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My likely wrong understanding of light is this:

By some way the molecules are structured, a photon hits an atom or a structure, is absorbed, then re-emitted and it's that photon wavelength that I see as light when my eyes absorb the photon/wave.

So if say something is painted black, does it follow that it would absorb light? And if so, when compared to an object that was painted white or not naturally black in color would it have a cooler temperature than the surface painted black?

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You are totally right about photons and their reflection and absorption on bright or dark surfaces if you illuminate these surfaces with visible light. The photons in the range of visible light will be reflected or absorbed (and re-emitted with a longer wavelength) and that is the reason we see these surfaces as bright or as dark.

And the dark surface has a higher temperature. When re-emitting the before received photons some part of their momentum goes over to the electrons on the surface. The electrons will get a higher energetic level. The re-emitted photons will leave the surface with a longer wavelength and they are lower energetic.

If one use invisible light such as microwaves, infrared, ultraviolet or gamma radiation (electromagnetic radiation) the heating depends on the absorption characteristics of the surface. If to be more precise it depends on the material of the outer layer (for example if it is painted) and it depends on the relation between thickness of such a layer and the penetration depth of the radiation. But the temperature of the body depends from the re-emission characteristics too, it depends from the wavelength of the re-emissioned photons.

And to finish, if you work with painted bodies of course it is importend form which material is the rigid body, what is his mass, what is his form and which part of the body is illuminated.

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Lower temperature. Cooler temperature has wrong units. Yes. In fact in the study of radiative transfer, surfaces have properties that can be measured called absorbtivity and emissivity and reflectivity, and plenty more. Telescope domes are painted with a titanium oxide that has very high emissivity in the IR. They feel strangely cool to the touch under direct sunlight.

The photons are only absorbed and emitted by electrons (leaving out gamma rays from binding energy of the deuteron, etc.)

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