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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 StefanBoltzman 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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 Spring '09
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