Energy flux in optics in hydrogen gas

[kirikoo]

Homework Statement

There is a half space z>0 full with hydrogen gas with density n atoms / metres cube.
An incident wave plane with pulsation ω coming from z = -∞ arrives at the surface of incidence. This wave transports a flux of energy ∅0 at z=0.
We consider a elementary cylinder whose axe along z with section S between z and z+dz
Prove that the flux of energy of the wave is given by d∅/dz= -nσ(ω)∅(z) , σ(ω) is the diffusion cross-section. And therefore ∅(z) = ∅0(z)exp(-z/L).
I suppose L is the luminance.

Thank you for your help.

Homework Equations

The Attempt at a Solution

 

[tman12321]

I don't think L is the luminance. Shouldn't it have the same units as z?

 

[kirikoo]

Yes, of course stupid mistake from me. L has the same dimension as z. But still i have no answer for my question