Chapter 17 continued ␪ ϭ ␪ r i ϭ 42° ␪ ϭ ␪ r, mirror 90° r ϭ 90° 42° ϭ 48° C F 17.2 Curved Mirrors page 480 Level 1 61. A concave mirror has a focal length of I Figure 17-21 10.0 cm. What is its radius of curvature? real; inverted; larger r 2f 2(10.0 cm) 20.0 cm Level 2 62. An object located 18 cm from a convex 65. Star Image Light from a star is collected by mirror produces a virtual image 9 cm from a concave mirror. How far from the mirror the mirror. What is the magnification of the is the image of the star if the radius of image? curvature is 150 cm? Ϫd m ϭ ᎏᎏi Stars are far enough away that the do light coming into the mirror can be Ϫ(Ϫ9 cm) considered to be parallel and parallel ϭ ᎏᎏ 18 cm light will converge at the focal point. ϭ 0.5 Since r 2f, r 150 cm f ᎏᎏ ϭ ᎏᎏ 75 cm 63. Fun House A boy is standing near a 2 2 convex mirror in a fun house at a fair. He notices that his image appears to be 66. Find the image position and height for the Inc. Companies, a division of The McGraw-Hill © Glencoe/McGraw-Hill, Copyright 0.60 m tall. If the magnification of the object shown in Figure 17-22. mirror is ᎏ1ᎏ, what is the boy’s height? 3 h m ϭ ᎏᎏi ho h h ϭ ᎏᎏi 3.8 cm F o m 16 cm ϭ ᎏ0.60 m ΂ᎏ1ᎏ΃ 31 cm 3 ϭ 1.8 m 64. Describe the image produced by the object I Figure 17-22 in Figure 17-21 as real or virtual, inverted or upright, and smaller or larger than the ᎏ1ᎏ ϭ ᎏ1ᎏ ᎏ1ᎏ f d d object. o i d f ϭ ᎏoᎏ di Ϫ do f (31 cm)(16 cm) ϭ ᎏᎏ 31 cm Ϫ 16 cm 366 Solutions Manual Physics: Principles and Problems Chapter 17 continued ϭ 33 cm what is the magnification of the image? Ϫ r (40 mm) hi di f ϭ ᎏᎏ ϭ ᎏᎏ 20 mm m ϵ ᎏᎏ ϭ ᎏᎏ 2 2 ho do ᎏ1ᎏ ϩ ᎏ1ᎏ ϭ ᎏ1ᎏ Ϫd h d d f h ϭ ᎏᎏi o o i i d o d f (16 mm)(20 mm) ᎏoᎏ ϭϭᎏᎏ Ϫ Ϫ(33 cm)(3.8 cm) di Ϫ Ϫ 80 mm ϭ ᎏᎏᎏ do f 16 mm 20 mm 31 cm Ϫ di Ϫ(Ϫ80 mm) ϭϪ4.1 cm m ᎏᎏ ᎏᎏ 5 do 16 mm 67. Rearview Mirror How far does the image 70. A 3.0-cm-tall object is 22.4 cm from a of a car appear behind a convex mirror, concave mirror. If the mirror has a radius of Ϫ with a focal length of 6.0 m, when the car curvature of 34.0 cm, what are the image is 10.0 m from the mirror? position and height? 1 1 1 ᎏᎏ ϭ ᎏᎏ ϩ ᎏᎏ r f d d f ϭ ᎏᎏ o i 2 d f ϭ ᎏoᎏ ϭ ᎏ34.0ᎏcm di Ϫ do f 2 (10.0 m)(Ϫ6.0 m) ϭ 17.0 cm ϭ ᎏᎏᎏ 10.0 m Ϫ (Ϫ6.0 m) ᎏ1ᎏ ϭ ᎏ1ᎏ ᎏ1ᎏ ϭϪ3.8 m f do di d f ϭ ᎏoᎏ 68. An object is 30.0 cm from a concave mirror di Ϫ do f of 15.0 cm focal length. The object is (22.4 cm)(17.0 cm) 1.8 cm tall. Use the mirror equation to ϭ ᎏᎏᎏ 22.4 cm Ϫ 17.0 cm find the image position. What is the image height? ϭ 70.5 cm ᎏ1ᎏ ϩ ᎏ1ᎏ ϭ ᎏ1ᎏ h Ϫd m ϭ ᎏᎏi ϭ ᎏᎏi do di f ho do d f ᎏoᎏ Ϫd h di Ϫ ϭ ᎏᎏi o do f hi do (30.0 cm)(15.0 cm) ϭ ᎏᎏᎏ Ϫ(70.5 cm)(3.0 cm) 30.0 cm Ϫ 15.0 cm ϭ ᎏᎏᎏ 22.4 cm 30.0 cm ϭϪ9.4 cm h Ϫd m ϵ ᎏᎏi ϭ ᎏᎏi ho do Level 3 71. Jeweler’s Mirror A jeweler inspects a Ϫd h h ϭ ᎏᎏi o watch with a diameter of 3.0 cm by placing i d o it 8.0 cm in front of a concave mirror of Ϫ(30.0 cm)(1.8 cm) ϭ ᎏᎏᎏ 12.0-cm focal length. (30.0 cm) a. Where will the image of the watch Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Companies, a division of The McGraw-Hill © Glencoe/McGraw-Hill, Copyright ϭϪ1.8 cm appear? 1 1 1 69. Dental Mirror A dentist uses a small mir- ᎏᎏ ϩ ᎏᎏ ϭ ᎏᎏ do di f ror with a radius of 40 mm to locate a cavity in a patient’s tooth. If the mirror is concave and is held 16 mm from the tooth, Physics: Principles and Problems Solutions Manual 367 Chapter 17 continued d f (8.0 cm)(12.0 cm) ᎏoᎏ ϭ ᎏᎏᎏ ᎏ1ᎏ ϩ ᎏ1ᎏ ϭ ᎏ1ᎏ di Ϫ Ϫ do f 8.0 cm 12.0 cm do di f Ϫ24 cm fd ᎏᎏo di Ϫ b. What will be the diameter of the image? do f h Ϫd (Ϫ10.0 cm)(150 cm) ᎏᎏi ϭ ᎏᎏi ϭϭᎏᎏᎏ Ϫ Ϫ Ϫ 9.4 cm ho do 150 cm ( 10.0 cm) Ϫd h Ϫ(Ϫ24 cm)(3.0 cm) Ϫd Ϫ(Ϫ9.4 cm) ᎏᎏi o ᎏᎏᎏ m ᎏᎏi ᎏᎏ ϩ0.063 hi d 150 cm do 8.0 cm o ϭ 9.0 cm hi mho (0.063)(12 cm) 0.75 cm 72. Sunlight falls on a concave mirror and Mixed Review forms an image that is 3.0 cm from the pages 480–481 mirror. An object that is 24 mm tall is Level 1 placed 12.0 cm from the mirror. 74. A light ray strikes a plane mirror at an angle a. Sketch the ray diagram to show the of 28° to the normal. If the light source is location of the image. moved so that the angle of incidence increases by 34°, what is the new angle of O1 Ray 1 reflection? Ray 2 ␪ ϭ ␪ ϩ i i, initial 34° C F ϭ 28° ϩ 34° Horizontal scale: I cm 1 ϭ 62° 1.0 ؍ block 1 Vertical scale: ␪ ϭ ␪ mm r i 4 ؍ block 1 ϭ 62° b. Use the mirror equation to calculate the image position. 75. Copy Figure 17-23 on a sheet of paper. Draw rays on the diagram to determine the Inc. Companies, a division of The McGraw-Hill © Glencoe/McGraw-Hill, Copyright 1 1 1 ᎏᎏ ϩ ᎏᎏ ϭ ᎏᎏ height and location of the image. do di f fd (3.0 cm)(12.0 cm) ᎏo ϭ ᎏᎏᎏ di Ϫ do f 12.0 cm 3.0 cm 4.0 cm c. How tall is the image? 3.0 cm F Ϫd Ϫ m ᎏᎏi ϭ ᎏ4.0ᎏcm ϭϪ0.33 8.0 cm 4.0 cm do 12.0 cm Ϫ hi mho ( 0.33)(24 mm) ϭϪ8.0 mm 73. Shiny spheres that are placed on pedestals I Figure 17-23 on a lawn are convex mirrors. One such sphere has a diameter of 40.0 cm. A 12-cm-tall robin sits in a tree that is 1.5 m from the sphere. Where is the image of the robin and how tall is the image? r 20.0 cm, f Ϫ10.0 cm 368 Solutions Manual Physics: Principles and Problems Chapter 17 continued b. What is the image height? O1 h ؍ I hi 1.0 cm i ؊ m ϭ ᎏᎏ ؍ 1 di 2.7 cm ho Horizontal scale: F Ϫ diho cm h ϭ ᎏᎏ 1.0 ؍ block 1 i d Vertical scale: o (cm Ϫ(22.9 cm)(2.4 cm 1.0 ؍ blocks 2 ϭ ᎏᎏᎏ 30.0 cm The image height is 1.0 cm, and its ϭϪ1.8 cm location is 2.7 cm from the mirror. 78. What is the radius of curvature of a concave Level 2 mirror that magnifies an object by a factor 76. An object is located 4.4 cm in front of a of ϩ3.2 when the object is placed 20.0 cm concave mirror with a 24.0-cm radius. from the mirror? Locate the image using the mirror equation. hi r m ϭ ᎏᎏ f ϭ ᎏᎏ h 2 o d ϭϪmd ϭ ᎏ24.0ᎏcm i o 2 ϭϪ(3.2)(20.0 cm) ϭ 12.0 cm ϭϪ64 cm ᎏ1ᎏ ϭ ᎏ1ᎏ ᎏ1ᎏ f do di ᎏ1ᎏ ϭ ᎏ1ᎏ ᎏ1ᎏ f d d d f o i d ϭ ᎏoᎏ i d Ϫ f d d o f ϭ ᎏoᎏi d ϩ d (4.4 cm)(12.0 cm) o i ϭ ᎏᎏᎏ Ϫ (20.0 cm)(Ϫ64 cm) 4.4 cm 12.0 cm ϭ ᎏᎏᎏ Ϫ ϭϪ6.9 cm 20.0 cm ( 64 cm) ϭ 29 cm 77. A concave mirror has a radius of curvature r ϭ 2f of 26.0 cm. An object that is 2.4 cm tall is ϭ (2)(29 cm) placed 30.0 cm from the mirror. ϭ 58 cm a. Where is the image position? r f ϭ ᎏᎏ 79. A convex mirror is needed to produce an 2 image one-half the size of an object and ϭ ᎏ26.0ᎏcm located 36 cm behind the mirror.