What is the equatin relating the fcal pint, bject psitin, anmage psitin? (17.) 1 f 1 1 i 40. What is the relatinsp between the center f curvature an the fcal length f a cncave mirrr? (17.) C f 36 Slutins Manual Physics: Principles an Prblems Cpyright Glence/McGraw-Hill, a ivisin f The McGraw-Hill Cmpanies, Inc.

7 Chapter 17 cntinue 41. If yu knw the image psitin an bject psitin relative t a curve mirrr, hw can yu etermine the mirrr s magnificatin? (17.) The magnificatin is equal t the negative f the image istance ivie by the bject istance. 4. Why are cnvex mirrrs use as rearview mirrrs? (17.) Cnvex mirrrs are use as rearview mirrrs because they allw fr a wie range f view, allwing the river t see a much larger area than is affre by rinary mirrrs. 43. Why is it impssible fr a cnvex mirrr t frm a real image? (17.) The light rays always iverge. Applying Cncepts pages Wet Ra A ry ras mre f a iffuse reflectr than a wet ra. Base n igure 17-16, explain why a wet ra appears blacker t a river than a ry ra es. 46. Lcate an escribe the physical prperties f the image pruce by a cncave mirrr when the bject is lcate at the center f curvature. The image will be at C, the center f curvature, inverte, real, an the same size as the bject. 47. An bject is lcate beyn the center f curvature f a spherical cncave mirrr. Lcate an escribe the physical prperties f the image. The image will be between C an, an will be inverte, real, an smaller than the bject. 48. Telescpe Yu have t rer a large cncave mirrr fr a telescpe that pruces gh-quality images. Shul yu rer a spherical mirrr r a parablic mirrr? Explain. Yu shul rer a parablic mirrr t eliminate spherical aberratins. 49. Describe the prperties f the image seen in the single cnvex mirrr in igure Cpyright Glence/McGraw-Hill, a ivisin f The McGraw-Hill Cmpanies, Inc. igure Wet asphalt Dry asphalt Less light is reflecte back t the car frm a wet ra. 45. Bk Pages Why is it esirable that the pages f a bk be rugh rather than smth an glssy? The smther an glssier the pages are, the lesser the iffuse reflectin f light an the greater the glare frm the pages. igure The image in a single cnvex mirrr is always virtual, erect, smaller than the bject, an lcate clser t the mirrr than the bject. Physics: Principles an Prblems Slutins Manual 363

8 Chapter 17 cntinue 50. List all the pssible arrangements in wch yu cul use a spherical mirrr, either cncave r cnvex, t frm a real image. Yu can use nly a cncave mirrr with the bject beyn the fcal pint. A cnvex mirrr will nt frm a real image. 51. List all pssible arrangements in wch yu cul use a spherical mirrr, either cncave r cnvex, t frm an image that is smaller cmpare t the bject. Yu may use a cncave mirrr with the bject beyn the center f curvature r a cnvex mirrr with the bject anywhere. 5. Rearview Mirrrs The utsie rearview mirrrs f cars ften carry the warning Objects in the mirrr are clser than they appear. What kin f mirrrs are these an what avantage they have? Cnvex mirrr; it prvies a wier fiel f view. Mastering Prblems 17.1 Reflectin frm Plane Mirrrs page 479 Level A ray f light strikes a mirrr at an angle f 38 t the nrmal. What is the angle that the reflecte angle makes with the nrmal? r i A ray f light strikes a mirrr at an angle f 53 t the nrmal. a. What is the angle f reflectin? r i 53 b. What is the angle between the incient ray an the reflecte ray? i r A ray f light incient upn a mirrr makes an angle f 36 with the mirrr. What is the angle between the incient ray an the reflecte ray? i r i 54 i r Level 56. Picture in a Mirrr Penny wishes t take a picture f her image in a plane mirrr, as shwn in igure If the camera is 1. m in frnt f the mirrr, at what istance shul the camera lens be fcuse? igure The image is 1. m ben the mirrr, s the camera lens shul be set t.4 m. 57. Tw ajacent plane mirrrs frm a right angle, as shwn in igure A light ray is incient upn ne f the mirrrs at an angle f 30 t the nrmal. Cpyright Glence/McGraw-Hill, a ivisin f The McGraw-Hill Cmpanies, Inc. 364 Slutins Manual Physics: Principles an Prblems

9 Chapter 17 cntinue the feet ts the mirrr halfway between the eyes an the feet. The istance between the pint the tw rays t the mirrr is half the ttal height. Cpyright Glence/McGraw-Hill, a ivisin f The McGraw-Hill Cmpanies, Inc. igure a. What is the angle at wch the light ray is reflecte frm the ther mirrr? Reflectin frm the first mirrr: r1 i1 30 Reflectin frm the secn mirrr: i 90 r r i 60 b. A retrreflectr is a evice that reflects incming light rays back in a irectin ppsite t that f the incient rays. Draw a iagram shwing the angle f incience n the first mirrr fr wch the mirrr system acts as a retrreflectr. 58. Draw a ray iagram f a plane mirrr t shw that if yu want t see yurself frm yur feet t the tp f yur hea, the mirrr must be at least half yur height. Eye level eet Mirrr Image The ray frm the tp f the hea ts the mirrr halfway between the eyes an the tp f the hea. The ray frm Level Tw plane mirrrs are cnnecte at their sies s that they frm a 45 angle between them. A light ray strikes ne mirrr at an angle f 30 t the nrmal an then reflects ff the secn mirrr. Calculate the angle f reflectin f the light ray ff the secn mirrr. Reflectin frm the first mirrr is r, 1 i, The angle the ray frms with the mirrr is thus Because the tw mirrrs frm a 45 angle, the angle the ray reflecting ff the first mirrr frms with the secn mirrr is The angle the ray frms with the secn mirrr is thus i, The angle f reflectin frm the secn mirrr is r, i, A ray f light strikes a mirrr at an angle f 60 t the nrmal. The mirrr is then rtate 18 clckwise, as shwn in igure What is the angle that the reflecte ray makes with the mirrr? Nrmal i i, l Incient light Mirrr igure 17-0 Physics: Principles an Prblems Slutins Manual 365

10 Chapter 17 cntinue r i 4 r, mirrr 90 r C 17. Curve Mirrrs page 480 Level A cncave mirrr has a fcal length f 10.0 cm. What is its raius f curvature? r f (10.0 cm) 0.0 cm 6. An bject lcate 18 cm frm a cnvex mirrr pruces a virtual image 9 cm frm the mirrr. What is the magnificatin f the image? m i ( 9 cm) 18 cm un Huse A by is staning near a cnvex mirrr in a fun huse at a fair. He ntices that s image appears t be 0.60 m tall. If the magnificatin f the mirrr is 1, what is the by s height? 3 m h h m 0.60 m m 64. Describe the image pruce by the bject in igure 17-1 as real r virtual, inverte r upright, an smaller r larger than the bject. real; inverte; larger igure 17-1 Level 65. Star Image Light frm a star is cllecte by a cncave mirrr. Hw far frm the mirrr is the image f the star if the raius f curvature is 150 cm? Stars are far enugh away that the light cming int the mirrr can be cnsiere t be parallel an parallel light will cnverge at the fcal pint. Since r f, r 150 cm f 75 cm 66. in the image psitin an height fr the bject shwn in igure f 1 1 f f 3.8 cm 31 cm (31 cm)(16 cm) 31 cm 16 cm 16 cm igure 17- Cpyright Glence/McGraw-Hill, a ivisin f The McGraw-Hill Cmpanies, Inc. 366 Slutins Manual Physics: Principles an Prblems

11 Cpyright Glence/McGraw-Hill, a ivisin f The McGraw-Hill Cmpanies, Inc. Chapter 17 cntinue 33 cm m i h ih 4.1 cm 67. Rearview Mirrr Hw far es the image f a car appear ben a cnvex mirrr, with a fcal length f 6.0 m, when the car is 10.0 m frm the mirrr? 1 f 1 1 f f 3.8 m 68. An bject is 30.0 cm frm a cncave mirrr f 15.0 cm fcal length. The bject is 1.8 cm tall. Use the mirrr equatin t fin the image psitin. What is the image height? f f f 30.0 cm m i h ih (33 cm)(3.8 cm) 31 cm (10.0 m)(6.0 m) 10.0 m (6.0 m) (30.0 cm)(15.0 cm) 30.0 cm 15.0 cm (30.0 cm)(1.8 cm) (30.0 cm) 1.8 cm 69. Dental Mirrr A entist uses a small mirrr with a raius f 40 mm t lcate a cavity in a patient s tth. If the mirrr is cncave ans hel 16 mm frm the tth, what is the magnificatin f the image? f r ( f f f mm) 0 mm m i ( 80 mm) 5 16 mm 80 mm 70. A 3.0-cm-tall bject is.4 cm frm a cncave mirrr. If the mirrr has a raius f curvature f 34.0 cm, what are the image psitin an height? f r 34.0 cm 17.0 cm 1 f 1 1 f f 70.5 cm m i h ih (.4 cm)(17.0 cm).4 cm 17.0 cm (70.5 cm)(3.0 cm).4 cm 9.4 cm Level Jeweler s Mirrr A jeweler inspects a watch with a iameter f 3.0 cm by placing it 8.0 cm in frnt f a cncave mirrr f 1.0-cm fcal length. a. Where will the image f the watch appear? f (16 mm)(0 mm) 16 mm 0 mm Physics: Principles an Prblems Slutins Manual 367

12 Chapter 17 cntinue f f 4 cm b. What will be the iameter f the image? i h ih 9.0 cm 7. Sunlight falls n a cncave mirrr an frms an image that is 3.0 cm frm the mirrr. An bject that is 4 mm tall is place 1.0 cm frm the mirrr. a. Sketch the ray iagram t shw the lcatin f the image. b. Use the mirrr equatin t calculate the image psitin f f f 4.0 cm c. Hw tall is the image? m i 4. 0 cm cm mh (0.33)(4 mm) 8.0 mm (8.0 cm)(1.0 cm) 8.0 cm 1.0 cm (4 cm)(3.0 cm) 8.0 cm Ray 1 Ray C Hrizntal scale: I 1 blck 1.0 cm 1 Vertical scale: 1 blck 4 mm (3.0 cm)(1.0 cm) 1.0 cm 3.0 cm 73. Sny spheres that are place n peestals n a lawn are cnvex mirrrs. One such sphere has a iameter f 40.0 cm. A 1-cm-tall rbin sits in a tree that is 1.5 m frm the sphere. Where is the image f the rbin an hw tall is the image? r 0.0 cm, f 10.0 cm f f f 9.4 cm m i ( 9.4 cm) cm mh (0.063)(1 cm) 0.75 cm Mixe Review pages Level A light ray strikes a plane mirrr at an angle f 8 t the nrmal. If the light surce is mve s that the angle f incience increases by 34, what is the new angle f reflectin? i i, initial r i 6 (10.0 cm)(150 cm) 150 cm (10.0 cm) 75. Cpy igure 17-3 n a sheet f paper. Draw rays n the iagram t etermine the height an lcatin f the image. 3.0 cm 8.0 cm 4.0 cm igure 17-3 Cpyright Glence/McGraw-Hill, a ivisin f The McGraw-Hill Cmpanies, Inc. 368 Slutins Manual Physics: Principles an Prblems

13 Chapter 17 cntinue The image height is 1.0 cm, ants lcatin is.7 cm frm the mirrr. Level 76. An bject is lcate 4.4 cm in frnt f a cncave mirrr with a 4.0-cm raius. Lcate the image using the mirrr equatin. f r Hrizntal scale: 1 blck 1.0 cm Vertical scale: blcks 1.0 cm I cm.7 cm b. What is the image height? m h ih 1.8 cm 78. What is the raius f curvature f a cncave mirrr that magnifies an bject by a factr f 3. when the bject is place 0.0 cm frm the mirrr? m h (.9 cm)(.4 cm) 30.0 cm Cpyright Glence/McGraw-Hill, a ivisin f The McGraw-Hill Cmpanies, Inc. 4.0 cm 1.0 cm 1 f 1 1 f f (4.4 cm)(1.0 cm) 4.4 cm 1.0 cm 6.9 cm 77. A cncave mirrr has a raius f curvature f 6.0 cm. An bject that is.4 cm tall is place 30.0 cm frm the mirrr. a. Where is the image psitin? f r 6.0 cm 13.0 cm 1 f 1 1 f f (30.0 cm)(13.0 cm) 30.0 cm 13.0 cm.9 cm m (3.)(0.0 cm) 64 cm 1 f 1 1 f i 9 cm r f (0.0 cm)(64 cm) 0.0 cm (64 cm) ()(9 cm) 58 cm 79. A cnvex mirrr is neee t pruce an image ne-half the size f an bject an lcate 36 cm ben the mirrr. What fcal length shul the mirrr have? m i h ih h i 7 cm 1 f 1 1 (36 cm)h h Physics: Principles an Prblems Slutins Manual 369

14 Chapter 17 cntinue f (7 cm)(36 cm) 7 cm (36 cm) 7 cm 80. Surveillance Mirrr A cnvenience stre uses a surveillance mirrr t mnitr the stre s aisles. Each mirrr has a raius f curvature f 3.8 m. a. What is the image psitin f a custmer wh stans 6.5 m in frnt f the mirrr? A mirrr that is use fr surveillance is a cnvex mirrr. S the fcal lengts the negative f half the raius f curvature. f r 3. 8m 1.9 m 1 f 1 1 f f 1.5 m b. What is the image height f a custmer ws 1.7 m tall? m i h ih (6.5 m)(1.9 m) 6.5 m (1.9 m) 0.38 m (1.5 m)(1.7 m) 6.5 m Level Inspectin Mirrr A pructin-line inspectr wants a mirrr that pruces an image that is upright with a magnificatin f 7.5 when it is lcate 14.0 mm frm a macne part. a. What kin f mirrr wul ts jb? An enlarge, upright image results nly frm a cncave mirrr, with the bject insie the fcal length. b. What is its raius f curvature? m i m (7.5)(14.0 mm) 105 mm f f i 16 mm r f ()(16mm) 3 mm 8. The bject in igure 17-4 mves frm psitin 1 t psitin. Cpy the iagram nt a sheet f paper. Draw rays shwing hw the image changes. 1 C Ray 1 O Ray 1 Ray 1 C (14.0 mm)(105 mm) 14.0 mm (105 mm).5 m Ray I 1 I Hrizntal scale: 1 blck 10 cm igure A ball is psitine cm in frnt f a spherical mirrr an frms a virtual image. If the spherical mirrr is replace with a plane mirrr, the image appears 1 cm clser t the mirrr. What kin f spherical mirrr was use?.0 m 1.5 m 1.0 m Cpyright Glence/McGraw-Hill, a ivisin f The McGraw-Hill Cmpanies, Inc. 370 Slutins Manual Physics: Principles an Prblems

15 Cpyright Glence/McGraw-Hill, a ivisin f The McGraw-Hill Cmpanies, Inc. Chapter 17 cntinue The bject psitin fr bth mirrrs is cm. S, the image psitin fr the plane mirrr is cm. Because the spherical mirrr frms a virtual image, the image is lcate ben the mirrr. Thus, the image psitin fr the spherical mirrr is negative., plane 1 cm cm 1 cm 34 cm 1 f 1 1 f i 6 cm The fcal lengts psitive, s the spherical mirrr is a cncave mirrr. 84. A 1.6-m-tall girl stans 3. m frm a cnvex mirrr. What is the fcal length f the mirrr if her image appears t be 0.8 m tall? m i h i h h 0.56 m 1 f 1 1 f i ( cm)(34 cm) cm (34 cm) (0.8 m)(3. m) 1.6 m (3. m)(0.56 m) 3. m (0.56 m) 0.68 m 85. Magic Trick A magician uses a cncave mirrr with a fcal length f 8.0 m t make a 3.0-m-tall en bject, lcate 18.0 m frm the mirrr, appear as a real image that is seen by s auience. Draw a scale ray iagram t fin the height an lcatin f the image..4 m 14 m The image is.4 m tall, ant is 14 m frm the mirrr. 86. A 4.0-cm-tall bject is place 1.0 cm frm a cnvex mirrr. If the image f the bject is.0 cm tall, an the image is lcate at 6.0 cm, what is the fcal length f the mirrr? Draw a ray iagram t answer the questin. Use the mirrr equatin an the magnificatin equatin t verify yur answer. 1 f 1 1 f i C I 1 Hrizntal scale: 1 blck 1.0 cm Vertical scale: 3 blcks.0 cm (1.0 cm)(6.0 cm) 1.0 cm (6.0 cm) 1 cm Tnking Critically pages Apply Cncepts The ball in igure 17-5 slwly rlls twar the cncave mirrr n the right. Describe hw the size f the ball s image changes as it rlls alng. igure 17-5 Ray 1 Ray 1 Ray C Ray Hrizntal scale: 1 blck 1.0 m Vertical scale: blcks 1.0 m I 1 f 1 cm Physics: Principles an Prblems Slutins Manual 371

16 Chapter 17 cntinue Beyn C, the image is smaller than the ball. As the ball rlls twar the mirrr, the image size increases. The image is the same size as the ball when the ball is at C. The image size cntinues t increase until there is n image when the ball is at. Past, the size f the image ecreases until it equals the ball s size when the ball tuches the mirrr. 88. Analyze an Cnclue The bject in igure 17-6 is lcate cm frm a cncave mirrr. What is the fcal length f the mirrr? mirrr, what is the fcal length f the cncave mirrr?, initial, initial 6.0 cm, initial (8.0 cm) 6.0 cm (8.0 cm) 14.0 cm 1 f 1 1 f i f (6.0 cm)(14.0 cm) 6.0 cm (14.0 cm) f cm igure 17-6 f r cm 11 cm cm 89. Use Equatins Shw that as the raius f curvature f a cncave mirrr increases t infinity, the mirrr equatin reuces t the relatinsp between the bject psitin an the image psitin fr a plane mirrr. As f, 1/f 0. The mirrr equatin then becmes 1/ 1/,r. 90. Analyze an Cnclue An bject is lcate 6.0 cm frm a plane mirrr. If the plane mirrr is replace with a cncave mirrr, the resulting image is 8.0 cm farther ben the mirrr. Assuming that the bject is lcate between the fcal pint an the cncave 91. Analyze an Cnclue The layut f the tw-mirrr system shwn in igure is that f a Gregrian telescpe. r ts questin, the larger cncave mirrr has a raius f curvature f 1.0 m, an the smaller mirrr is lcate 0.75 m away. Why is the secnary mirrr cncave? The smaller mirrr is cncave t pruce a real image at the eyepiece that is upright. The light rays are inverte by the first cncave mirrr an then inverte again by the secnary cncave mirrr. 9. Analyze an Cnclue An ptical arrangement usen sme telescpes is the Cassegrain fcus, shwn in igure Ts telescpe uses a cnvex secnary mirrr that is psitine between the primary mirrr an the fcal pint f the primary mirrr. Cnvex secnary mirrr Telescpe tube Cncave primary mirrr Eyepiece igure 17-7 a. A single cnvex mirrr pruces nly virtual images. Explain hw the cnvex 37 Slutins Manual Physics: Principles an Prblems Cpyright Glence/McGraw-Hill, a ivisin f The McGraw-Hill Cmpanies, Inc.

17 Cpyright Glence/McGraw-Hill, a ivisin f The McGraw-Hill Cmpanies, Inc. Chapter 17 cntinue mirrr in ts telescpe functins witn the system f mirrrs t pruce real images. The cnvex mirrr is place t intercept the rays frm a cncave mirrr befre they cnverge. The cnvex mirrr places the pint f cnvergence in the ppsite irectin back twar the cncave mirrr, an lengthens the ttal istance the light travels befre cnverging. Ts effectively increases the fcal length cmpare t using the cncave mirrr by itself, thus increasing the ttal magnificatin. b. Are the images pruce by the Cassegrain fcus upright r inverte? Hw es ts relate t the number f times that the light crsses? Inverte; each time the light rays crss the image inverts. Writing in Physics page Research a meth use fr grining, plisng, an testing mirrrs usen reflecting telescpes. Yu may reprt either n meths use by amateur astrnmers wh make their wn telescpe ptics, r n a meth use by a prject at a natinal labratry. Prepare a ne-page reprt escribing the meth, an present it t the class. Answers will vary epening n the mirrrs an meths chsen by the stuents. Amateur meths usually invlve rubbing tw blanks against each ther with varying grits between them. Meths use at natinal labs vary. 94. Mirrrs reflect light because f their metallic cating. Research an write a summary f ne f the fllwing: a. the ifferent types f catings use an the avantages an isavantages f each Answers will vary. Stuent answers shulnclue infrmatin abut sniness as well as tarnish resistance. b. the precisin ptical plisng f aluminum t such a egree f smthness that n glass is neeen the prcess f making a mirrr Answers will vary. Stuent answers might inclue infrmatin abut efrmatin f a mirrr frm its wn weight as size increases an hw a mirrr mae f aluminum cul impact ts prblem. Cumulative Review page A cl runs wn the schl hallway an then slies n the newly waxe flr. He was running at 4.7 m/s befre he starte sliing an he sli 6. m befre stpping. What was the cefficient f frictin f the waxe flr? (Chapter 11) The wrk ne by the waxe flr equals the cl s initial kinetic energy. KE 1 mv W k mg The mass f the cl cancels ut, giving v k g A 1.0 g piece f cpper falls frm a height f m frm an airplane t the grun. Because f air resistance it reaches the grun mving at a velcity f 70.0 m/s. Assuming that half f the energy lst by the piece was istribute as thermal energy t the cpper, hw muct heat uring the fall? (Chapter 1) Ptential energy f the piece E mgh ( kg)(9.80 m/s )( m) 9.8 J inal energy E f 1 mv (4.7 m/s) ()(9.80 m/s )(6. m) 1 ( kg)(70.0 m/s).4 J Physics: Principles an Prblems Slutins Manual 373

18 Chapter 17 cntinue Heat ae t the piece Q 1 (E E f ) 1 (9.8 J.4 J) 3.7 J Q T m c 9.5 C 97. It is pssible t lift a persn ws sitting n a pillw mae frm a large seale plastic garbage bag by blwing air int the bag thrugh a sa straw. Suppse that the crss-sectinal area f the persn sitting n the bag is 0.5 m an the persn s weight is 600 N. The sa straw has a crss-sectinal area f 10 5 m. With what pressure must yu blw int the straw t lift the persn that is sitting n the seale garbage bag? (Chapter 13) Apply Pascal s principle. 1 1 A A (600 N) 10 5 m 0.5 m N P A.4 kpa r kpa t ne significant igit nt a very large pressure at all 98. What wul be the peri f a.0-m-lng penulum n the Mn s surface? The Mn s mass is kg, ants raius is m. What is the peri f ts penulum n Earth? (Chapter 14) g m 3.7 J ( kg)(385 J/kg C) Gm m m 1.6 m/s T Mn g l T Earth g l N 10 5 m ( Nm /kg )( kg) m m /s 7.0 s.0 m 0 m /s.8 s 99. Organ pipes An rgan builer must esign a pipe rgan that will fit int a small space. (Chapter 15) a. Shul he esign the instrument t have pen pipes r clse pipes? Explain. The resnant frequency f an pen pipe is twice that f a clse pipe f the same length. Therefre, the pipes f a clse-pipe rgan nee be nly half as lng as pen pipes t pruce the same range f funamental frequencies. b. Will an rgan cnstructe with pen pipes sun the same as ne cnstructe with clse pipes? Explain. N. Wle the tw rgans will have the same funamental tnes, clse pipes pruce nly the harmnics, s they will have ifferent timbres than pen pipes ilters are ae t flashlights s that ne snes re light an the ther snes green light. The beams are crsse. Explain in terms f waves why the light frm bth flashlights is yellw where the beams crss, but revert back t their riginal clrs beyn the intersectin pint. (Chapter 16) Waves can interfere, a, an then pass thrugh unaffecte. Chapter 14 shwe the amplitue f waves aing. In ts case, the waves retain their clr infrmatin as they crss thrugh each ther. Challenge Prblem page 470 An bject f height h is lcate at relative t a cncave mirrr with fcal length f. 1. Draw an label a ray iagram shwing the fcal length an lcatin f the bject if the image is lcate twice as far frm the mirrr as the bject. Prve yur answer mathematically. Calculate the fcal length as a functin f bject psitin fr ts placement. Cpyright Glence/McGraw-Hill, a ivisin f The McGraw-Hill Cmpanies, Inc. 374 Slutins Manual Physics: Principles an Prblems

19 Chapter 17 cntinue 1 f 1 1 f i () 3 O C Ray 1 Ray f O 3 1 f 1 1 fi i f f m i h ih f(f) f f (f)h f. Draw an label a ray iagram shwing the lcatin f the bject if the image is lcate twice as far frm the mirrr as the fcal pint. Prve yur answer mathematically. Calculate the image height as a functin f the bject height fr ts placement. h 3. Where shul the bject be lcate s that n image is frme? The bject shul be place at the fcal pint. Ray 1 Cpyright Glence/McGraw-Hill, a ivisin f The McGraw-Hill Cmpanies, Inc. f h O Ray C I 1 Physics: Principles an Prblems Slutins Manual 375