The range of validity of the Rayleigh limit for computing mie scattering and extinction efficiencies

For the small particle limit for scattering by either absorbing or dielectric spheres, values of the size parameter are determined below which various approximate expressions for the scattering and extinction efficiencies are accurate to within 1%. Simple, analytical criteria for ensuring 1% accuracy are given in terms of the size parameter and the complex refractive index. A much broader range of refractive indices is considered than has been studied previously.