1. Chapter 26 The Refraction of Light: Lenses and Optical Instruments

5. Chapter 26: The Refraction of Light: Lenses and Optical Instruments Section 1: The Index of Refraction

9. 26.1.1. In which one of the following substances does light have the largest speed? a) diamond b) benzene c) carbon dioxide d) water e) None of the above. The speed of light has the same value everywhere in the Universe.

10. 26.1.2. Through experiment, the speed of light passing through material A is 1.4 times greater than when the same light passes through material B. What is the ratio of the refractive index of material A to that of material B? a) 0.71 b) 0.84 c) 1.0 d) 1.2 e) 1.4

11. 26.1.3. If the index of refraction for a given material is 1.5, what is the speed of light in that material relative to the speed of light in a vacuum, c ? a) No material can have an index greater than 1 since light cannot travel faster than c . b) c / 2 c) 2 c / 3 d) c e) 1.5 c

12. Chapter 26: The Refraction of Light: Lenses and Optical Instruments Section 2: Snell’s Law and the Refraction of Light

13. SNELL’S LAW SNELL’S LAW OF REFRACTION When light travels from a material with one index of refraction to a material with a different index of refraction, the angle of incidence is related to the angle of refraction by

14. Example 1 Determining the Angle of Refraction A light ray strikes an air/water surface at an angle of 46 degrees with respect to the normal. Find the angle of refraction when the direction of the ray is (a) from air to water and (b) from water to air. (a) (b)

15. APPARENT DEPTH Example 2 Finding a Sunken Chest The searchlight on a yacht is being used to illuminate a sunken chest. At what angle of incidence should the light be aimed?

16. Apparent Depth Apparent depth, observer directly above object

17. Conceptual Example 4 On the Inside Looking Out A swimmer is under water and looking up at the surface. Someone holds a coin in the air, directly above the swimmer’s eyes. To the swimmer, the coin appears to be at a certain height above the water. Is the apparent height of the coin greater, less than, or the same as its actual height? Since: and n 2 (air) is less than n 1 (water), the object will appear farther away

18. THE DISPLACEMENT OF LIGHT BY A SLAB OF MATERIAL Refraction will occur at both surfaces, with each surface bending according to Snell’s Law

19. THE DERIVATION OF SNELL’S LAW

20. 26.2.1. A spherical ball is submerged in a shallow pan of water as shown. As we look directly at the ball, it appears spherical, what does the ball look like if you are looking at the rays emerging from above the surface of the water at Point P? P

21. 26.2.2. One dark evening, you are standing at the edge of a swimming pool that is 1.21 m deep. Directing a flashlight down into the water, you notice a shiny metal plate at the bottom and hold the light there. The light from the flashlight enters the pool at an incident angle of 50.0  at a point 0.85 m from the edge you are standing near. How far from this edge is the metal plate? a) 0.85 m b) 1.1 m c) 1.5 m d) 1.7 m e) 1.9 m

22. 26.2.3. You are standing directly above a fish in an aquarium. The actual depth of the fish is one-half the distance from the surface to the bottom. As you look down at it, where does the fish appear to be? a) I see it at its actual depth. b) I see it at the surface of the water. c) I see it below its actual depth, but above the bottom of the aquarium. d) I see it above its actual depth, but below the surface of the water. e) I see it at the bottom of the aquarium.

23. 26.2.4. A laser beam is directed at the left side of a plastic block as shown. Through which side and at what angle does the light leave the block? a) top side, 40  b) right side, 40  c) top side, 68.8  d) right side, 68.8  e) bottom side, 40 

24. 26.2.5. Is light bent more, less, or not at all when entering a medium with a larger index of refraction than that of the incident medium when the angle of incidence is greater than 0  ? a) more b) less c) not at all

25. 26.2.6. Is light bent more, less, or not at all when entering a medium with a smaller index of refraction than that of the incident medium when the angle of incidence is greater than 0  ? a) more b) less c) not at all

26. 26.2.7. Blue light travels from air into glass that has an index of refraction of 1.54. How does the wavelength of the light in air compare with the wavelength of the light in the glass? a) The wavelength of the light is the same in both media, only the frequency changes upon entering the glass. b) The wavelength of the light becomes shorter in the glass. c) The wavelength of the light becomes longer in the glass.

27. 26.2.8. A single light beam is split into two equal beams, denoted A and B. Beam A travels through a medium with a higher index of refraction than the medium that beam B travel through. When both beams exit their media back into air, how do their wavelengths compare? a) Beam A has a longer wavelength. b) Beam B has a longer wavelength. c) Both beams have the same wavelength.

29. Chapter 26: The Refraction of Light: Lenses and Optical Instruments Section 3: Total Internal Reflection

30. Total Internal Reflection When light passes from a medium of larger refractive index into one of smaller refractive index, the refracted ray bends away from the normal. Critical angle

31. Example 5 Total Internal Reflection A beam of light is propagating through diamond and strikes the diamond-air interface at an angle of incidence of 28 degrees. (a) Will part of the beam enter the air or will there be total internal reflection? (b) Repeat part (a) assuming that the diamond is surrounded by water. (a) (b)

32. Conceptual Example 6 The Sparkle of a Diamond The diamond is famous for its sparkle because the light coming from it glitters as the diamond is moved about. Why does a diamond exhibit such brilliance? Why does it lose much of its brilliance when placed under water?

33. Another use for Total Internal Reflection

34. T.I.R. in Fiber Optics

35. 26.3.1. A laser beam is directed at the left side of a plastic block ( n = 1.53) as shown at an angle  . The beam then undergoes total internal reflection as the light strikes the top interface at the critical angle for the block and the surrounding air. What is the value of the angle  ? Note: The drawing is not drawn to scale and the angles shown are not the actual angles. a) 40.8  b) 49.2  c) 63.1  d) 68.7  e) This is not possible since no angle  will satisfy this situation.

36. 26.3.2. If total internal reflection is to occur, what must be incident angle be relative to the critical angle? a) It must be equal to the critical angle. b) It must be larger than or equal to the critical angle. c) It must be smaller than or equal to the critical angle. d) It must be smaller than the critical angle. e) Total internal reflection only depends on the indices of refraction of the two materials, so it doesn’t matter what the incident angle is.

37. Chapter 26: The Refraction of Light: Lenses and Optical Instruments Section 4: Polarization and the Refraction of Light

38. Polarized Light & Reflection Brewster’s law

39. 26.4.1. A beam of unpolarized light is directed at a liquid within a transparent container. When the light strikes the air-liquid interface, Jason observes that the reflected ray and the refracted ray are perpendicular to one another. Investigating, Jason places a polarizer in the path of the reflected ray. What does Jason observe when the transmission axis of the polarizer is perpendicular to the surface of the water? a) No light is transmitted through the polarizer. b) About one quarter of the light is transmitted through the polarizer. c) About one half of the light is transmitted through the polarizer. d) About three quarters of the light is transmitted through the polarizer. e) All of the light is transmitted through the polarizer.

40. 26.4.2. Unpolarized light from a laser is directed toward a horizontal, flat sheet of glass mounted on a stand as shown. Some of the light that reflects from the sheet passes through a polarizer with a vertical transmission axis. Any light that passes through the polarizer may be observed on the wall behind the polarizer. Janet holds the polarizer as shown and observes the wall as Andrew varies the angle of incidence, which equals the angle of reflection  , of the laser light. What will Janet observe as Andrew gradually varies  from 80  to 40  ? a) The intensity of the light will increase uniformly as the angle is decreased. b) The intensity of the light will decrease uniformly as the angle is decreased. c) The intensity of the light will decrease to zero near 60  , but otherwise some light will reach the wall. d) The light on the wall will appear to be at constant intensity. e) No light will pass through the polarizer sheet at any of these angles.

41. Chapter 26: The Refraction of Light: Lenses and Optical Instruments Section 5: The Dispersion of Light: Prisms and Rainbows

42. Dispersion Of Light The net effect of a prism is to change the direction of a light ray. Light rays corresponding to different colors bend by different amounts.

44. Rainbows

45. 26.5.1. Which one of the following statements concerning refraction of light by a prism is true? a) Light of higher frequency is refracted more than light of lower frequency. b) Light of lower frequency is refracted more than light of higher frequency. c) Light of longer wavelength is refracted more than light of shorter wavelength. d) Orange light is refracted more than blue light. e) All light is refracted the same amount, it only depends on the index of refraction of the prism.

46. 26.5.2. Usually when we see a rainbow, we see a single bow with red at the top and violet at the bottom. The process of rainbow formation is described in the text. On rare occasions, we may see a “double rainbow,” which is one rainbow below another. The lower one appears to be the usual rainbow, while other has the colors reversed with red at the bottom and violet at the top. Which of the following provides the best explanation of a double rainbow? a) The upper rainbow is formed from water droplets that are higher than those that form the lower rainbow; and it is formed in the same way as the lower rainbow. b) The upper rainbow is formed from water droplets that are higher than those that form the lower rainbow; and it is formed by light that is reflected two times within multiple water droplets, unlike the single reflections within multiple droplets that form the lower rainbow. c) The upper rainbow is formed from the water droplets that form the lower rainbow, but it is formed by light that is reflected two times within multiple water droplets, in addition to the single reflections within the same droplets that form the lower rainbow. d) The upper rainbow is formed by the light that is transmitted out the each water droplet at the point where the light is also reflected within each droplet. This transmitted light is then reflected from other droplets to our eyes.

47. 26.5.3. Which of the following is an example of dispersion? a) A rainbow seems to connect two mountain peaks. b) A magnifying glass is used to focus light to start a fire. c) A spoon in a glass of water looks bent. d) Snell’s law is a direct result from chromatic dispersion. e) Laser light is used to accurately cut parts for an automobile.

48. Chapter 26: The Refraction of Light: Lenses and Optical Instruments Section 6: Lenses

50. Examples of Lenses

51. 26.6.1. Parallel rays of blue light enter a transparent plastic block at 0  and pass through without being diverted. The rays then pass through a converging lens and are focused at a point P. If the block is then rotated so that the parallel rays approach the block at an angle of 45  , as shown, without moving the lens, were will the light be focused relative to the point P? a) above point P b) below point P c) to the left of point P d) to the right of point P e) at point P

52. 26.6.2. Parallel rays of red light that are directed at a converging lens are focused at a point P on the principle axis to the right of the lens when the lens is surrounded by air. If the lens is surrounded by water instead of air, where will the red parallel rays be focused relative to point P? a) above point P b) below point P c) to the left of point P d) to the right of point P e) at point P

53. Chapter 26: The Refraction of Light: Lenses and Optical Instruments Section 7: The Formation of Images by Lenses

55. IMAGE FORMATION BY A CONVERGING LENS In this example, when the object is placed further than twice the focal length from the lens, the real image is inverted and smaller than the object.

56. When the object is placed between F and 2F, the real image is inverted and larger than the object. IMAGE FORMATION BY A CONVERGING LENS

57. When the object is placed between F and the lens, the virtual image is upright and larger than the object. IMAGE FORMATION BY A CONVERGING LENS

58. IMAGE FORMATION BY A DIVERGING LENS A diverging lens always forms an upright, virtual, diminished image.

59. 26.7.1. The knight from a chess set is placed at the focal point of a diverging lens as shown. By carefully constructing a ray diagram, determine where the image of the knight will appear? a) no image is formed b) the image is at a distance f to the left of the lens, but it is inverted c) the image is at a distance f to the right of the lens, but it is upright d) the image is at a distance f/2 to the right of the lens, but it is inverted e) the image is at a distance f/2 to the left of the lens, but it is upright

60. 26.7.2. The knight from a chess set is placed at the focal point of a converging lens as shown. By carefully constructing a ray diagram, determine where the image of the knight will appear? a) no image is formed b) the image is at a distance greater than f to the left of the lens, but it is inverted c) the image is at a distance greater than f to the right of the lens, but it is upright d) the image is at a distance f/2 to the right of the lens, but it is inverted e) the image is at a distance f/2 to the left of the lens, but it is upright

61. 26.7.3. An object is located 25 cm to the left of a converging lens that has a focal length of 12 cm. Consider a carefully drawn ray diagram for this situation. A real image is produced by this configuration. If you wanted to produce a larger real image without changing the relative distance of the object and lens, which of the following choices would produce the desired result? a) Replace the lens with a diverging lens with a focal length of 4 cm. b) Replace the lens with a converging lens with a focal length of 4 cm. c) Replace the lens with a diverging lens with a focal length of 12 cm. d) Replace the lens with a converging lens with a focal length of 20 cm. e) Replace the lens with a diverging lens with a focal length of 20 cm.

62. 26.7.4. A real object is placed to the right of a converging lens at a distance 2 f . The focal length of the lens is f . By carefully drawing a ray diagram for this situation, determine which of the following statements best describes the image formed. a) An observer on the left side of the lens would see a real image to the left of the lens that is inverted and larger than the object. b) An observer on the left side of the lens would see a real image to the left of the lens that is inverted and smaller than the object. c) An observer on the right side of the lens would see a real image to the left of the lens that is upright and larger than the object. d) An observer on the right side of the lens would see a real image to the right of the lens that is upright and smaller than the object. e) An observer on the left side of the lens would see a virtual image to the right of the lens that is inverted and smaller than the object.

63. 26.7.5. Consider the two rays drawn from the top of an object. One of the rays crosses the principle axis at point A as shown. Using the information provided, which one of the following statements best describes the location of the focal point on the right side of the converging lens. a) The focal point is a short distance to the left of point A. b) The focal point is a large distance to the right of point A, where the rays converge. c) The focal point is a short distance to the right of point A. d) The focal point is at point A.

64. 26.7.6. An object is placed to the left of a converging lens. The distance from the object to the lens is one and one-half times the focal length of the lens. A screen is used to view the image of the object on the right side of the lens. If the top half of the lens is covered with black electrical tape such that no light can enter the lens on that half, what would you see on the screen? a) The top half of the image is no longer seen. b) The bottom half of the image is no longer seen. c) The upper most portion and lower most portion of the image are no longer seen. d) The entire image is seen just as before. e) The entire image is seen, but about one half as bright.

65. 26.7.7. Which one of the following phrases best describes images formed by diverging lenses? a) always smaller than the object b) always larger than the object c) always inverted d) always virtual e) always real

66. 26.7.8. A physics student desires to create a beam of light that consists of parallel rays. Which one of the following arrangements would allow her to accomplish this task? a) A light bulb is placed at the focal point of a convex mirror. b) A light bulb is placed at the focal point of a diverging lens. c) A light bulb is placed at the focal point of a converging lens. d) A light bulb is located at twice the focal length from a concave mirror. e) A light bulb is located at twice the focal length from a converging lens.

67. Chapter 26: The Refraction of Light: Lenses and Optical Instruments Section 8: The Thin-Lens Equation and the Magnification Equation

68. Lens Equations

69. Summary of Sign Conventions for Lenses

71. 26.8.1. An object is placed at a distance 2 f to the left of a converging lens with a focal length f . Using the thin lens equation and the magnification equation, determine the location and magnification of the image formed by this configuration. a) The image is formed at a distance f to the right of the lens and it has a magnification of  1/2. b) The image is formed at a distance 2 f to the right of the lens and it has a magnification of  1/2. c) The image is formed at a distance f to the right of the lens and it has a magnification of  1. d) The image is formed at a distance 2 f to the right of the lens and it has a magnification of  1. e) The image is formed at a distance f/2 to the right of the lens and it has a magnification of  1/4.

72. 26.8.2. An object is placed at a distance 5.0 cm to the left of a converging lens with a focal length 2.5 cm. Using the thin lens equation and the magnification equation, determine the location and magnification of the image formed by this configuration. a) The image is formed 2.5 cm to the right of the lens and it has a magnification of  1/2. b) The image is formed 5.0 cm to the right of the lens and it has a magnification of  1/2. c) The image is formed 2.5 cm to the right of the lens and it has a magnification of  1. d) The image is formed 5.0 cm to the right of the lens and it has a magnification of  1. e) The image is formed 1.25 cm to the right of the lens and it has a magnification of  1/4.

73. 26.8.3. An object is placed at a distance 5.0 cm to the left of a diverging lens with a focal length 2.5 cm. Using the thin lens equation and the magnification equation, determine the location and magnification of the image formed by this configuration. a) The image is formed 1.7 cm to the left of the lens and it has a magnification of +1/3. b) The image is formed 0.6 cm to the left of the lens and it has a magnification of +3/25. c) No image is formed in this configuration. d) The image is formed 0.6 cm to the right of the lens and it has a magnification of  3/25. e) The image is formed 1.7 cm to the right of the lens and it has a magnification of  1/3.

74. Chapter 26: The Refraction of Light: Lenses and Optical Instruments Section 9: Lenses in Combinations

75. Lens Combos The image produced by one lens serves as the object for the next lens.

76. 26.9.1. The compound microscope described in the text is made from two lenses. Which one of the following statements is true concerning the operation of this microscope? a) Both lenses form real images. b) Both lenses form virtual images. c) Only the lens closest to the eye forms an image. d) The lens closest to the object forms a real image; the other lens forms a virtual image. e) The lens closest to the object forms a virtual image; the other lens forms a real image.

77. 26.9.2. In her biology class, Chris examines an insect wing under a compound microscope that has an objective lens with a focal length of 0.70 cm, an eyepiece with a focal length of 3.0 cm, and a lens separation distance of 16.00 cm. Chris has a near point distance of 22.5 cm. What is the approximate angular magnification of the microscope as Chris views the insect wing? a)  75 b)  110 c)  140 d)  190 e)  250

78. Chapter 26: The Refraction of Light: Lenses and Optical Instruments Section 10: The Human Eye

79. ANATOMY

80. OPTICS The lens only contributes about 20-25% of the refraction, but its function is important.

81. NEARSIGNTEDNESS The lens creates an image of the distance object at the far point of the nearsighted eye.

82. Example 12 Eyeglasses for the Nearsighted Person A nearsighted person has a far point located only 521 cm from the eye. Assuming that eyeglasses are to be worn 2 cm in front of the eye, find the focal length needed for the diverging lens of the glasses so the person can see distant objects.

83. FARSIGNTEDNESS The lens creates an image of the close object at the near point of the farsighted eye.

84. Chapter 26: The Refraction of Light: Lenses and Optical Instruments Section 11: Angular Magnification and the Magnifying Glass

85. Angular Magnification The size of the image on the retina determines how large an object appears to be.

86. Angular Magnification

87. Example 14 A Penny and the Moon Compare the angular size of a penny held at arms length with that of the moon. Penny Moon

88. Angular Magnification Angular magnification Angular magnification of a magnifying glass

89. Chapter 26: The Refraction of Light: Lenses and Optical Instruments Section 12: The Compound Microscope

90. THE REFRACTIVE POWER OF A LENS – THE DIOPTER Optometrists who prescribe correctional lenses and the opticians who make the lenses do not specify the focal length. Instead they use the concept of refractive power.

91. Compound Microscope To increase the angular magnification beyond that possible with a magnifying glass, an additional converging lens can be included to “premagnify” the object. Angular magnification of a compound microscope

92. Chapter 26: The Refraction of Light: Lenses and Optical Instruments Section 13: The Telescope

93. Telescope Angular magnification of an astronomical telescope

94. Chapter 26: The Refraction of Light: Lenses and Optical Instruments Section 14: Lens Aberrations

95. Lens Aberration In a converging lens, spherical aberration prevents light rays parallel to the principal axis from converging at a single point. Spherical aberration can be reduced by using a variable-aperture diaphragm.

96. Chromatic Aberration Chromatic aberration arises when different colors are focused at different points along the principal axis.

97. 26.14.1. Which one of the following statements best explains why chromatic aberration occurs in lenses, but not in mirrors? a) The shape of the mirror prevents chromatic aberration. b) The thickness of a lens varies from top to bottom. c) The frequency of light changes when it passes through glass. d) The angle of incidence varies over the surface of a lens for incident parallel rays of light. e) Different colors of light are refracted by different amounts as the light passes through a lens.

98. END