White sunlight contains many colours
Sunlight reaching Earth contains a range of visible wavelengths. When it enters the atmosphere, molecules in the air scatter some of that light in different directions. This is called Rayleigh scattering, and for particles much smaller than the wavelength, it is much stronger at shorter wavelengths—approximately proportional to 1/λ⁴.
Why blue fills the daytime sky
Air molecules scatter blue and violet light more strongly than red light. The scattered light arrives at our eyes from across the sky, making the sky appear blue. It is not simply that blue is the only colour scattered: violet is scattered even more, but the Sun’s spectrum, atmospheric absorption and the sensitivity of human vision all contribute to the colour we perceive.
Why sunsets often look red
When the Sun is low, its light travels through a longer slant path in the atmosphere before reaching you. More of the shorter-wavelength light is scattered out of the direct beam. The remaining direct sunlight is relatively richer in longer wavelengths, so the Sun and nearby sky can look yellow, orange or red.
Dust, smoke, pollution and other aerosols can change the scattering and absorption, sometimes making twilight colours more vivid and sometimes muting them. A red sunset is therefore not guaranteed; atmospheric conditions matter.
One process, two views: scattered short-wavelength light makes the daytime sky blue; the loss of much of that light from the direct solar beam helps make sunsets look red.