ELI5: Why sitting next to a fire doesn't tan us but exposing us to the sun does?

Are you sure? The modal frequency of the radiation is determined by the temperature of the object. Charcoal is barely above infrared spectrum, a hot flame emits IR and visible light, an arc welding emits a higher frequency and mostly light, then we have UV lamps that don’t heat at all but give massive UV output. The sun is so hot to emit almost the entire electromagnetic spectrum including gamma rays, because it is actually a gigantic fusion reactor that’s just so big that it last billions of years. They can’t be similar in spectrum. Ok the sun gases coming to the surface do cool down to 6000K so they emit a lower frequency, but it’s still a lot hotter than a bonfire, which is around 1000 K.

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