Why do we use Mie scattering to describe light scattering off large objects?

Question

I'm an undergraduate student who has recently come across Rayleigh and Mie scattering and I'm trying to understand them a little better.

As I understand it Rayligh scattering is used only when the particles that scatter light have diameters smaller than the wavelength of light, this seems to include atoms and molecules. I also know that Rayleigh scattering predicts that the intensity of the scattered light is inversely proportional to the wavelength to the fourth power.

I also know that Mie scattering is a generalization for all other sizes of particles and that if the size of the particle is much bigger than the wavelength of light the intensity is pretty much independent of the wavelength.

Every particle is ultimately composed of atoms and molecules... so why can't we use the Rayleigh approximation all the time?

I know that small water particles scatter light according to the Mie solution, and look white in clouds as a result... but water molecules, for instance at sea, scatter light in a way which can be described by Rayleigh scattering, this adds to my confusion!

Answer 1

Creative thinking with this question.

Rayleigh scattering is the scattering of a plane wave from a single small particle well-separated from other particles. If a second small particle is somewhat nearby, it will scatter coherently with the first and create interference. The far-field will not be Rayleigh anymore; you cannot just add the intensity, the phases also matter.

Say enough small particles aggregate very close together to form a large sphere, with the spacing between particles much less than the wavelength of the light. Then the combined interference effects from each scattering point produce the Mie solution. The idea is nicely illustrated in this method, for example, http://en.wikipedia.org/wiki/Discrete_dipole_approximation. The interference from each discrete dipole slowly builds up to give the scattering from arbitrary scattering-particle shapes. (Mie is for spheres.)

The molecules in a glass of water are separated by a distance much less than the wavelength of the light, so Rayleigh is not applicable. The water is effectively a homogeneous medium with a uniform index of refraction.