Willis High School Physics Workbook Unit 7 Waves and Optics

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1 Willis High School Physics Workbook Unit 7 Waves and Optics This workbook belongs to Period

2 Waves and Optics Pacing Guide DAY DATE TEXTBOOK PREREADING CLASSWORK HOMEWORK ASSESSMENT M 2/25 T 2/26 W 2/ to 7.5 T 2/ F 3/ M 3/4 T 3/5 Quiz 1 (CW 1 14) W 3/6 3 T 3/ F 3/ M 3/ , T 3/19 Quiz 2 (CW 1-30) W 3/20 T 3/ to 7.10 F 3/ M 3/25 T 3/26 Quiz 3 (CW 1-50) W 3/27 T 3/28 Test Workbook Due F 3/29 Workbook Completion Evaluation Instructor Use Only Section Maximum Points Awarded Points Warm-Up Problems 10 Textbook Reading 20 Classwork 30 Homework 30 Lab Reports 10 TOTAL

3 Warm-Up Problems 1 Date: Givens and Unknowns Relationship 2 Date: Givens and Unknowns Relationship Solution: 3 Date: Givens and Unknowns Relationship Solution: Solution: Page 1 of 3

4 Warm-Up Problems 4 Date: Givens and Unknowns Relationship 5 Date: Givens and Unknowns Relationship Solution: 6 Date: Givens and Unknowns Relationship Solution: Solution: Page 2 of 3

5 Warm-Up Problems 7 Date: Givens and Unknowns Relationship 8 Date: Givens and Unknowns Relationship Solution: 9 Date: Givens and Unknowns Relationship Solution: Solution: Page 3 of 3

6 Waves and Optics Textbook Reading Assignments Answer All Items With Complete Sentences Reading 1 Chapter 14 Light and Reflection Section 14-2 Flat Mirrors Pages 526 to 529 a) How does the texture of a surface affect how it reflects light? b) What is the angle of incidence? c) What is the angle of reflection? d) How are the angle of incidence and the angle of reflection related? e) What is a virtual image? T1 Waves and Optics

7 Waves and Optics Textbook Reading Assignments Answer All Items With Complete Sentences Reading 2 Chapter 14 Light and Reflection Section 14-3 Curved Mirrors Page 670 a) What is a concave spherical mirror? b) What is a real image? c) What are the sign conventions for magnification? d) What are the rules for drawing reference rays? e) What is a convex spherical mirror? Waves and Optics T2

8 Waves and Optics Textbook Reading Assignments Answer All Items With Complete Sentences Reading 3 Chapter 12 Vibrations and Waves Section 12-3 Properties of Waves Pages 452 to 458 a) What is a mechanical wave? b) What are the differences between a pulse wave and a periodic wave? c) What are the crest, trough, amplitude, and wavelength of a wave? d) What are the differences between a transverse wave and a longitudinal wave? e) How is wave speed, frequency, and wave length related? T3 Waves and Optics

9 Reading 4 Chapter 15 Refraction Section 15-1 Refraction Pages 562 to 567 Waves and Optics Textbook Reading Assignments Answer All Items With Complete Sentences a) What is refraction? b) When does refraction occur? c) Which model of light can explain refraction? d) What is the index of refraction? List a few examples. e) What is Snell s Law? Waves and Optics T4

10 Reading 5 Chapter 15 Refraction Section 15-2 Thin Lenses Pages 568 to 576 Waves and Optics Textbook Reading Assignments Answer All Items With Complete Sentences a) What are the rules for drawing converging lens reference rays? b) What are the rules for drawing diverging lens reference rays? c) What are the characteristics of converging lenses? d) What are the characteristics of diverging lenses? e) What are the sign conventions for lenses? T5 Waves and Optics

11 OPTICS Unit REFLECTION OF LIGHT All light obeys the law of reflection. The law of reflection states that the angle of incidence, θ i, is equal to the angle of reflection, θ r. Both angles are measured with respect to the normal line, N, as shown below. Light reflection from a smooth surface is called regular or specular reflection. An example of specular reflection is found when a lazer reflects off the smooth surface of a mirror. In this case, the angle of incidence will equal the angle of reflection on the macroscopic scale. Light reflection from a rough or irregular surface is called diffuse reflection. As shown in the figure below, each ray of light obeys the law of reflection, but as a whole, the light appears to scatter randomly. 7.2 FLAT MIRRORS A flat mirror reflects light rays in the same order as they approach it. Flat mirrors are made from pieces of plate glass that have been coated on the back with a reflecting material such as silver or aluminum. The image is the same size as the object, and the image is the same distance behind the mirror as the object is in front of the mirror. Notice that the images formed by a flat mirror are reflections of real objects. These images are not real because no light passes through them. The images which appear to the eye to be formed by rays of light but which in truth do not exist are called virtual images. Conversely, real images are formed when rays of light intersect at a single point. 7.3 CURVED MIRRORS A curved mirror is a mirror that may be thought of as a portion of a reflecting sphere. It has a center of curvature, C, equal to the radius, R. The focal length, f, of the mirror is half the radius: f = 1 2 R If the inside of the spherical surface is the reflecting surface, the mirror is said to be concave or converging. If the outside portion is the reflecting surface, the mirror is convex or diverging. UNIT 7: OPTICS 136

12 7.4 GEOMETRICAL OPTICS The best method of understanding the formation of images by mirrors is through geometrical optics or ray tracing. The three principal rays are: Ray 1 Ray 2 Ray 3 A ray parallel to the mirror axis passes through the focal point of a concave mirror or seems to come from the focal point of a convex mirror. A ray that passes through the focal point of a concave mirror or proceeds toward the focal point of a convex mirror is reflected parallel to the mirror axis. A ray that proceeds along a radius of the mirror is reflected back along its original path. Image Characteristics 1. Size: Is the image greater (enlarged), smaller (reduced) or the same size as the object? 2. Position: Is the image inverted (upside down) or upright? 3. Nature: Is the image on the same side as the object (real image) or is it on the other side of the mirror (virtual image)? Concave Mirror 1. Pick a point on the top of the object and draw one incident ray traveling parallel towards the mirror. 2. Reflect that ray through the focal point F. This is Ray Draw one incident ray traveling through F towards the mirror. 4. Reflect that ray parallel to the principal axis. This is Ray Where the two rays intersect, mark the image of the top of the object with a dot and complete the image. 6. Write down the three characteristics of the image. Convex Mirror 1. Pick a point on the top of the object and draw one incident ray traveling parallel towards the mirror. 2. Reflect that ray as it seems to come from the focal point F inside the mirror. This is Ray Draw one incident ray traveling through C inside the mirror. This is Ray Where the two rays intersect, mark the image of the top of the object with a dot and complete the image. 5. Write down the three characteristics of the image. UNIT 7: OPTICS 137

13 CLASSWORK 1. Find the images formed by the following mirrors using the ray tracing method. Then determine the characteristics of each image: real or virtual, size of object, and inverted or upright. (a) (b) (c) (d) UNIT 7: OPTICS 138

14 (e) (f) (g) (h) 2. Find the images formed by the following mirrors using the ray tracing method. Then determine the characteristics of each image: real or virtual, size of object, and inverted or upright. (a) UNIT 7: OPTICS 139

15 (b) (c) (d) 3. Find the images formed by the following mirrors using the ray tracing method. Then determine the characteristics of each image: real or virtual, size of object, and inverted or upright. (a) (b) UNIT 7: OPTICS 140

16 (c) (d) (e) 7.5 THE MIRROR EQUATION The mirror equation can be used to locate the image, where M is called the magnification. Sign Convention R radius of curvature + for converging, - for diverging f focal length + for converging, - for diverging d i image distance + for real images, - for virtual images h i image size + if upright, - if inverted 1 d o + 1 d i = 1 f d i = dof d o f M = hi h o = di d o R = 2f UNIT 7: OPTICS 141

17 CLASSWORK 4. An object stands 18 cm from a concave mirror. An image forms 36 cm in front of the mirror. What is the focal length of the mirror? (12 cm) 5. A 3.5 cm candle is placed 6 cm away from a concave mirror with a focal length of 24 cm. (a) Where does the image of the candle form? (-8 cm) (b) Is it virtual or real? (c) What is the height of the image? (4.67 cm) (d) Is it inverted or upright? UNIT 7: OPTICS 142

18 6. When you hold a convex mirror 21 cm from your eye; your image forms 7 cm behind the mirror. (a) What is the magnification of the image? (0.33) (b) What are the mirror s focal length and the radius of curvature? (-10.5 cm, -21 cm) 7. A ray of light strikes a mirror lying on a table at an angle of 62 o with the horizontal. (a) Draw a sketch showing the incident ray, reflected ray and angle of incidence. (b) What is the angle of reflection? (28 o ) (c) Why isn t the answer 62 o? 8. Chelsea s face is 75 cm in front of a plane mirror. Where is the image of Chelseas face? Is it virtual or real? (-75 cm) UNIT 7: OPTICS 143

19 9. A concave mirror has a focal length of 10.0 cm. What is its radius of curvature? (20 cm) 10. A girl stands 1.5 meters in front of a flat mirror. (a) What is the position (d i) at which her image appears? (-1.5 m) (b) Is her image real or virtual? 11. A spherical concave mirror has a radius of curvature of 30 cm. An object that is 8.0 cm tall is placed 20 cm in front of the mirror. (a) What is the location at which the image is formed? (60 cm) (b) Is the image real or virtual? (c) What is the height of the image? (-24 cm) UNIT 7: OPTICS 144

20 (d) Is it inverted or upright? 12. An object 5 cm in height is placed 10 cm in front of a spherical concave mirror with a 15 cm focal length. (a) What is the position at which the image is formed? (-30 cm) (b) Is the image real or virtual? (c) What is the height of the image? (15 cm) (d) Is it inverted or upright? 13. A store clerk uses a diverging (convex) mirror with a radius of curvature of 1 m to keep an eye on shoplifters. How tall would the image of the man 1.85 m in height be if he were standing 5 m in front of the mirror? (0.17 m) UNIT 7: OPTICS 145

21 14. A spherical concave mirror is used to produce an inverted image of a light bulb located the same distance from the mirror as the object. The bulb is located 1.2 meters in front of the mirror. What is the focal length of the mirror? (0.6 m) 7.6 INTRODUCTION TO WAVES A wave is, in general, a disturbance that moves through a medium. (An exception is an electromagnetic wave such as light and radio waves which can travel through a vacuum.) A wave carries energy, but does not transport matter. Examples of mechanical waves include water waves, waves on a string, and sound waves. There are two types of mechanical waves: transverse and longitudinal. In a transverse wave, the particles of the medium move up and down perpendicular to the direction of the wave. Waves that travel down a stretched string when one end is shaken are transverse. In a longitudinal wave, the particles of the medium move back and forth in the same direction as the wave. For example, when one end of a coiled spring is pulled and released like a slinky the resulting wave is longitudinal. Sound waves are also longitudinal. The period, T, of a wave is the time required for one complete wave to pass a given point. The frequency, f, is the number of waves that pass that point per second. The amplitude, A, of a wave is the maximum displacement of the particles of the medium through which the wave passes on either side of their equilibrium positions. In a transverse wave, the amplitude is half the distance between the maximum and minimum positions. The wavelength, λ (lambda), of a wave is the distance between adjacent wave crests. We can find the velocity of a wave by relating it to the velocity equation: v = x t = λ T = λf The speed of a mechanical wave is constant in a given medium. The amplitude of a wave does not affect its wavelength, frequency, or velocity. CLASSWORK 15. Transverse waves traveling along a rope have a frequency of 12 Hz and are 2.40 m long. What is the velocity of the waves? (28.8 m/s) UNIT 7: OPTICS 146

22 16. Water waves in a small tank are 6.0 cm long. They pass a given point at the rate of 4.8 waves per second. (a) What is the speed of the water waves? (0.288 m/s) (b) What is the period of the waves? (0.21 s) 17. For the motion shown below, find the following: (a) Amplitude (b) Period (c) Frequency UNIT 7: OPTICS 147

23 18. For the motion shown below, find the following: (a) Amplitude (b) Period (c) Frequency 19. For the motion shown below, find the following: (a) Amplitude (b) Period (c) Frequency 20. Microwaves are electromagnetic waves that travel through space at a speed of m/s. Most microwave ovens operate at a frequency of Hz. (a) What is the period of these microwaves? ( s) UNIT 7: OPTICS 148

24 (b) How long is the wavelength of these microwaves? (0.122 m) 21. A sound wave is directed toward a vertical cliff 680 m from the source. A reflected wave is detected 4.0 s after the wave is produced. (a) What is the speed of sound in air? (340 m/s) (b) The sound has a frequency of 500 Hz. What is its wavelength? (0.68 m) (c) What is the period of the wave? (0.002 s) UNIT 7: OPTICS 149

25 22. A metronome is set so that it makes ten complete vibrations in 12 s. Find the frequency of the metronome. (0.83 Hz) 23. While sitting on a pier, Trevor notices that incoming waves are 2.0 m between crests. If the waves lap against the pier every 0.5 s, find: (a) The frequency (2 Hz) (b) the speed of the waves. (4 m/s) 24. Light travels at a speed of m/s in a vacuum, and for practical purposes, through air as well. The wavelength of a shade of yellow light is m. Find the frequency of this light. ( Hz) UNIT 7: OPTICS 150

26 25. A gamma ray is high-frequency light that travels at m/s. Find the wavelength of a gamma ray with a frequency of Hz. ( m) 26. If the speed of a longitudinal sound wave is 340 m/s, and the frequency is 1000 Hz, what is the wavelength of the wave? (0.34 m) 27. The frequency range for a normal human ear is between 20 Hz and 20,000 Hz. Using 330 m/s as the speed of sound, (a) Calculate the shortest wavelength of sound that can be heard. (1.65 cm) (b) Calculate the longest wavelength of sound that can be heard. (16.5 m) UNIT 7: OPTICS 151

27 28. The local hit music radio station can be found at on the FM dial. This means that they broadcast at a frequency of (103.6 Megahertz). These waves travel at m/s. What is the wavelength of these radio waves? (2.894 m) 29. A student sets up a standing wave of wavelength 6 meters in a coiled spring by moving his hand up and down twice each second. What is the velocity of the wave? (12m/s) 30. A sound wave has a frequency of 192 Hz and travels a length of 91.4 m in s. (a) What is the speed of the wave? (337 m/s) (b) What is the wavelength of the wave? (1.76 m) UNIT 7: OPTICS 152

28 (c) What is the period of the wave? ( s) (d) If the frequency was changed to 442 Hz, what would be the new wavelength and period? (0.762 m, s) 7.7 ELECTROMAGNETIC WAVES, REFRACTION, AND SNELL S LAW Electromagnetic waves consist of oscillating electric and magnetic fields with different wavelengths. The wave speed equation is: c = fλ where c is the speed of light ( m/s). The bending of a ray of light as it passes from one medium to another is called refraction. The speed of light c in a material is generally less than the free-space velocity of m/s. In water, light travels about three-fourths of its velocity in air. Light travels about two-thirds as fast in glass. The ratio of the velocity, c, of light in a vacuum to the velocity, v, of light in a particular medium is called the index of refraction, n. n = c v And finally, Snell s law states that the ratio of the sine of the incident angle to the sine of the refracted angle is constant. n 1sinθ 1 = n 2sinθ 2 n 1: index of refraction of the incident medium n 2: index of refraction of the second medium Medium n vacuum 1.00 air 1.00 water 1.33 ethanol 1.36 crown glass 1.52 quartz 1.54 flint glass 1.61 diamond 2.42 CLASSWORK 31. The speed of light in a plastic is m/s. What is the index of refraction of the plastic? (1.5) UNIT 7: OPTICS 153

29 32. Find the velocity of yellow light in a diamond whose refractive index is ( m/s) 33. Light is incident upon a piece of crown glass at an angle of 45 o. What is the angle of refraction? (27.7 o ) 34. A ray of light travels from air into liquid. The ray is incident upon the liquid at an angle of 30 o. The angle of refraction is 22 o. (a) What is the index of refraction of the liquid? (1.33) (b) Look at the table of values. What might the liquid be? 35. Light passes at an angle of incidence of 35 o from water into air. What is the angle of refraction if the index of refraction for water is 1.33? (49.7 o ) UNIT 7: OPTICS 154

30 36. Light travels through an unknown transparent substance at a speed of m/s. What is the index of refraction of the substance? (1.40) 37. At what speed does light travel through a diamond? ( m/s) 38. A ray of light traveling in air enters a transparent substance with an angle of incidence of 40 o and it is refracted at an angle of 25 o. How fast does the light travel through the substance? ( m/s) 39. A ray of light traveling in air enters a square container made of crown glass and filled with water. It strikes the container at an angle of incidence of 45 o. What is the angle of refraction as the light ray goes from the glass wall into the water? (32 o ) UNIT 7: OPTICS 155

31 40. A light beam in air (n = 1.00) makes an angle of 45 o with the normal to a glass window pane (n = 1.44). (a) What is the angle to the normal of the light beam after it is refracted into the glass? (29.4 o ) (b) What is the angle to the normal of the light beam after it exits the other side of the glass into air? (45 o ) 7.8 THIN LENSES Lenses are an essential part of telescopes, eyeglasses, cameras, microscopes and other optical instruments. A lens is usually made of glass, or transparent plastic. The two main types of lenses are convex and concave lenses. The focal length, f, of a lens depends on its shape and its index of refraction. A converging (convex) lens is thick in the center and thin at the edges. Below is a figure diagraming the anatomy of a lens. A diverging (concave) lens is thin in the center and thick at the edges. UNIT 7: OPTICS 156

32 7.9 IMAGE FORMATION BY LENSES The three principal rays are: Ray 1 Ray 2 Ray 3 A ray parallel to the axis passes through the far focal point of a converging lens or appears to come from the near focal point of a diverging lens. A ray which passes through the near focal point of a converging lens or proceeds toward the far focal point of a diverging lens is refracted parallel to the lens axis. A ray through the geometrical center of a lens will not be deviated. A real image is always formed on the side of the lens opposite to the object. A virtual image will appear to be on the same side of the lens as the object. Principal Rays for Convex Lenses Principal Rays for Concave Lenses CLASSWORK 41. Find the images formed by the following mirrors using the ray tracing method. Then determine the characteristics of each image: real or virtual, size of object, and inverted or upright. (a) (b) UNIT 7: OPTICS 157

33 (c) (d) (e) (f) UNIT 7: OPTICS 158

34 (g) 42. Find the images formed by the following mirrors using the ray tracing method. Then determine the characteristics of each image: real or virtual, size of object, and inverted or upright. (a) (b) (c) UNIT 7: OPTICS 159

35 (d) 43. Find the images formed by the following mirrors using the ray tracing method. Then determine the characteristics of each image: real or virtual, size of object, and inverted or upright. (a) (b) (c) UNIT 7: OPTICS 160

36 (d) (e) 7.10 THE LENS EQUATION The mirror equation can be used to locate the image, where M is called the magnification. Sign Convention R radius of curvature + for converging, - for diverging f focal length + for converging, - for diverging d i image distance + for real images, - for virtual images h i image size + if upright, - if inverted 1 d o + 1 d i = 1 f d i = dof d o f M = hi h o = di d o R = 2f CLASSWORK 44. (a) Find the location of the image of a 5 cm tall object located 30 cm from a convex lens of 10 cm focal length. (15 cm) UNIT 7: OPTICS 161

37 (b) Is the image real or virtual? (c) What is the height of the image? (-2.5 cm) (d) Is the image inverted or upright? 45. A 1.25 cm tall object is 4 cm from a concave lens of 6 cm focal length. (a) Locate the image formed and determine if it is real or virtual. (-2.4 cm) (b) Find the size of the image and determine if it is inverted or upright. (0.75 cm) UNIT 7: OPTICS 162

38 46. A converging lens of focal length 25 cm is used to form an image of an object located 1.0 m from the lens. The object has a height of 4.0 cm. (a) What is the position and nature at which the image is formed? (33.3 cm, real) (b) What is the height of the image? (-1.3 cm, inverted) 47. A diverging lens has a focal length of -30 cm. An object of height 10 cm is located 30 cm from the lens. (a) What is the position and nature at which the image is formed? (-15 cm, virtual) (b) What is the height of the image? (5 cm, upright) UNIT 7: OPTICS 163

39 48. If an object is 10.0 cm from a converging lens that has a focal length of 5 cm, how far from the lens will the image be? (10 cm) 49. The focal length of a lens in a box camera is 10.0 cm. The fixed distance between the lens and the film is 11.0 cm. If an object is clearly focused on the film, how far must the object be from the lens? (110 cm) 50. An object 3.0 cm tall is placed 22 cm in front of a converging lens. A real image is formed 11 cm from the lens. What is the size of the image? (-1.5 cm) UNIT 7: OPTICS 164

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41 OPTICS Homework 1. is a property of light that enables us to understand how images are formed in mirrors. 2. How would you write an equation to illustrate the Law of Reflection? 3. Below draw a sketch of a Concave Mirror. 4. Below draw a sketch of a Convex Mirror. 5. When the image of an object is seen in a plane mirror, the image is (a) real and upright. (b) real and inverted. (c) virtual and upright. (d) virtual and inverted. 6. When the image of an object is seen in a concave mirror the image will (a) always be real. (b) always be virtual. (c) be either real or virtual. (d) will always be magnified. UNIT 7: HOMEWORK A107

42 7. When the image of an object is seen in a convex mirror the image will (a) always be real. (b) always be virtual. (c) may be either real or virtual. (d) will always be magnified. 8. The angle of incidence on a reflecting surface is measured from the horizontal as 25 o, what is the reflected angle? Draw a labeled diagram to illustrate your answer. (25 o ) 9. Construct ray diagrams to show where the images of the following objects are located. Dray in the complete image and describe its characteristics (real or virtual, enlarged or reduced in size, inverted or upright). (a) (b) UNIT 7: HOMEWORK A108

43 (c) (d) (e) (f) UNIT 7: HOMEWORK A109

44 10. Write Snell s law and use a diagram to illustrate the meaning of each variable: 11. If you stand 1.5 m in front of a plane mirror, how far away would you see yourself in the mirror? Draw a labeled diagram to illustrate your answer. (3 m) 12. A concave mirror with a focal length of 10 cm creates a real image 30 cm away on its principal axis; the corresponding object is located how far from the mirror? (15 cm) 13. A concave mirror forms a real image at 25 cm from the mirror surface along the principal axis. If the corresponding object is at a 10 cm distance, what is the mirror s focal length? (7.1 cm) UNIT 7: HOMEWORK A110

45 14. If a virtual image is formed along the principal axis 10 cm from a concave mirror with the focal length 15 cm, what is the object distance from the mirror? (6.0 cm) 15. If a man s face is 30 cm in front of a concave shaving mirror creating an upright image 1.5 times as large (this is the magnification!) as the object, what are the image distance and the mirror s focal length? (- 45 cm, 90 cm) 16. What is the frequency of a wave traveling at 342 m/s with a wavelength of 2.1 m? (162.9 Hz) 17. Assuming the same wave properties as the previous problem, what is the wavelength if the wave frequency is 12,000 Hz? (2.85 cm) UNIT 7: HOMEWORK A111

46 18. Sound travels across a 21 km valley in one minute. (a) What is the velocity of the sound wave? (350 m/s) (b) If the sound has a frequency of 1200 Hz, what is its wavelength? (0.29 m) (c) What is the period of the wave? ( s) 19. During a storm, waves crash against the California coast at a rate of 15 waves per minute. The incoming waves are 2 m between crests. (a) Find the frequency. (0.25 Hz) UNIT 7: HOMEWORK A112

47 (b) Find the velocity of the waves. (0.5 m/s) 20. An electromagnetic wave is traveling at m/s with a frequency of Hz. (a) What is the wave s period? ( s) (b) What is the wavelength? ( m) 21. If the speed of a wave is 321 m/s, and the frequency is 1300 Hz, what is the wavelength of the wave? (24.7 cm) UNIT 7: HOMEWORK A113

48 22. A physics student creates waves in a 20 meter pool with her arms. If she stands at one end of the pool, and the waves hit the other end 10 s later: (a) Find the velocity of the waves. (2 m/s) (b) If she creates one wave every 4 seconds, what is the wavelength? (8 m) 23. Carbon tetrachloride (n = 1.46) is poured into a container made of crown glass (n=1.52). If the light ray in glass incident on the glass-to-liquid boundary makes an angle of 30 o with the normal, what is the angle of the corresponding refracted ray with respect to the normal? (31.3 o ) 24. A light ray in air is incident on an air to glass boundary at an angle of 45 o and is refracted in the glass of 30 o with the normal. What is the index of refraction of the glass? (1.41) UNIT 7: HOMEWORK A114

49 25. What is the angle of incidence on an air-to- glass (n = 1.52) boundary if the angle of refraction in the glass is 25 o? (40 o ) 26. If carbon tetrachloride has an index of refraction of 1.461, what is the speed of light through this liquid? ( m/s) 27. A ray of light in air is incident on an air-to-glass boundary at an angle of 30 o with the normal. If the index of refraction of the glass is 1.65, what is the angle of the refracted ray within the glass with respect to the normal? (17.6 o ) 28. A beam of light in air is incident at an angle of 35 o to the surface of a rectangular block of clear plastic (n=1.49). The light beam first passes through the block and re-emerges from the opposite side into air at what angle to the normal to that surface? (35 o ) UNIT 7: HOMEWORK A115

50 29. For the law of reflection and Snell s law, the angles must be read from respect to the. 30. is a property of light that enables us to understand how images are formed in lenses. 31. Which of the following best describes the image for a thin converging lens that forms whenever the object is at a distance less than one focal length from the lens? (a) inverted, enlarged and real (b) upright, enlarged and virtual (c) upright, reduced and virtual (d) inverted, reduced and real 32. Which of the following best describes the image for a thin diverging lens that forms whenever the magnitude of the object distance is less than that of the lens focal length? (a) inverted, enlarged and real (b) upright, enlarged and virtual (c) upright, reduced and virtual (d) inverted, reduced and real 33. Construct ray diagrams to show where the images of the following objects are located. Dray in the complete image and describe its characteristics (real or virtual, enlarged or reduced in size, inverted or upright). (a) (b) UNIT 7: HOMEWORK A116

51 (c) (d) (e) (f) UNIT 7: HOMEWORK A117

52 34. A 3 cm tall object is placed along the principal axis of a thin converging lens of 30 cm focal length. If the object distance is 40 cm, calculate the image distance and height. (120 cm, -9.0 cm) 35. An object is placed at a distance of 30 cm from a thin converging lens along its axis. The lens has a focal length of 10 cm. Calculate the image distance and magnification. (15 cm, -0.5) 36. An object is placed at a distance of 6 cm from a thin converging lens along its axis. The lens has a focal length of 9 cm. Calculate the image distance and magnification. (-18 cm, 3) UNIT 7: HOMEWORK A118

53 37. An object is placed at a distance of 30 cm from a thin diverging lens along the axis. If an image forms at a distance of 10 cm from the lens, what is the focal length of the lens? (- 15 cm) 38. An object is placed at a distance of 40 cm from a thin lens along the axis. A virtual image forms at a distance of 50 cm from the lens. Calculate the focal length of the lens. (200 cm) 39. Below draw a Convex Lens. 40. Below draw a Concave Lens. UNIT 7: HOMEWORK A119

54 41. Which type of Mirrors and which type of Lenses are converging? 42. Which type of Mirrors and which type of Lenses are diverging? For the following four questions, please answer one of the following: d o < f, do > f, C > d o > f, d o = C, d o = f, everywhere, all, none. 43. How can a plane mirror, concave mirror, convex mirror, convex lens and/or concave lens be used to produce an image that has the same size as the object? Plane Mirror Concave Mirror Convex Mirror Concave Lens Convex Lens 44. How can a plane mirror, concave mirror, convex mirror, convex lens and/or concave lens s be used to produce a magnified (larger) image? Plane Mirror Concave Mirror Convex Mirror Concave Lens Convex Lens 45. How can a plane mirror, concave mirror, convex mirror, convex lens and/or concave lens be used to produce an upright image? Plane Mirror Concave Mirror Convex Mirror Concave Lens Convex Lens 46. How can a plane mirror, concave mirror, convex mirror, convex lens and/or concave lens be used to produce a real image? Plane Mirror Concave Mirror Convex Mirror Concave Lens Convex Lens UNIT 7: HOMEWORK A120

55 47. The image of an object is found to be upright and reduced in size. What type of mirror and/or lens is used to produce such an image? 48. If a virtual image is formed 10 cm along the principal axis from a convex mirror of focal length 15 cm, what is the object distance from the mirror? (30 cm) UNIT 7: HOMEWORK A121

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