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According to this tool I've calculated that a modern, regular LED light bulb (LED 16W) would emit ~2767 lux at a 0.5 meter distance. Would this imply, that a persons face, exposed at such distance is subject to a ray of light that is ~2767 lux bright?

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Since a half-meter radius sphere is about 3 m^2 area, the bulb would have to emit about 8300 lumens, which is around eight times what an actual 16W LED puts out. Also, a person's face is nowhere near a square meter area, so the actual flux would be much lower than 2767 lumens even if that number were correct.

A typical 16W bulb will have a flux at 0.5m of closer to 350 lux, and without calculating facial effective area, I'd guess the total lumens in a human face at that distance to be about 20.

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