Name PH206 Exam III Spring 2000 Some Constants: % = 3.14159 sin(a±b)=sinacosb ± cosasinb ) = 5.6696 10-8 W/m 2 #K 4 cos(a±b)=cosacosb. sinasinb k B = 1.38 10-23 J/K sina ± sinb = 2 sin ½(A±B) cos½(a.b) R = 8.315 J/mol#K cosa ± cosb = 2 cos½(a+b) sin½[±(a-b)] A V = 6.02 10 23 molecules/mol 1 cal = 4.184 J c = 2.99793 10 8 m/s 1 atm = 101 kpa m e c 2 = 0.511 MeV monatomic ideal gas: = C p /C V = 1.6667 1 ev = 1.602 10-19 J I 0 = 1.00 10-12 W/m 2 velocity of sound in air (room temp, 1 atm) = 343 m/s. Write your solutions on these pages, and turn in the entire exam. If you need extra paper, just ask. For problems 11 to 15: to receive full credit for correct answers, you must show your work! Report numerical answers to three (3) significant figures. Score Summary (to be filled in by instructor) Mult Choice Short Answer Problems 1. 6. 11. 2. 7. 12. 3. 8. 13. 4. 9. 14. 5. 10. 15. Totals + + =
PH206 Spring 2000 Page 2 Multiple Choice: (Circle your choice) 1. For two point sources of light, a diffraction pattern on a distant screen is observed which has a dark spot in the center (i.e. at = 0 ). Which of the following can be concluded from this observation? a. The two sources are coherent and in phase. b. The two sources are coherent and 180 o out of phase. c. The two sources are incoherent and in phase d. The two sources are incoherent and 180 o out of phase. e. Such a pattern is impossible. 2. In a two-slit optical interference pattern the wavelength and frequency of the light are a. the same everywhere b. both greater in regions with destructive interference. c. both smaller in regions with destructive interference. d. the wavelength is smaller and the frequency higher in regions with destructive interference. e. the wavelength is larger and the frequency smaller in regions with destructive interference. 3. For a single slit diffraction pattern produced on a screen using red light, you see a central maximum, and a number of smaller maxima on either side. If the light were changed to blue light (blue light has a shorter wavelength than does red light), then a. the pattern will shrink in size (central maximum less wide, other maxima closer to it) b. the pattern increases in size (central maximum wider, other maxima farther from it) c. the width of the central maximum increases, but the positions of the other maxima do not change. d. the width of the central maximum decreases, but the positions of the other maxima do not change. e. the width of the central maximum stays the same, but the other maxima move farther from it. 4. A rocket is traveling by the Earth with a speed of 0.9 c. Just when it passes the Earth, the rocket ejects a shuttle craft in the backwards direction with a speed of 0.5 c relative to the rocket. Just after the shuttle is ejected, the shuttle emits a pulse of light. What is the speed of the light pulse as seen by an observer on the Earth? a. 1.4 c b. 0.73 c c. 0.4 c d. 1.0 c e. None of these 5. Unpolarized light is sent through a single polarizing sheet which has its axis vertical. How much intensity gets through the sheet? (Assume a perfect polarizer, with no additional losses). a. 100% b. 70.7% c. 50% d. 29.3% e. None of these
PH206 Spring 2000 Page 3 Short Answer Provide a short answer (1 or 2 sentences and/or appropriately labeled diagram) for each. 6. Why can you easily hear around corners, but not see around corners? 7. If you hold two small flashlights near each other and shine the light from both at the same spot on distant wall, you do not see a diffraction pattern. Why? 8. The small angle approximation was used for some of our equations and for some of the solutions to problems. Where does the small angle approximation come from and how small of an angle is generally necessary for it to work?
PH206 Spring 2000 Page 4 9. What are proper time, proper length, and rest energy and why are they useful? 10. The Andromeda galaxy is 2 million light-years from our Milky Way. That is, it takes light 2 million years to get to the Andromeda galaxy. Though nothing can travel faster than light, how is it possible that an Earth-born astronaut could get to the Andromeda galaxy in their own lifetime if only they had a fast enough rocket?
PH206 Spring 2000 Page 5 Problems (SHOW YOUR WORK, you will not get credit unless we can see how you got your answer.) 11. Laser light ( = 694 nm) is incident on two narrow slits which are 0.130 mm apart. What is the spacing between the bright fringes of the diffraction pattern observed on a screen 5.00 m away? 12. A single narrow slit is illuminated with yellow light ( = 590 nm). If the central maximum is 9.32 cm wide on a screen 10.0 m away, how wide is the slit? 13. A radar installation operates at 9000 MHz (9.00 10 9 Hz) with a dish antenna that is 15.0 m across. What is the maximum distance for which this system could expect to be able to distinguish two aircraft which are 150 m apart?
PH206 Spring 2000 Page 6 14. As a rocket passes by the Earth with a speed of 0.840 c an observer on the Earth measures the length of the rocket to be 9.32 m. How long is the rocket as measured by an astronaut on the rocket? 15. In a particular color television picture tube, the electrons are accelerated through a potential difference of 30.0 kv (30000 V). What is the speed of the electrons when they strike the screen? (Put your value in units of c ). END