The sky appears blue to us because we are seeing part of the sunlight that has been scattered towards our eyes, and blue light is most readily scattered by the earth’s atmosphere.
The sun emits light of all frequencies (colors). Were it not for the scattering of the atmosphere, we would see the sun as a pure white disk surrounded by a black sky. However, a portion of the sun’s light is scattered by the gas molecules in the atmosphere.
Colors having the highest frequency (or shortest wavelength) are most readily scattered. These are the colors at the blue end of the rainbow. As a result, we see the sun as slightly yellowish, because that’s how our eyes see white light after some of its blue component has been removed. In the rest of the sky, away from the sun, we see the blue light that was scattered away from the sun’s light that was heading towards other parts of the earth, and ended up reaching us instead.
Interestingly, we see clouds as white even if they are in the middle of an otherwise-blue sky. That’s because the light falling on the cloud consists of the direct yellowish light from the sun and the blue light from the surrounding sky, and when these are combined they again form a white light.
Wikipedia has good articles about diffuse sky radiation (the indirect light falling on earth from the sky) and Rayleigh scattering (the scattering of light by particles whose size is smaller than the wavelength of the light).
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