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Why does the bluish color predominate in a clear sky?

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Predominance of bluish colour in a clear sky is due to the phenomena of scattering of light in the atmosphere around earth. If size of the air particles are smaller than the wavelength, the scattering is proportional to 1/λ4 . This is the Rayleigh’s law of scattering. The light of short wavelengths are strongly scattered by the air molecules and reach the observer. 

Among the shorter wavelengths, the colour blue is present in large proportion in sunlight.

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