Energy flux in optics in hydrogen gas

AI Thread Summary
The discussion focuses on deriving the energy flux equation for a plane wave incident on hydrogen gas. The key equation presented is d∅/dz = -nσ(ω)∅(z), where σ(ω) represents the diffusion cross-section. The solution indicates that the energy flux ∅(z) can be expressed as ∅(z) = ∅0 exp(-z/L), with L having the same dimensions as z, clarifying a common misconception about its interpretation. Participants emphasize the importance of understanding the physical meaning of the variables involved. The thread concludes with a request for further clarification on the relationship between L and z.
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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.



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The Attempt at a Solution

 
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I don't think L is the luminance. Shouldn't it have the same units as z?
 
Yes, of course stupid mistake from me. L has the same dimension as z. But still i have no answer for my question:approve:
 
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