Scattering by Particles Small Compared to the Wavelength

The dipole moment, p, induced in the particle is proportional to the instantaneous electric field vector  

This expression defines the polarizability, a, which has the dimensions of a volume and which is a scalar for an isotropic spherical particle. From the energy of the electric field produced by the oscillating dipole, an expression can be derived for the intensity of the scattered radiation  

Because the intensity of the scattered light varies inversely with the fourth power of the wavelength, blue light (short wavelength) is scattered preferentially to red. This strong dependence leads to the blue of the sky (in the absence of aerosol particles) and 

Both scattering and absorption can be taken into account by writing the refractive index as the sum of a real and an imaginary component  

For scattering alone, an expansion of the efficiency factor in a based on Mie theory discussed below gives 

---