Rayleigh scattering of photons by Earth's atmosphere is dependant upon the size of the particles causing the scattering and the wavelength of the photon being scattered. This results in blue photons being scattered across the sky to a greater extent than photons of a longer wavelength, and so one sees blue light coming from all regions of the sky whereas the rest is still mainly coming directly from the Sun.
A notable exception is during sunrise? and sunset?, when the Sun's light must pass through a much greater thickness of the atmosphere to reach an observer on the ground. This extra distance allows the scattering of longer wavelengths to become more pronounced as well, resulting in red-hued skies.
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