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# faq6 - FREQUENTLY ASKED QUESTIONS February 8 2012 Content...

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FREQUENTLY ASKED QUESTIONS February 8, 2012 Content Questions How do we use the formula I ν , where it’s all differentials? The formula for I ν , the specific intensity, is a distribution (sometimes called a “differential distribution”): this is a very important kind of function that is used often in science and engineering. I think the best way to think of a distribution f ( x ) = dn ( x ) dx is as a his- togram , for which the bins are taken to be infinitesimally small. First think of a histogram, with M bins of finite size Δ x i . You have a total of N “items” (people, photons, chunks of energy, gallons of water, whatever) to be dis- tributed among the bins. Bin i has n i of them, such that Σ M i =1 n i = N . So what the histogram describes is “number of items per Δ x ” as a function of x , or, for a continuous quantity, “amount of stuff per Δ x ” as a function of x . In the limit that the bin width gets infinitesimally small, Δ x dx , the distribution can be described as dn dx .

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faq6 - FREQUENTLY ASKED QUESTIONS February 8 2012 Content...

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