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Unformatted text preview: Homework 5 Physics 204, summer 2008 Part 1 1. Read sections 11.1, 11.4, and the parts of 11.6 involving reflection and plane mirrors in Physics: The First Science. 2. A generator uses a coil that has 60 turns and a 0.50 T magnetic field. The frequency of this generator is 60.0 Hz, and its emf has an maximum value of 170 V. Assuming that each turn of the coil is a square (an approximation), determine the length of the wire from which the coil is made. 3. A generating station is producing 2.00 106 W of power that is to be sent to a small town located 9.0 km away. Each of the two wires that comprise the transmission line has a resistance per kilometer of length of 5.00 10‐2 /km. a. Find the power lost in heating the wires if the power is transmitted at 1250 V. b. A 130:1 (ratio between the number of windings on the output side to the number of windings on the input side) step‐up transformer is used to raise the voltage before the power is transmitted. How much power is now lost in heating the wires? 4. Neil A. Armstrong was the first person to walk on the moon. The distance between the earth and the moon is 3.85 108 m. a. Find the time it took for his voice to reach earth via radio waves. b. Someday a person will walk on Mars, which is 5.6 1010 m from earth at the point of closest approach. Determine the minimum time that will be required for that person's voice to reach earth. 5. Two plane mirrors are separated by 120°, as the drawing illustrates. If a ray strikes mirror M1 at a 1 = 70° angle of incidence, at what angle 2 does it leave mirror M2? 6. Review the conceptual example on the last page of this homework before attempting this problem. A person whose eyes are 1.80 m above the floor stands in front of a plane mirror. The top of her head is 0.12 m above her eyes. a. What is the height of the shortest mirror in which she can see her entire image? b. How far above the floor should the bottom edge of the mirror be placed? Part 2 7. Read the parts of 11.6 involving curved mirrors and refraction in Physics: The First Science. 8. The outside mirror on the passenger side of a car is convex and has a focal length of ‐8.1 m. Relative to this mirror, a truck traveling in the rear has an object distance of 7 m. a. Draw a ray diagram for this situation. b. Find the image distance of the truck. c. Find the magnification of the mirror. 9. A clown is using a concave makeup mirror to get ready for a show and is 21 cm in front of the mirror. The image is 64 cm behind the mirror. a. Draw a ray diagram for this situation. b. Find the focal length of the mirror. c. Find the magnification. 10. A spotlight on a boat is y = 2.3 m above the water, and the light strikes the water at a point that is x = 9.5 m horizontally displaced from the spotlight (see the drawing). The depth of the water is 4.0 m. Determine the distance d, which locates the point where the light strikes the bottom. 11. A ray of light is traveling in glass and strikes a glass/liquid interface. The angle of incidence is 54.0°, and the index of refraction of glass is n = 1.50. a. What must be the index of refraction of the liquid such that the direction of the light entering the liquid is not changed? b. What is the largest index of refraction that the liquid can have, such that none of the light is transmitted into the liquid and all of it is reflected back into the glass? Conceptual | ull‐Length Versus Half‐Length Mirrors F
Example In the diagram a woman is standing in front of a plane mirror. What is the minimum mirror height necessary for her to see her full image? For the woman to see her full‐sized image, only a half‐sized mirror is needed. Reasoning and Solution The mirror is labeled ABCD in the drawing and is the same height as the woman. Light emanating from her body is reflected by the mirror, and some of this light enters her eyes. Consider a ray of light from her foot F. This ray strikes the mirror at B and enters her eyes at E. According to the law of reflection, the angles of incidence and reflection are both . Any light from her foot that strikes the mirror below B is reflected toward a point on her body that is below her eyes. Since light striking the mirror below B does not enter her eyes, the part of the mirror between B and A may be removed. The section BC of the mirror that produces the image is one‐half the woman’s height between F and E. This follows because the right triangles FBM and EBM are identical. They are identical because they share a common side BM and have two angles, and 90°, that are the same. The blowup in the diagram illustrates a similar line of reasoning, starting with a ray from the woman’s head at H. This ray is reflected from the mirror at P and enters her eyes. The top mirror section PD can be removed without disturbing this reflection. The necessary section CP is one‐
half the woman’s height between her head at H and her eyes at E. We find, then, that only the sections BC and CP are needed for the woman to see her full height. The height of section BC plus section CP is exactly one‐half the woman’s height. The conclusions here are valid regardless of how far the person stands from the mirror. Thus, to view one’s full length in a mirror, only a half‐length mirror is needed. ...
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- Spring '09