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Let's say we have two people of similar skin areas but of different skin complexions, it is a known fact that all human skin tones have similar emissivity constants. Then from the Stefan-Boltzmann law they should absorb same amount of radiation in a given time(they are at the same temperature) but we know that darker skins are dark as they absorb all the light that falls on it and fairer skins reflect all of that. Then shouldn't fairer skins not radiate lesser radiation than darker skins?

Please tell me what I'm missing.

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    $\begingroup$ “it is known”: by whom? A link to a source would be helpful. $\endgroup$
    – rob ♦
    Commented Jun 4, 2022 at 13:12
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    $\begingroup$ Here's a study that finds that the "emissivity" of human skin does not significantly vary with pigmentation, but look at how they measure it. They used a thermal imaging camera to measure the subject's radiated body heat. They're measuring wavelengths that are very far from visible. $\endgroup$
    – Solomon Slow
    Commented Jun 4, 2022 at 13:32
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    $\begingroup$ Darker skinned people clearly absorb more visible light than lighter skinned people, hence the visible colour difference. However it is not only visible light that gets absorbed by human bodies ( and thus re radiated), I would suspect that the percentage of all absorbed light from dark and light skinned people would be almost identicle as visible light is only a small portion of the total light being absorbed. ( all my conclusions are based on the assumption that you are correct in that the radiation emmitted for dark and light skinned people are relatively the same) $\endgroup$
    – jensen paull
    Commented Jun 4, 2022 at 13:37

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If the object's color is neutral gray at all wavelengths, the absorptivity and emissivity constants (α and ε) are the same. Or, if you take them as functions of wavelength, they are the same functions. However, what we commonly do is quote an average α for the incoming radiation and an average ε for the outgoing radiation. Since terrestrial temperatures are ~5% of the solar photosphere, the wavelengths involved in absorbing and reradiating solar energy are very different, so α (optical) and ε (infrared) may differ.

In spacecraft design, we exploit this to keep things cool. We'll cover low α metal with optically transparent, high ε plastic to make an effective radiating surface that stays cool even in direct sunlight.

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