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I don't understand why the following should hold in light transport theory:

let p(x) be the number of particles per unit volume at the point x, then the total number of particles P(x) in a small differential volume dV is

$$P(x)=p(x)dV$$

How come?

I don't understand: is the "small differential volume" even smaller than the unit volume where p(x) particles are counted? I can't visualize this thing geometricaly or physically

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Think of $p(x)$ as a density: at point $x$ there are $p(x)$ particles per cubic meter, say. Then for a small volume, say $dV=$ 1 cubic millimeter, how many particles are in that small volume?

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  • $\begingroup$ Thanks, you're right. I got to that conclusion before your answer but you helped me anyway. Thanks! $\endgroup$ – Marco A. Sep 3 '13 at 11:16

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