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I was wondering if there is a way to mathematically work out the color of the sky, using the laws of geometric/wave optics.

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The blue color of the sky is explained by Raleigh scattering of light on air molecules and density fluctuations that are smaller than the wavelength of the visible solar radiation. The scattering cross section is proportional to the light frequency $\omega^4$. Therefore, the scattering of blue light is much stronger than that of red light, which produces the apparent blue color of the sky due to diffuse sky radiation during the day and the red color of the sun during sunrise and sunset.

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