Relating Radiancy to Energy Density?

AI Thread Summary
Radiancy, denoted as R(ν, T), is related to energy density, u(ν, T), through the equation R(ν, T) = (c/4)u(ν, T). The factor c/4 arises from the geometry of radiation emission and the distribution of energy in a black body. Specifically, this factor accounts for the average intensity of radiation emitted in all directions from a surface. Understanding this relationship is crucial for analyzing black body radiation and its applications in physics. Clarifying the derivation of this factor can enhance comprehension of radiative transfer concepts.
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I'm looking through some of my physics notes where we derived radiancy equations for black body radiation (Rayleigh-Jeans and Planck), and I have a quick question. In class, we went through the derivation for the energy density as a function of frequency and temperature. However, I can't find anything in my notes about how radiancy is related to energy density. I tried to look online, and didn't find anything helpful, other than the equation that relates them: R(\nu ,T) = c/4 u(\nu ,T), where u is the energy density and R is the radiancy. From the units it looks like radiancy is the power per area per time, but I am totally mystified by the factor c/4. Can anyone quickly go over where this comes from?
 
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Sorry, the TeX came out wrong. It should be one-fourth times c times u (nu, T).
 

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