Transmissivity of stacked absorbing foils with multiple reflections

[Christofer Br]

Suppose I have an infinitely thin foil that absorbs 1% of incoming radiation. It therefore emits 0.5% of the incoming radiation in both directions perpendicular to the plane of the foil. That is, transmission is 0.5%. How to calculate transmission for a series of such foils? There will be a lot of absorption and reemission between the layers and I don't know how to integrate all of this

 

[sophiecentaur]

That is, transmission is 0.5%

I am wondering what happens to the remaining 99% of the radiation after the first foil in your thought experiment. The reflection will depend on the Dielectric constant of the foil. See this link on Fresnel Equations.

 

[Christofer Br]

I am wondering what happens to the remaining 99% of the radiation after the first foil in your thought experiment. The reflection will depend on the Dielectric constant of the foil. See this link on Fresnel Equations.

It will be reflected, the foil is a conductor (lets assume it's gold because it has relatively constant emissivity across a very broad spectrum, exact properties are not important) - so it REFLECTED 99% and emitted additional 0.5% in one direction

 

[sophiecentaur]

An "infinitely thin" foil is a bit too much of an abstraction for this question. Loads of light will pass through a thin enough gold foil. Just how thick are you suggesting?

 

[Christofer Br]

An "infinitely thin" foil is a bit too much of an abstraction for this question. Loads of light will pass through a thin enough gold foil. Just how thick are you suggesting?

Just consider that all the light is either reflected or absorbed, and the absorbed light is immediately emitted equally in both directions perpendicular to the plane of the foil (thats why I insisted on an infinitely thin foil, so we can ignore emmisions from the "sides")

 

[sophiecentaur]

Just consider that all the light is either reflected or absorbed, and the absorbed light is immediately emitted equally in both directions perpendicular to the plane of the foil (thats why I insisted on an infinitely thin foil, so we can ignore emmisions from the "sides")

You are assuming that the transmitted light is not relevant here then? I have a problem with that.
Also, when light is absorbed, it will warm up the material and not re emit the same optical wavelength.
I think you need to modify your model to include some extra relevant parameters if you want to obtain a relevant result.