2012 Spring Chapters 23 & 24. Optics Outline

Transcription

1 Outline Monday February 27 Lecture Ch 23: Geometric Introduce Ray Project Candle Lab Homework Chapter 23 Practice Questions (30) MCAT (28) Physlet Practice Problems (0) NONE Wednesday February 29 Turn in Candle Lab Lecture: Ch 24 Wave nature of light: Diffraction, thin films, polarization Lab: Converging Lenses Homework Chapter 24 Practice Questions (27) MCAT (0) NONE Physlet Practice Problems (8) Friday March 2 Turn in Converging Lenses Lab Finish notes Tuesday March 6 Turn in Ray Project Review MC due end of class Thursday March 8 Exam Unit 13 : Chapters 23 and 24 Chapter 27, 28, 30, 31, 32 Warmups and Applications (Extra Credit) 68

2 Ray Project AP Physics B OBJECTIVES In this laboratory, students will produce optical ray tracing diagrams. INTRODUCTION/THEORY Ray diagrams follow three principle rays: a. In parallel, out through focal point b. In through focal point, out parallel c. Center Ray a. For Lenses: Straight through center b. For Mirrors: i. Through Center of curvature OR ii. In at Center Out at same angle Each image is described by three Characteristics: a. Size: a. Magnified M>1, b. Reduced M<1, c. Same M=1 b. Position a. Real d i >0 b. Virtual d i <0 c. Orientation a. Inverted (M< 0) b. Upright (M>0) APPARATUS Examples of materials: Poster, string, spaghetti, markers, push pins RAYS MUST BE STRAIGHT USE A RULER! You may use thing to show the straight line of the rays EXCEPT a computer generated model: That is, you cannot download from internet, cut from book, etc. The objects do not have to be arrows you may draw or print out objects/images from computer. Must be larger than 8.5 x 11. PROCEDURES Construct a model of the image of an object using the three principle rays for each of the following cases: d o < f d o = f R >d o >f Lens Mirror 69 d 0 = Converging X X X X Diverging X Flat X Concave X X X X Convex X Summary Chart: Make a chart with a column for object distance, d o, image distance, d i, magnification, orientation and position for each. Rubric: 7pts for each diagram (7 x 11 = 77 pts) 10 Pts for Summary Chart 10 pts creativity 3 pts neatness

3 CONVERGING LENS: IMAGE AND OBJECT RELATIONSHIPS AP Physics B OBJECTIVES This experiment is designed to explore lenses and their production of images. INTRODUCTION/THEORY Given a lens of any shape and index of refraction, you could determine the shape and location of the images it forms based only on the Law of Refraction. You need only apply the law along with some of the ray tracing techniques you have already used. However, for spherical lenses (and for spherical mirrors as well), there is a more general equation that can be used to determine the location and magnification of an image. This equation is called the Fundamental Lens Equation: 1 f 1 1 (1) d o d i where f is the focal length of the lens, and d i and d o are the distance from the mirror to the image and object respectively. The magnification of the image is given by the equation: d m i (2) d o In this experiment you will have an opportunity to test and apply these equations. APPARATUS For this lab, you will need optics bench, light source, 75 mm focal length convex lens, crossed arrow target, component holders (3), and a viewing screen. PROCEDURES CASE 1 Setup the equipment as shown in Figure 1. Turn on the light source and slide the lens toward or away from the crossed arrow target, as needed to focus the image of the target onto the viewing screen. CASE 2 Now set d o to the values (in millimeters) listed in the table below (500 mm, 450 mm, 400 mm, 350 mm, 300 mm, 250 mm, 200 mm, 150 mm, 100 mm, 75 mm, 50 mm). At each setting, locate the image and measure d i. Also measure h i, the height of the image. (h o is the height of the arrow on the crossed arrow target.) Record Values. 70

4 ANALYSIS CASE 1 Is the image magnified or reduced? Is the image inverted? Based on the Fundamental Lens Equation, what would happen to d i if you increased d o even further? What would happen to d i if d o were very, very large? Using your answer to the last question, measure the focal length of the lens. Record this value. CASE 2 Record your data in a table similar to the one shown below: Data Calculations d o (mm) d i h i h i d i d o d i f h o d o Using the data you have collected, perform the calculations shown in the table. Are your results in complete agreement with the Fundamental Lens Equation? If not, to what do you attribute the discrepancies? For what values of d o were you unable to focus an image onto the screen? Use the Fundamental Lens Equation to explain why. 1) For a lens of focal length f, what value of d o would give an image with a magnification of one? 2) Is it possible to obtain a non-inverted image with a converging spherical lens? Explain. 3) For a converging lens of focal length f, where would you place the object to obtain an image as far away from the lens as possible? How large would the image be? 71

5 Candle Lab AP Physics B OBJECTIVES This lab will determine the focal length of a given lens by using an optical bench to make measurements of object and image distances. In addition, you will be asked to make other observations that further your knowledge of properties of your lens. Use the thin lens formula or equivalently,, along with your measured values for d o and d i to calculate the focal length of your lens. INTRODUCTION/THEORY Part IV: Magnification 11. Notice from the following diagram that the geometry of similar triangles shows that: Rearranging these ratios gives us the expressions: These are two alternative ways to determine the magnification of an image. and APPARATUS Quarter (or other object), Optical Bench, 2 Lens holders, light source, White notecard, Meterstick, Converging lens PROCEDURES Part I: Experimentally Determining Focal Length 1. Measure the diameter of the quarter (object, h o) and record. 2. Place your quarter (object) and lens so the diameter of the image the quarter on the screen is less than 1.5 cm. Make sure that the image is brought into sharp focus. 3. Measure the distance between the object and the lens (d o). 4. Measure the distance between the lens and the screen (d i). 5. Repeat steps 2-4 for image diameter equal to the diameter of your quarter and then for an image diameter greater than 5.0 cm. Part II: Affect of Covering the Lens 72

6 6. Using the last setup on your optical bench (h i > 5.0 cm) take a card and slowly cover the lens while watching the affect of the image. Describe what happens to the image (what part of the image disappears; what happens to the brightness of the image; at what point are you unable to see the image?) Part 3: Images Located at Infinity To complete this section, you must take your lens (in its holder) and your screen (with its holder) to the window station. With the blinds partially open, use your lens to form an image of an object located outside the room. Once you have a clear image, measure the distance from the lens to the screen. Part 4: Images within the Focal Len Take your lens and place it on the candle printed on your paper below: Slowly lift the lens above to candle printed on your paper while looking through the lens, until you reach the focal length. Could the image that you see through the lens be projected onto a screen? Why or why not? Describe what you see when you have lifted the lens the focal length above the paper? ANALYSIS Image Height Criteria h i < 1.5 cm h i = h o h i > 5.0 cm Measured Image Height Object Distance Image Distance Focal Length Average Focal Length Trial h i / h o d i / d o h i < 1.5 cm h i = h o h i > 5.0 cm Graph do vs di. What is this shape? Graph 1/do vs 1/di. What is the type of shape? How could you find f? Make a scale ray tracing of your experiments to verify calculations. 73

7 Multiple Choice 1. The speed of light in vacuum is about: A) 1100 ft/s B) mi/s C) m/s D) cm/s E) 186,000 mph 2. The sun is about m away. The time for light to travel this distance is about: A) s B) 8 s C) 8 min D) 8 hr E) 8 yr 3. Visible light has a frequency of about: A) Hz B) Hz C) Hz D) Hz E) Hz 4. Polarization experiments provide evidence that light is: A) a longitudinal wave B) a stream of particles C) a transverse wave D) some type of wave E) nearly monochromatic 5. For linearly polarized light the plane of polarization is: A) perpendicular to both the direction of polarization and the direction of propagation B) perpendicular to the direction of polarization and parallel to the direction of propagation C) parallel to the direction of polarization and perpendicular to the direction of propagation D) parallel to both the direction of polarization and the direction of propagation E) none of the above 6. Light from any ordinary source (such as a flame) is usually: A) unpolarized B) plane polarized C) circularly polarized D) elliptically polarized E) monochromatic 74

8 7. The relation n 1sin 1 = n 2 sin 2 which applies as a ray of light strikes an interface between two media, is known as: A) Gauss' law B) Snell's law C) Faraday's law D) Cole's law E) law of sines 8. As used in the laws of reflection and refraction, the "normal" direction is: A) any convenient direction B) tangent to the interface C) along the incident ray D) perpendicular to the electric field vector of the light E) perpendicular to the interface 9. The index of refraction of a substance is: A) the speed of light in the substance B) the angle of refraction C) the angle of incidence D) the speed of light in vacuum divided by the speed of light in the substance E) measured in radians 10. The diagram shows the passage of a ray of light from air into a substance X. The index of refraction of X is: A) 0.53 B) 0.88 C) 1.9 D) 2.2 E)

9 11. Which diagram below illustrates the path of a light ray as it travels from a given point X in air to another given point Y in glass? A) I B) II C) III D) IV E) V 12. A ray of light passes through three media as shown. The speeds of light in these media obey: A) v 1 > v 2 > v 3 B) v 3 > v 2 > v 1 C) v 3 > v 1 > v 2 D) v 2 > v 1 > v 3 E) v 1 > v 3 > v As light goes from one medium to another, it is bent away from the normal. Then: A) the speed of the light has increased B) dispersion must occur C) the second medium has a higher index of refraction D) no change in speed has occurred E) refraction has not occurred because refraction means a bending toward the normal 14. The separation of white light into colors by a prism is associated with: A) total internal reflection B) partial reflection from each surface C) variation of index of refraction with wavelength D) a decrease in the speed of light in the glass E) selective absorption of various colors 76

10 15. The index of refraction of benzene is The critical angle for total internal reflection, at a benzene-air interface, is about: A) 56 B) 47 C) 34 D) 22 E) A virtual image is one: A) toward which light rays converge but do not pass through B) from which light rays diverge but do not pass through C) from which light rays diverge as they pass through D) toward which light rays converge and pass through E) with a ray normal to a mirror passing through it 17. Which of the following is true of all virtual images? A) They can be seen but not photographed B) They are ephemeral C) They are smaller than the objects D) They are larger than the objects E) None of the above 18. The term "virtual" as applied to an image made by a mirror means that the image: A) is on the mirror surface B) cannot be photographed by a camera C) is in front of the mirror D) is the same size as the object E) cannot be shown directly on a screen 19. An object is 2 m in front of a plane mirror. Its image is: A) virtual, inverted, and 2 m behind the mirror B) virtual, inverted, and 2 m in front of the mirror C) virtual, erect, and 2 m in front of the mirror D) real, erect, and 2 m behind the mirror E) none of the above 20. A candle C sits between two parallel mirrors, a distance 0.2d from mirror 1. Here d is the distance between the mirrors. Multiple images of the candle appear in both mirrors. How far behind mirror 1 are the nearest three images of the candle in that mirror? A) 0.2d, 1.8d, 2.2d B) 0.2d, 2.2d, 4.2d C) 0.2d, 1.8d, 3.8d D) 0.2d, 0.8d, 1.4d E) 0.2d, 1.8d, 3.4d 77

11 21. Real images formed by a spherical mirror are always: A) on the side of the mirror opposite the source B) on the same side of the mirror as the source but closer to the mirror than the source C) on the same side of the mirror as the source but closer to the mirror than the focal point D) on the same side of the mirror as the source but further from the mirror than the focal point E) none of the above 22. The image produced by a convex mirror of an erect object in front of the mirror is always: A) virtual, erect, and larger than the object B) virtual, erect, and smaller than the object C) real, erect, and larger than the object D) real, erect, and smaller than the object E) none of the above 23. An erect object is located between a concave mirror and its focal point. Its image is: A) real, erect, and larger than the object B) real, inverted, and larger than the object C) virtual, erect, and larger than the object D) virtual, inverted, and larger than the object E) virtual, erect, and smaller than the object 24. An erect object is in front of a convex mirror a distance greater than the focal length. The image is: A) real, inverted, and smaller than the object B) virtual, inverted, and larger than the object C) real, inverted, and larger than the object D) virtual, erect, and smaller than the object E) real, erect, and larger than the object 25. As an object is moved from the center of curvature of a concave mirror toward its focal point its image: A) remains virtual and becomes larger B) remains virtual and becomes smaller C) remains real and becomes larger D) remains real and becomes smaller E) remains real and approaches the same size as the object 26. As an object is moved from a distant location toward the center of curvature of a concave mirror its image: A) remains virtual and becomes smaller B) remains virtual and becomes larger C) remains real and becomes smaller D) remains real and becomes larger E) changes from real to virtual 78

12 27. A concave mirror forms a real image which is twice the size of the object. If the object is 20 cm from the mirror, the radius of curvature of the mirror must be about: A) 13 cm B) 20 cm C) 27 cm D) 40 cm E) 80 cm 28. A concave spherical mirror has a focal length of 12 cm. If an object is placed 6 cm in front of it the image position is: A) 4 cm behind the mirror B) 4 cm in front of the mirror C) 12 cm behind the mirror D) 12 cm in front of the mirror E) at infinity 29. A concave spherical mirror has a focal length of 12 cm. If an object is placed 18 cm in front of it the image position is: A) 7.2 cm behind the mirror B) 7.2 cm in front of the mirror C) 36 cm behind the mirror D) 36 cm in front of the mirror E) at infinity 30. An erect object is located on the central axis of a spherical mirror. The magnification is 3. This means its image is: A) real, inverted, and on the same side of the mirror B) virtual, erect, and on the opposite side of the mirror C) real, erect, and on the same side of the mirror D) real, inverted, and on the opposite side of the mirror E) virtual, inverted, and on the opposite side of the mirror 31. An erect object is placed on the central axis of a thin lens, further from the lens than the magnitude of its focal length. The magnification is This means: A) the image is real and erect and the lens is a converging lens B) the image is real and inverted and the lens is a converging lens C) the image is virtual and erect, and the lens is a diverging lens D) the image is virtual and erect, and the lens is a converging lens E) the image is virtual and inverted and the lens is a diverging lens 32. An erect object placed outside the focal point of a converging lens will produce an image that is: A) erect and virtual B) inverted and virtual C) erect and real D) inverted and real E) impossible to locate 79

13 33. An object is 30 cm in front of a converging lens of focal length 10 cm. The image is: A) real and larger than the object B) real and the same size than the object C) real and smaller than the object D) virtual and the same size than the object E) virtual and smaller than the object 34. A camera with a lens of focal length 6.0 cm takes a picture of a 1.4-m man standing 11 m away. The height of the image is about: A) 0.39 cm B) 0.77 cm C) 1.5 cm D) 3.0 cm E) 6.0 cm 35. An erect object is 2f in front of a convex lens of focal length f. The image is: A) real, inverted, magnified B) real, erect, same size C) real, inverted, same size D) virtual, inverted, reduced E) real, inverted, reduced 36. An object is in front of a converging lens, at a distance less than the focal length from the lens. Its image is: A) virtual and larger than the object B) real and smaller than the object C) virtual and smaller than the object D) real and larger than the object E) virtual and the same size as the object 37. A 3-cm high object is in front of a thin lens. The object distance is 4 cm and the image distance is 8 cm. The image height is: A) 0.5 cm B) 1 cm C) 1.5 cm D) 6 cm E) 24 cm 38. What type of eyeglasses should a nearsighted person wear? A) diverging lenses B) bifocal lenses C) converging lenses D) plano-convex lenses E) double convex lenses 80

14 39. The two lenses shown are illuminated by a beam of parallel light from the left. Lens B is then moved slowly toward lens A. The beam emerging from lens B is: A) initially parallel and then diverging B) always diverging C) initially converging and finally parallel D) always parallel E) initially converging and finally diverging 40. A "wave front" is a surface of constant: A) phase B) frequency C) wavelength D) amplitude E) speed 41. Consider (I) the law of reflection and (II) the law of refraction. Huygens' principle can be used to derive: A) only I B) only II C) both I and II D) neither I nor II E) the question is meaningless because Huygen's principle is for wave fronts whereas both I and II concern rays 42. Interference of light is evidence that: A) the speed of light is very large B) light is a transverse wave C) light is electromagnetic in character D) light is a wave phenomenon E) light does not obey conservation of energy 43. In a Young's double-slit experiment the center of a bright fringe occurs wherever waves from the slits differ in phase by a multiple of: A) /4 B) /2 C) D) 3 /4 E) 2 81

15 44. A monochromatic light source illuminates a double slit and the resulting interference pattern is observed on a distant screen. Let d = center-to-center slit spacing, a = individual slit width, D = screen-to-slit distance, adjacent dark line spacing in the interference pattern. The wavelength of the light is then: A) d / D B) Ld/a C) da/d D) D/ a E) Dd / 45. In a Young's double-slit experiment, light of wavelength 500 nm illuminates two slits which are separated by 1 mm. The separation between adjacent bright fringes on a screen 5 m from the slits is: A) 0.10 cm B) 0.25 cm C) 0.50 cm D) 1.0 cm E) none of the above 46. In a Young's experiment, it is essential that the two beams: A) have exactly equal intensity B) be exactly parallel C) travel equal distances D) come originally from the same source E) be composed of a broad band of frequencies 47. If two light waves are coherent: A) their amplitudes are the same B) their frequencies are the same C) their wavelengths are the same D) their phase difference is constant E) the difference in their frequencies is constant 82

16 48. Binoculars and microscopes are frequently made with coated optics by adding a thin layer of transparent material to the lens surface as shown. One wants: A) constructive interference between waves 1 and 2 B) destructive interference between waves 3 and 4 C) constructive interference between 3 and 4 D) the coating to be more transparent than the lens E) the speed of light in the coating to be less than that in the lens 49. A student wishes to produce a single-slit diffraction pattern in a ripple tank experiment. He considers the following parameters: I. frequency II. wavelength III. water depth IV. slit width Which two of the above should be decreased to produce more bending? A) I, III B) I, IV C) II, III D) II, IV E) III, IV 50. Sound differs from light in that sound: A) is not subject to diffraction B) is a torsional wave rather than a longitudinal wave C) does not require energy for its origin D) is a longitudinal wave rather than a transverse wave E) is always monochromatic 83

17 Answer Key 1. D 2. C 3. C 4. C 5. D 6. A 7. B 8. E 9. D 10. C 11. E 12. C 13. A 14. C 15. C 16. B 17. E 18. E 19. E 20. A 21. E 22. B 23. C 24. D 25. C 26. D 27. C 28. C 29. D 30. A 31. C 32. D 33. C 34. B 35. C 36. A 37. D 38. A 39. A 40. A 41. C 42. D 43. C 44. A 45. B 46. D 47. D 48. C 49. B 84

18 50. D 85