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Physics LibreTexts

2.6: Net Flux and Exitance

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Formerly known as emittance, the exitance M refers to a point on a reflecting or emitting surface and is defined as the total power emitted in all directions per unit physical area, so that

M=2π0π/20L(ϑ,φ)sinϑcosϑdϑdφ

where it may be seen from the limits of integration that “in all directions” means over a hemisphere. The factor sinϑdϑdφ is an element of solid angle, dω, and the factor cosϑ is needed to convert the projected area of radiance back into physical area. Using the notation of Chapter 1., i.e. let μ=cosϑ, dμ=sinϑdϑ, we have

M=2π010L(μ, φ)μdμdφ.

If we compare M to Chandrasekhar’s quantity the net flux πF, which, in particular, he uses for a plane parallel beam of radiation

πF=2π02π0L(ϑ, φ)sinϑcosϑdϑdφ =2π011L((μ, φ)μdμdφ

we see that the net flux is indeed the result of integration over all directions, i.e. over a sphere. It follows that net flux and exitance are not the same thing (although there may be situations in which they amount to the same), and nor does πF always mean the strength of a plane parallel beam of radiant flux density F. Indeed, we can calculate the net flux of a plane parallel beam incident on a surface in the direction (μ0, φ0), using the radiance of a plane parallel beam given by Chapter1, equation (7), as

πF=2π011Fδ(μμ0)δ(φφ0)μdμdφ,

which results in

πF=Fμ0,

this result being the irradiance E of the surface, as we knew it should be!


This page titled 2.6: Net Flux and Exitance is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Max Fairbairn & Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform.

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