# PHYSICS. Chapter 34 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT

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1 PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 34 Lecture RANDALL D. KNIGHT

2 Chapter 34 Ray Optics IN THIS CHAPTER, you will learn about and apply the ray model of light Slide 34-2

3 Chapter 34 Preview Slide 34-3

4 Chapter 34 Preview Slide 34-4

5 Chapter 34 Preview Slide 34-5

6 Chapter 34 Preview Slide 34-6

7 Chapter 34 Preview Slide 34-7

8 Chapter 34 Content, Examples, and QuickCheck Questions Slide 34-8

9 The Ray Model of Light Let us define a light ray as a line in the direction along which light energy is flowing. Any narrow beam of light, such as a laser beam, is actually a bundle of many parallel light rays. You can think of a single light ray as the limiting case of a laser beam whose diameter approaches zero. Slide 34-9

10 The Ray Model of Light Slide 34-10

11 The Ray Model of Light Slide 34-11

12 Objects Objects can be either self-luminous, such as the sun, flames, and lightbulbs, or reflective. Most objects are reflective. Slide 34-12

13 Objects The diverging rays from a point source are emitted in all directions. Each point on an object is a point source of light rays. A parallel bundle of rays could be a laser beam or light from a distant object. Slide 34-13

14 Ray Diagrams Rays originate from every point on an object and travel outward in all directions, but a diagram trying to show all these rays would be messy and confusing. To simplify the picture, we use a ray diagram showing only a few rays. Slide 34-14

15 Apertures A camera obscura is a darkened room with a single, small hole, called an aperture. The geometry of the rays causes the image to be upside down. The object and image heights are related by Slide 34-15

16 Apertures We can apply the ray model to more complex apertures, such as the L-shaped aperture below. Slide 34-16

17 Specular Reflection of Light Reflection from a flat, smooth surface, such as a mirror or a piece of polished metal, is called specular reflection. Slide 34-17

18 Reflection The law of reflection states that 1. The incident ray and the reflected ray are in the same plane normal to the surface, and 2. The angle of reflection equals the angle of incidence: θ r = θ i Slide 34-18

19 Example 34.1 Light Reflecting from a Mirror Slide 34-19

20 Example 34.1 Light Reflecting from a Mirror Slide 34-20

21 Example 34.1 Light Reflecting from a Mirror Slide 34-21

22 Example 34.1 Light Reflecting from a Mirror Slide 34-22

23 Diffuse Reflection Most objects are seen by virtue of their reflected light. For a rough surface, the law of reflection is obeyed at each point but the irregularities of the surface cause the reflected rays to leave in many random directions. This situation is called diffuse reflection. It is how you see this slide, the wall, your hand, your friend, and so on. Slide 34-23

24 The Plane Mirror Consider P, a source of rays that reflect from a mirror. The reflected rays appear to emanate from P, the same distance behind the mirror as P is in front of the mirror. That is, s = s Slide 34-24

25 The Plane Mirror Slide 34-25

26 Example 34.2 How High Is the Mirror? Slide 34-26

27 Example 34.2 How High Is the Mirror? Slide 34-27

28 Example 34.2 How High Is the Mirror? Slide 34-28

29 Example 34.2 How High Is the Mirror? Slide 34-29

30 Example 34.2 How High Is the Mirror? Slide 34-30

31 Refraction Two things happen when a light ray is incident on a smooth boundary between two transparent materials: 1. Part of the light reflects from the boundary, obeying the law of reflection. 2. Part of the light continues into the second medium. The transmission of light from one medium to another, but with a change in direction, is called refraction. Slide 34-31

32 Refraction Slide 34-32

33 Refraction Slide 34-33

34 Indices of Refraction Slide 34-34

35 Refraction The figure shows a wave crossing the boundary between two media, where we re assuming n 2 > n 1. Because the wavelengths differ on opposite sides of the boundary, the wave fronts can stay lined up only if the waves in the two media are traveling in different directions. Slide 34-35

36 Tactics: Analyzing Refraction Slide 34-36

37 Example 34.4 Measuring the Index of Refraction Slide 34-37

38 Example 34.4 Measuring the Index of Refraction Slide 34-38

39 Example 34.4 Measuring the Index of Refraction Slide 34-39

40 Example 34.4 Measuring the Index of Refraction n 1 = 1.59 Slide 34-40

41 Total Internal Reflection When a ray crosses a boundary into a material with a lower index of refraction, it bends away from the normal. As the angle θ 1 increases, the refraction angle θ 2 approaches 90º, and the fraction of the light energy transmitted decreases while the fraction reflected increases. The critical angle of incidence occurs when θ 2 = 90º: The refracted light vanishes at the critical angle and the reflection becomes 100% for any angle θ 1 > θ c. Slide 34-41

42 Total Internal Reflection Slide 34-42

43 Example 34.5 Total Internal Reflection Slide 34-43

44 Example 34.5 Total Internal Reflection Slide 34-44

45 Example 34.5 Total Internal Reflection Slide 34-45

46 Fiber Optics The most important modern application of total internal reflection (TIR) is optical fibers. Light rays enter the glass fiber, then impinge on the inside wall of the glass at an angle above the critical angle, so they undergo TIR and remain inside the glass. The light continues to bounce its way down the tube as if it were inside a pipe. Slide 34-46

47 Fiber Optics In a practical optical fiber, a small-diameter glass core is surrounded by a layer of glass cladding. The glasses used for the core and the cladding have n core > n cladding Slide 34-47

48 Image Formation by Refraction If you see a fish that appears to be swimming close to the front window of the aquarium, but then look through the side of the aquarium, you ll find that the fish is actually farther from the window than you thought. Slide 34-48

49 Image Formation by Refraction Rays emerge from a material with n 1 > n 2. Consider only paraxial rays, for which θ 1 and θ 2 are quite small. In this case: where s is the object distance and s is the image distance. The minus sign tells us that we have a virtual image. Slide 34-49

50 Example 34.6 An Air Bubble in a Window Slide 34-50

51 Example 34.6 An Air Bubble in a Window Slide 34-51

52 Example 34.6 An Air Bubble in a Window Slide 34-52

53 Lenses The photos below show parallel light rays entering two different lenses. The left lens, called a converging lens, causes the rays to refract toward the optical axis. The right lens, called a diverging lens, refracts parallel rays away from the optical axis. Slide 34-53

54 Converging Lenses A converging lens is thicker in the center than at the edges. The focal length f is the distance from the lens at which rays parallel to the optical axis converge. The focal length is a property of the lens, independent of how the lens is used. Slide 34-54

55 Diverging Lenses A diverging lens is thicker at the edges than in the center. The focal length f is the distance from the lens at which rays parallel to the optical axis appear to diverge. The focal length is a property of the lens, independent of how the lens is used. Slide 34-55

56 Thin Lenses: Ray Tracing Three situations form the basis for ray tracing through a thin converging lens. Situation 1: A ray initially parallel to the optic axis will go through the far focal point after passing through the lens. Slide 34-56

57 Thin Lenses: Ray Tracing Three situations form the basis for ray tracing through a thin converging lens. Situation 2: A ray through the near focal point of a thin lens becomes parallel to the optic axis after passing through the lens. Slide 34-57

58 Thin Lenses: Ray Tracing Three situations form the basis for ray tracing through a thin converging lens. Situation 3: A ray through the center of a thin lens is neither bent nor displaced but travels in a straight line. Slide 34-58

59 Thin Lenses: Ray Tracing Rays from an object point P are refracted by the lens and converge to a real image at point P. Slide 34-59

60 Image Formation The figure is a close-up view of the rays very near the image plane. To focus an image, you must either move the screen to coincide with the image plane or move the lens or object to make the image plane coincide with the screen. Slide 34-60

61 Tactics: Ray Tracing for a Converging Lens Slide 34-61

62 Tactics: Ray Tracing for a Converging Lens Slide 34-62

63 Lateral Magnification The image can be either larger or smaller than the object, depending on the location and focal length of the lens. The lateral magnification m is defined as A positive value of m indicates that the image is upright relative to the object. A negative value of m indicates that the image is inverted relative to the object. The absolute value of m gives the size ratio of the image and object: h /h = m Slide 34-63

64 Virtual Images Consider a converging lens for which the object is inside the focal point, at distance s < f. You can see all three rays appear to diverge from point P. Point P is an upright, virtual image of the object point P. Slide 34-64

65 Virtual Images You can see a virtual image by looking through the lens. This is exactly what you do with a magnifying glass, microscope, or binoculars. Slide 34-65

66 Example 34.8 Magnifying a Flower Slide 34-66

67 Example 34.8 Magnifying a Flower Slide 34-67

68 Example 34.8 Magnifying a Flower Slide 34-68

69 Thin Lenses: Ray Tracing Three situations form the basis for ray tracing through a thin diverging lens. Situation 1: A ray initially parallel to the optic axis will appear to diverge from the near focal point after passing through the lens. Slide 34-69

70 Thin Lenses: Ray Tracing Three situations form the basis for ray tracing through a thin diverging lens. Situation 2: A ray directed along a line toward the far focal point becomes parallel to the optic axis after passing through the lens. Slide 34-70

71 Thin Lenses: Ray Tracing Three situations form the basis for ray tracing through a thin diverging lens. Situation 3: A ray through the center of a thin lens is neither bent nor displaced but travels in a straight line. Slide 34-71

72 Tactics: Ray Tracing for a Diverging Lens Slide 34-72

73 Example 34.9 Demagnifying a Flower Slide 34-73

74 Example 34.9 Demagnifying a Flower Slide 34-74

75 Example 34.9 Demagnifying a Flower Slide 34-75

76 Thin Lenses: Refraction Theory Consider a spherical boundary between two transparent media with indices of refraction n 1 and n 2. The sphere has radius of curvature R and is centered at point C. Slide 34-76

77 Thin Lenses: Refraction Theory If an object is located at distance s from a spherical refracting surface, an image will be formed at distance s given by Slide 34-77

78 Example A Goldfish in a Bowl Slide 34-78

79 Example A Goldfish in a Bowl Slide 34-79

80 Example A Goldfish in a Bowl Slide 34-80

81 Example A Goldfish in a Bowl s = 8.3 cm Slide 34-81

82 Lenses In an actual lens, rays refract twice, at spherical surfaces having radii of curvature R 1 and R 2. Slide 34-82

83 The Thin Lens Equation The object distance s is related to the image distance s by where f is the focal length of the lens, which can be found from where R 1 is the radius of curvature of the first surface, and R 2 is the radius of curvature of the second surface, and the material surrounding the lens has n = 1. Slide 34-83

84 Example Focal Length of a Meniscus Lens Slide 34-84

85 Example Focal Length of a Meniscus Lens Slide 34-85

86 Example A Magnifying Lens Slide 34-86

87 Example A Magnifying Lens Slide 34-87

88 Example A Magnifying Lens Slide 34-88

89 Image Formation with Concave Spherical Mirrors The figure shows a concave mirror, a mirror in which the edges curve toward the light source. Rays parallel to the optical axis reflect and pass through the focal point of the mirror. Slide 34-89

90 A Real Image Formed by a Concave Mirror Slide 34-90

91 Image Formation with Convex Spherical Mirrors The figure shows parallel light rays approaching a mirror in which the edges curve away from the light source. This is called a convex mirror. The reflected rays appear to come from a point behind the mirror. Slide 34-91

92 A Real Image Formed by a Convex Mirror Slide 34-92

93 Image Formation with Spherical Mirrors A city skyline is reflected in this polished sphere. Slide 34-93

94 Tactics: Ray Tracing for a Spherical Mirror Slide 34-94

95 Tactics: Ray Tracing for a Spherical Mirror Slide 34-95

96 The Mirror Equation For a spherical mirror with negligible thickness, the object and image distances are related by: where the focal length f is related to the mirror s radius of curvature by: Slide 34-96

97 Example Analyzing a Concave Mirror Slide 34-97

98 Example Analyzing a Concave Mirror Slide 34-98

99 Example Analyzing a Concave Mirror Slide 34-99

100 Example Analyzing a Concave Mirror Slide

101 Chapter 34 Summary Slides Slide

102 General Principles Slide

103 General Principles Slide

104 Important Concepts Slide

105 Important Concepts Slide

106 Applications Slide

107 Applications Slide

108 Applications Slide

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