Why is the daytime sky blue?

Answer

This is called Rayleigh scattering.

Context

Sunlight looks white but is a mix of colours. As it passes through the atmosphere, air molecules scatter short wavelengths such as blue much more strongly than long wavelengths such as red. The effect is named after Lord Rayleigh, the British physicist who worked out the mathematics in the 1870s, and the scattering strength rises sharply as wavelength gets shorter, roughly with the inverse fourth power of the wavelength.

Violet light is scattered even more than blue, so why is the sky not violet? There are a few reasons: the Sun emits less violet than blue, some violet is absorbed high in the atmosphere, and human eyes are less sensitive to violet than to blue. The combined result looks blue to us.

The same effect explains red sunsets. When the Sun is low, its light travels through much more air before reaching you, most of the blue is scattered out of the direct beam, and the remaining light looks orange or red. On Mars, where the thin atmosphere is full of fine dust, the daytime sky looks butterscotch and sunsets appear bluish.

Rayleigh scattering applies when particles are much smaller than the wavelength of light, as air molecules such as nitrogen and oxygen are. Larger particles, such as water droplets in clouds, scatter all visible wavelengths in a similar way (Mie scattering), which is why clouds look white or grey rather than blue. Scattered light reaches the eye from every part of the sky, so the whole dome appears blue and not just the direction of the Sun.

A common misconception is that the sky is blue because it reflects the ocean; the reverse is closer to the truth, since water absorbs red light and the sea gets part of its colour from that, plus reflected sky. Haze, smoke or dust can shift the sky towards white or yellow-grey, and the horizon often looks paler because light there has passed through a longer path of air, scattering many wavelengths multiple times.