What defines the surface of the Sun?

Hornbein
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The sun has no surface, but it appears to have a surface. I may recall that Feynman said that the apparent diameter is equal to the mean free path of a photon. That could be, but I don't get the relationship. Any help?
 
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Perhaps what Feynman meant is that the 'surface' is defined as the region where the mean free path of photons becomes large enough for most of them to leave the Sun without being absorbed?
 

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