# Relationship between Planck's law and absorbed frequencies

What is the relationship between the frequencies of radiation absorbed by a material and those emitted? I know that Planck's law tells us the spectral radiance, but how does this map to those frequencies absorbed? For example, a black material at room temperature is absorbing all visible light and emitting infrared; what is the relationship between these two?

As an aside, what is the origin of the term "black body", since many black bodies aren't black!? I imagine that early realizations of black bodies indeed had coatings of black material, and this is where the term came from, an I correct?

By time reversibility, the tendencies to absorb and emit radiation of a given frequency (known as absorptivity and emissivity) are exactly equal. Thus, for example, a perfect mirror will reflect all radiation incident upon it, and it will never radiate away any of its internal energy in the form of photons. Einstein used the fact that a single atom in a thermal bath of radiation had to absorb and radiate in a time-reversal-invariant way, to derive his $$A$$ and $$B$$ coefficients, which give the rates of spontaneous and stimulated emission by the atom.