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I mean to say if a blackbody ( the one represented by a cavity with a hole) emits at equilibrium a radiation at the same temperature as the cavity walls, and some of that radiation succeeds to run away from the hole, then Does that mean the intensity of the emitted radiation at the different wavelengths that succeeded to escape will equal the intensity of the emitted radiation at the different wavelengths that is still trapped inside of the cavity? In other words, Will the blackbody radiation curve inside the cavity (assuming we have a way to measure that) be identical to the blackbody radiation curve outside of it?

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Yes, that's the (w)hole idea of having a small opening in an otherwise sealed cavity. It allows you to sample the spectral intensity of the radiation field without (in principle) disturbing it.

The hole must not be too big. One of the defining characteristics of a blackbody radiation field is that it is isotropic. If the hole is too big then it acts like a piece of wall cavity that is at some different temperature and the radiation field would not be in equilibrium until the walls assumed that other temperature.

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