Hello all,(adsbygoogle = window.adsbygoogle || []).push({});

I already know that the radiant intensity of a point light source falls off with the inverse square of the distance to the source. This, however, only happens in a vacuum. My question is, what is the more general law for a point source inside an opaque medium with a known absorption coefficient σ(x) that may vary across space. From symmetry considerations alone, I would expect that the result will still be a function only of the distance to the light source, as before, just not an inverse square power anymore. The actual function will, of course, depend on σ(x) and should be the outcome of some 1D differential equation whose control variable is the distance to the source - it is the form of this 1D equation that I am looking for.

To clarify a bit further, the above absorption coefficient occurs in the light transport equation when stating that the derivative of radiance L(t) along a light ray parameterised by t is:

dL(t)/dt = -σ(t) L(t)

or stating the same in 3D space:

(ω.∇) L(x, ω) = -σ(x) L(x, ω)

where L(x, ω) is the radiance at point x in the direction ω.

Thank you,

manuel

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# The inverse square law for point light sources inside an opaque medium

**Physics Forums | Science Articles, Homework Help, Discussion**