“white” skin isn’t white. Its kind-of pink. Basically, “white” skin is translucent.
Translucent skin does a bad job of reflecting harmful UV rays.
As a side note, one of the most effective ways to protect yourself is to use zinc-oxide as a sun-block. Most people don’t because it looks ugly. It looks ugly because it is pure white.
Whiteness is good for reflecting *visible* light, but it’s the UV component of sunlight that causes damage.
Dark skin looks dark because it has more melanin, a dark pigment. Besides absorbing visible light, melanin also absorbs UV wavelength light well, protecting the tissues deeper than the surface melanin from being damaged.
Other answers here are lackluster. It’s not a question of physics; the statement you made is true if we were talking about a white nonorganic surface vs. a black nonorganic surface.
It’s a matter of biochemistry. 1. Sunburns are not due to heat, they’re due to radiation damaging cells of the epidermis. In fact, UV-A passes through windows, which will damage your skin without sunburning it (or you feeling hot). 2. Melanin’s UV-protective properties are not because of its color, but rather its molecular properties that allow it to dissipate UV radiation as heat. Chlorophyll in plants (green, not black) also isn’t bothered by UV radiation by other molecular means.
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