Concepts_and_Calculations_CH24_25_26

Concepts_and_Calculations_CH24_25_26 - Chapter 24...

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Unformatted text preview: Chapter 24 Conceptual Questions and Concepts and Calculations CONCEPTUAL QUESTIONS ssm Solution is in the Student Solutions Manual. 1. Which of the following concepts applies to both sound waves and electromagnetic waves: (a) intensity or (b) polarization? Account for your answer. 2. Refer to Figure 24.2. Between the times indicated in parts c and d in the drawing, what is the direction of the magnetic field at the point P for the electromagnetic wave being generated? ls it directed into or out of the plane of the paper? Justify your an- swer. 3. ssm A transmitting antenna is located at the origin of an x, y. z axis system and broadcasts an electromagnetic wave whose electric field oscillates along the y axis. The wave travels along the +.\' axis. Three possible wire loops are available for use with an LC-tuned circuit to detect this wave: One loop lies in the xy plane. another in the A: plane, and the third in the y: plane. Which of the loops will detect the wave? Why? 4. Why does the peak value of the emf induced in a loop antenna (see Figure 24.6) depend on the frequency of the electromagnetic wave, whereas the peak value of the emf induced in a straight-wire antenna (see Figure 24.5) does not? 5. Suppose that the electric field of an elecuomagnetic wave de- creases in magnitude. Does the magnetic field increase, decrease, or remain the same? Account for your answer. 6. ssm An astronomer measures the Doppler change in frequency for the light reaching the earth from a distant star. From this mea- surement. can the astronotner tell whether the star is moving away from the earth or whether the earth is moving away from the star“? Explain. 7. Is there any real difference between a polarizer and an analyzer? In other words, can a polarizer be used as an analyzer, and vice versa? 8. Malus‘ law applies to the setup in Figure 24.2l. which shows the analyzer rotated through an angle 6 and the polarizer held fixed. Does Malus’ law apply when the analyzer is held fixed and the po- larizer is rotated? Give your reasoning. 9. ln Example 7, we saw that when the angle between the polarizer and analyzer is 63.4", the intensity of the transmitted light drops to one-tenth of that of the incident unpolarized light. What happens to the light intensity that is not transmitted? 10. Light is incident from the left on two pieces of polarizing mater— ial, l and 2. As part a of the drawing illustrates. the transmission axis of material I is along the vertical direction, and that of material 2 makes an angle of 6 with respect to the vertical. In part b of the drawing the two polarizing materials are interchanged. (a) Assume that the incident light is unpolarizcd and determine whether the intensity of the transmitted light in drawing a is greater than, equal to, or less than that in drawing b. (b) Repeat part (a), assuming that the incident light is linearly polarized along the vertical direction. Justify your answers to both parts (a) and (b). i Transmitted light Ill) Incident light light I—‘—>— I i\ Transmitted I ll. ssm You are sitting upright on the beach near a lake on a sunny day. wearing Polaroid sunglasses. When you lie down on your side, facing the lake, the sunglasses don’t work as well as they did while you were sitting upright. Why not'.’ CONCEPTS 8: CALCULATIONS Note: Each of these problems consists of Concept Questions follmved by a related quantitative Problem. The C onccpt Questions involve little or no mathematics. Theyfocus on the concepts with \t-‘hich the pmblems deal. Recognizing the concepts is the essential initial step in (my pmblem- solving technique. 55. Q Concept Questions A certain type of laser emits light of known frequency. The light. however. occurs as a series of short pulses, each lasting for a time to. (a) How is the wavelength of the light related to its frequency? (b) How is the length (in me- ters) of each pulse related to the time to? Problem A laser emits a pulse of light that lasts for 2.7 X 10‘” s. The frequency of the light is 5.2 X IO” Hz. (a) How many wave- lengths are there in one pulse? (b) The light enters a pool of water. Its frequency remains the same, but the light slows down to a speed of 2.3 X l0“ m/s. How many wavelengths are there now in one pulse? 56. Q Concept Questions (3) Suppose that the magnitude E of the electric field in mi electromagnetic wave triples. By what factor does the intensity S of the wave change? (b) The magnitude 8 of the magnetic field is tnuch smaller than E because, according to Equa- tion 24.3, B = E/c, where c is the speed ol‘light in a vacuum. If B triples, by what factor does the intensity change? Account for your answers. Problem The magnitude of the electric field of an electromagnetic wave increases from 3l5 to 945 MC. (a) Determine the intensities for the two values of the electric field. (b) What is the magnitude of the magnetic field associated with each electric field? (c) Determine the intensity for each value of the magnetic field. Make sure your answers are consistent with your answers to the Concept Questions. 57- Q Concept Questions Consult Multiple-Concept Example 5 to review the concepts on which this problem depends. A source is radiating light waves uniformly in all directions. At a certain distance r from the source a person measures the average intensity of the waves. (a) Does the average intensity increase, decrease. or remain the same, as r increases? (b) If the magnitude of the electric field is determined front the average intensity, is the electn'c field the nns value or the peak value? In both cases, justify your answers. Problem A light bulb emits light uniformly in all directions. The average entitled power is 150.0 W. At a distance of 5.00 m from the bulb. determine (a) the average intensity of the light. (b) the rms value of the electric field, and (c) the peak valttc of the electric field. 58. ® Concept Questions An electric charge is placed in a laser beam. Does a stationary charge experience a force due to (a) the. electiic field and (b) the magnetic field of the electro- magnetic wave? Now suppose that the. charge is moving perpendicu— lar to the magnetic field of the beam. Does it experience (c) an elec- tric force and (d) a magnetic force? Account for your answers. Problem A stationary particle of charge (1 = 2.6 X 10‘“ C is placed in a laser beam whose intensity is 2.5 X [03 W/mz, Deter- mine the magnitude of the (a) electric and (b) magnetic forces exened on the charge. If the charge is moving perpendicular to the magnetic field with a speed of 3.7 X l04 m/s. find the magnitudes of the to) electric and (d) magnetic forces exerted on it. Verify that your answers are consistent with your answers to the Concept Questions. 59. Concept Ques- : tions The draw- _. -I‘\ ing shows light incident on a I 3. polarizer whose transmission Incident I ;Transmitted axts is parallel to the : axrs. I j light .1.- The polarizer is rotated clockwise through an angle a bctween 0 and 90°. While the polarizer is being rotated. does the average intensity of the transmitted light increase, decrease, or re- main the same if the incident light is (a) unpolan'zed, (b) polarized pzu'allel to the z axis, and (c) polarized parallel to the y axis? Provide a reason for each of your answers. Problem The average intensity of the incident light is 7.0 W/mz. Determine the average intensity of the transmitted light for each of the six cases shown in the table. Intensity of Transmitted Light Incident Light Unpolarized Polarized parallel to : axts Polarized parallel to y axrs Be sure that your answers are consistent with your answers to the Concept Questions. 60. Concept 300° 300° Question The drawing shows three polarizer/analyzcr pairs. The incident light on each pair is unpolan’zed and has the same aver- A age intensity. Rank the pairs according to the average intensity of the transmitted light, largest first. Provide reasons for your answers. Problem The average intensity of the unpolar- ized incident beam is 48 W/mz. Find the aver- age intensity of the trans— mitted beams for each of the three cases shown in the drawing. Be sure your answers are consis- tent with your answer to the Concept Question. l Transmitted Incident f beam beam *61. Q Concept Question The drawing shows three situations A. B. and C in which an observer and a source of electro- magnetic waves are moving along the same line. In each case the source emits a wave of the same frequency. The an'ows in each situ- ation denote velocity vectors relativc to the ground and have the magnitudes indicated, either it or 21!. Rank the frequencies of the 0b- servcd electromagnetic waves in descending order (largest first) ac— cording to magnitude. Explain your reasoning. Problem Each of the sources in the drawing emits a frequency of 4.57 X 10'4 Hz, and the speed 22 is 1.50 X It)" m/s. Calculate the ob served frequency in each of the three cases. Verify that your answers we consistent with your answer to the Concept Question. Observer Source A 1: 2n 3 9—2;» G u u ’3‘ 62. ® Concept Questions The drawing shows four sheets of polarizing material, each with its transmission axis ori— ented differently. Light that is polarized in the vertical direction is incident from the left. One of the sheets is to be removed, with the goal of having some light still pass through the remaining three sheets and emerge on the right. (a) There are a number of possi- bilities for the sheet that is removed. What are they? Account for your answer. (b) Of the possibilities identified in Concept Ques- tion (a), which one allows the greatest average light intensity to pass through the sheets? Justify your answer. Problem The light incident from the left in the drawing has an aver- age intensity of 27 W/mz. For each of the possibilities identified in Concept Question (a). determine the average intensity of the light that emerges on the right in the drawing. Be sure that your answer is consistent with your answer to Concept Question 0)). Horizontal A B C D Chapter 25 Conceptual Questions and Concepts and Calculations CONCEPTUAL QUESTIONS ssrn Solution is in the Student Solutions Manual. 1. ssm A sign painted on a store window is reversed when viewed from inside the store. If a person inside the store views the reversed sign in a plane min'or. does the sign appear as it would when viewed from outside the store? (Try it by writing some letters on a transpar- ent sheet of paper and then holding the back side of the paper up to a mirror.) Explain. 2. if a clock is held in front of a mirror, its image is reversed left to right. From the point of view of a person looking into the mirror. does the ilnage of the second hand rotate in the reverse (counter- clockwise) direction“? Justify your answer. 3. (a) Which kind of spherical mirror. concave or convex, can be used to start a fire with sunlight? (b) For the best results. how far from the mirror should the paper to be ignited be placed? Explain your answers. 4. The photograph shows an experimental device at Sandia National Labora- tories in New Mexico. This device is a mirror that focuses sunlight to heat sodium to a boil, which then heats helium gas in an engine. The engine does the work of driving a generator to produce electricity. The sodium tlnit and the en- gine are labeled in the photo. (a) What kind of mirror is being used, and (b) where is the sodium unit located relative [0 (Courtesy Sandia National Laboratories) Sodium unit the mirror? Express your answer in terms of the focal length of the mirror. Give your reasoning. 5. Refer to Figure 25.14 and the related discussion about spherical abcn‘ation. To bring the top ray closer to the focal point F after re— flection, describe how you would change the shape of the mirror. Would you open it up to produce a more gently curving shape or bring the top and bottom edges closer to the principal axis? Account for your answer using the law of reflection. 6. (a) Can the image formed by a concave mirror ever be projected directly onto a screen, without the help of other mirrors or lenses? If so, specify where the object should be placed rela— tive to the mirror. (b) Repeat part (a) assuming that the mirror is convex. 7. (a) When you look at the back side of a shiny teaspoon. held at arm’s length, you see yourself upright. Why? (b) When you look at the other side of the spoon, you see yourself upside down. Why? 8. ssm If you stand between two parallel plane mirrors. you see an infinite number of images of yourself. This occurs because an image in one mirror is reflected in the other minor to produce another im- age, which is then re—reflected. and so forth. The multiple images are equally spaced. Suppose that you are facing a convex mirror. with a plane mirror behind you. Describe what you would see and com- ment about the spacing between any multiple images. Explain your reasoning. 9. Sometimes news person— nel covering an event use a microphone iu‘rangement that is designed to increase the ability of the mike to pick up weak sounds. The drawing shows that the arrangement consists of a hollowed-out shell behind the mike. The shell acts like a mirror for sound waves. Explain how this :urangement enables the mike to detect weak sounds. Microphone 10. When you see the image of yourself formed by a mirror, it is because (l) light rays actually coming from a real image enter your eyes or (2) light rays appearing to come from a virtual image enter your eyes. If light rays from the image do not enter your eyes, you do not see yourself. Are there any places on the principal axis where you cannot see yourself when you are in front of a mirror that is (a) convex and (b) concave? If so, where are these places? 11. Concept Simulation 25.3 at www.wiley.com/college/cutnell reviews the concepts that are important in this question. Plane mirrors and convex mirrors form virtual images, With a plane mir— ror. the image may be infinitely far behind the mirror, depending on where the object is located in front of the mirror. For an object in front of a single convex mirror, what is the greatest distance behind the mirror at which the image can be found? Justify your answer. 12. Concept Simulation 25.3 at www.wiley.com/college/cutnell al~ lows you to explore the concepts to which this question relates. ls it possible to use a convex mirror to produce an image that is larger than the object? Provide a reason for your answer. 13. ssm Suppose you stand in front of a spherical mirror (concave or convex). ls it possible for your image to be (a) real and upright or (b) virtual and inverted? Justify your answers. CONCEPTS & CALCULATIONS Note: Each of these problems consists ofConcept Questions followed by a related quantitative Problem. The Concept Questions involve little or no mathematics. Theyfoctts on the concepts with which the problems deal. Recognizing the concepts is the essential initial step in any problem-solving technique. 42. ® Concept Questions A small mirror is attached to a ver— tical wall, and it hangs a distance y above the. floor. A ray of sunlight strikes the mirror, and the reflected ray forms a spot on the floor. (a) From a knowledge of y and the horizontal distance .r frotn the base of the wall to the spot, describe how one can deter— mine the angle of incidence of the ray striking the mirror. If it is morning and the mirror is facing due east. would (b) the angle of in— cidence and (c) the distance .r increase or decrease in time? Why? Problem Suppose the mirror is L80 m above the floor. The reflected ray of sunlight strikes the floor at a distance of 3.86 m from the base of the wall. Later in the morning, the ray is observed to strike the floor at a distance of 1.26 m from the wall. The earth rotates at a rate of 15.0° per hour. How much time (in hours) has elapsed between the two observations? 43. 6 Concept Questions (a) Suppose that you are walking perpendicularly toward a stationary plane mirror. Follow- ing the method discussed in Section 3.4. express your image’s veloc— ity V” relative to you in terms of the image’s velocity VIM relative to the mirror and the mirrors velocity VMy relative to you. (b) How is the mirror’s velocity VMV relative to you related to your velocity Vvs-r rela- tive to the mirror? Explain. (c) Consider both velocities ii“, and VIM. Do they have the same magnitudes and the same directions? Explain. Problem When you walk perpendicularly with a velocity of +0.90 m/s toward a stationary plane mirror, what is the velocity of your image relative to you? The direction in which you walk is the positive direction. 44. ® Concept Questions (21) For an inverted image that is in front of a mirror, is the image distance positive or negative and is the image height positive or negative? Explain. (b) Given the image distance, what additional information is needed to determine the focal length? Explain. to) Given the object and image heights and a statement as to whether the image is upright or inverted, what addi- tional information is needed to determine the object distance? Problem A small statue has a height of 3.5 cm and is placed in front of a concave mirror. The image of the statue is inverted, l.5 cm tall, and is located l3 cm in front of the mirror. Find the focal length of the mirror. 45. Concept Questions These questions refer to Figure 25.220. (a) As the object distance increases, does reflected ray I change? (b) As the object distance increases, does reflected ray 3 make a greater or smaller angle with respect to the principal axis? (c) Extending the reflected rays l and 3 behind the mirror allows us to locate the top of the image. As the object distance increases. does the image height increase or decrease? Problem A convex mirror has a focal length of —27.0 cm. Find the magnification produced by the mirror when the object distance is 9.0 cm and l8.0 cm. Verify that your answers are consistent with your answers to the Concept Questions. .2: 46. a Concept Questions (a) Sup- pose that you are walking to- ward a stationary plane mirror as in the drawing. The view is from above. Fol- lowing the method discussed in Section 3.4. express your image’s velocity Vn- rel- You alive to you in terms of the image’s veloc- _._ ity VIM relative to the minor and the mir- ror‘s velocity V3" relative to you. (b) How is the mirror’s velocity VMY relative to you related to your velocity V“. relative to the mirror? Explain. (c) Consider both velocities V“, and VIM. Do they have the same .r and y components? Explain. Problem You walk at an angle of 0 = 50.0° toward a plane mirror, as in the drawing. Your walking velocity has a magnitude of 0.90 m/s. What is the velocity of your image relative to you (magni- tude and direction)? ‘3 47. ® Concept Questions A tall tree is growing across a river from you. You would like to know the distance between yourself and the tree. as well as its height, but are unable to make the measurements directly. However, by using a mirror to form an image of the tree, and then measuring the image distance and the image height, you can calculate the distance to the tree. as well as its height. (a) What kind of mirror. concave or convex. must you use? Why? (b) You will need to know the focal length of the mirror. The sun is shining. You aim the tnirror at the sun tuid form an image of it. How is the image distance of the sun related to the focal length of the mirror? (c) Having measured the image distance (1; and the image height hi of the tree, as well as the image distance of the sun, describe how you would use these numbers to determine the distance and height of the tree. Problem A mirror produces an image of the sun. and the image is located 0.9000 m from the mirror. The same mirror is then used to produce an image of the tree. The image of the tree is 0.9l00 m from the mirror. (a) How far away is the tree? (b) The image height of the tree has a magnitude of 0. 12 m. How tall is the tree? Chapter 26 Conceptual Questions and C...
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