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Physics LibreTexts

1.6: Relation between Flux and Intensity

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For an isotropic radiator,

Φ=4πI.

For an anisotropic radiator

Φ=Idω,

the integral to be taken over an entire sphere. Expressed in spherical coordinates, this is

Φ=2π0π0I(θ,ϕ)sinθdθdϕ.

If the intensity is axially symmetric (i.e. does not depend on the azimuthal coordinate ϕ ) equation ??? becomes

Φ=2ππ0I(θ)sinθdθ.

These relations apply equally to subscripted flux and intensity and to luminous flux and luminous intensity.

Example:

Suppose that the intensity of a light bulb varies with direction as

I(θ)=0.5I(0)(1+cosθ)

(Note the use of parentheses to mean "at angle θ ".)

Draw this (preferably accurately by computer - it is a cardioid), and see whether it is reasonable for a light bulb. Note also that, if you put θ=0 in equation ???, you get I(θ)=I(0).

Show that the total radiant flux is related to the forward intensity by

Φ=2πI(0)

and also that the flux radiated between θ=0 and θ=π/2 is

Φ=32πI(0).


This page titled 1.6: Relation between Flux and Intensity is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform.

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