To understand scattering, we first have to look at light as waves instead of rays. So when light hits a spherical object, the light tends to scatter all around. This is because of something called Mie scattering. Since Mie scattering is not strongly wavelength dependent, it affects all colours of the spectrum. This effect is demonstrated in the picture below.

This is also the explanation as for why clouds are white. It also gives us the the white light from mist and fog. Mie scattering occurs on the many molecules and particles in the sky, as well as raindrops. A related form of scattering, called Rayleigh scattering, explains why the sky is blue.

Here is a more detailed picture as to what happens to light rays when Mie Scattering occurs:



The mathematical calculations involved with Mie Scattering are far too complicated for the scope of this course. It involves a lot of linear algebra and the calculations of Legendre polynomials. In the efforts of simplicity, you can visit this page for the precise calculations.