ECE594I, Prof. Brown, Fall Quarter 2009 1 Homework Problems #1: Fundamentals of Radiation and Fluctuations 1. Planck’s law of radiation is a triumph of quantum physics and very useful in many fields of science and engineering. (a). Given a 300 K blackbody of unity emissivity, find the frequency in THz (accurate to 100 GHz) and the wavelength in micron where the brightness form of Planck’s law is a maximum (can use numerical or analytic techniques). (b) What is this maximum brightness in MKS units ? (c) what is the brightness of this same blackbody at 1.0 THz and how much less is this than the maximum ? 2. A useful function for practically any electromagnetic sensor is the integrated brightness [i.e., integrated over frequency]. (a) Derive an expression for the integrated brightness IB in terms of the temperature and the Stefan-Boltzman constant, σ = (2 π h/15c 2 )( π k B T/h) 4 . (b) Evaluate IB at T = 300 K. (c) Now consider the fractions of IB that lies above and below a certain
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