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Sunlight looks white, but it mixes every colour of the rainbow. Some of it strikes the molecules of nitrogen and oxygen that make up most of the air and is sent off in new directions. The molecules are much smaller than the wavelength of light, and for obstacles that tiny the scattering grows sharply as the wavelength shortens, so blue light is scattered several times more strongly than red. Scattered blue light therefore reaches our eyes from every part of the sky, and the whole dome looks blue.
Violet light is scattered even more, yet the sky does not look violet. Sunlight carries less of it to begin with, and the human eye is less sensitive to it. At sunrise and sunset the light crosses a far thicker layer of air, and by then most of the blue has been scattered out of the beam, leaving the reds and oranges. Clouds behave differently: their water droplets are far larger than the molecules of the air and scatter all colours about equally, so they look white.