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A hollow cylinder of equal length and inner diameter (i.e., $L=D$) is sealed at both ends with flat plate, as shown in the figure. Its inner surfaces, $A_1$, $A_2$, and $A_3$ radiate energy.

$F_{ij}$ denotes the fraction of radiation energy leaving the surface $A_i$ which reaches the surface $A_j$. It is also known that $F_{13}=3-2\sqrt{2}$. Which one of the following is correct?

  1. $F_{21} = \sqrt{2}-1 \\$
  2. $F_{21} = \dfrac{\sqrt{2}-1}{2}$
  3. $F_{21} = \dfrac{\sqrt{2}-1}{4}$
  4. $F_{21} = \dfrac{\sqrt{2}-1}{8}$
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