Black Body Radiation: Facts & Overview

[LCSphysicist]

Homework Statement

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Relevant Equations

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I am really stuck at this question, i would appreciate any tips you have. I already try to goes with series but the calculation is getting harder and tiring, so probably this is not the right way.

 

[Charles Link]

Edit: I got a correct answer by assuming a left going and a right going power at each of the two surfaces. I then used the reflectivity as $R=1-\epsilon$ and multiplied this by the incident power (per unit area), and added this term to $\epsilon \sigma T^4$ to get the emerging power from the surface. You do this for both surfaces. You then get expressions for left going and right going power inside the cavity.
additional note: I initially misread their nomenclature. They do have the correct answer.

Edit 2: I have now also worked it by summing two geometric series. That method is also fairly straightforward=if you show a little of your own attempt at this method, I can probably show you any steps that you might be missing.
Hint: Compute the power incident on the $T_2$ surface that originates from the first surface using a series. Next compute the power that is incident on the $T_2$ surface that originated from the same surface using a series. They are both geometric series, and are readily summed. Once you have that, what is the power absorbed by the second surface?