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Unformatted text preview: Physics 112, Spring 2010, Holzapfel Problem Set 5 (6 problems). Due Wednesday, October 6th , 5 PM Problem 1 : Seeing in the Dark Consider a light bulb with a tungsten filament at a temperature of T f = 3500K. (a) If the power input is 100W and the emssivity is = . 30, what is the surface area A of the lightbulb filament. (b) The radiation reaching your retina consists of two components: The 300K blackbody radiation from 4 steradians inside the eye, and visible photons arriving in the solid angle filled by the source. Suppose the light bulb is 10 meters away. What is the ratio of the energy flux at your retina from these two sources. Even though the background provides much more flux than the source, the room still gets dark when you turn out the lights. Why is this? (c) The eyes can be treated as nearly ideal photon detectors operating in the (relatively) narrow band of visible radiation. Even though the number of visible wavelength photons produced by a 300K source is extremely low, it is not zero. Therefore, the T b = 300K background can present a fundamental limitation to the detection of faint sources. Assume that our eyes are operating in a narrow band at the peak of the lightbulb filament blackbody spectrum and that T f >> T b . Show that the maximum distance at which one could see a light bulb is: D = v u u t A 4 exp 2 . 82 T f T b [ exp ( 2 . 82 )- 1 ] . (1) Compare this result with your experience. How good a job does the human eye do at reaching this funda- mental limitation. How could the human eye be changed to improve its performance at this task? (hint: It may be somewhat uncomfortable) Problem 2 : Liquid 4 He Kittel 4.14 Problem 3 : The Big Bang Kittel, 4.18 Problem 4 : Melting of crystalline solids and the zero point motion We start with a perfect crystal i.e. a system of N atoms arranged in a periodic arrangement. As you know,We start with a perfect crystal i....
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