TPDSci Mie theory Number of terms

Mie theory: Number of terms in Mie series

The Mie series (Eqs. 3 and Eqs. 5 and 6 in Mie theory: Overview) converge because their terms approach 0 very rapidly for the summation index, n, exceeding a value on the order of x. Wiscombe (1980) gives the following formula to calculate the number of terms of the sums appearing in those equations:

n_max = {

x + 4x^1/3 + 1 for 0.02 ≤ x ≤ 8

x + 4.05x^1/3 + 2 for 8 < x < 4200

x + 4x^1/3 + 2 for 4200 ≤ x ≤ 20,000

(1)

where x is the relative size of the sphere.

CITATION:
Jonasz M. 2006. Mie theory: Number of terms in Mie series (www.tpdsci.com/Tpc/MieTheNmax.php). In: Top. Part. Disp. Sci. (www.tpdsci.com).

HISTORY:
Published: 03-Mar-2006
Modified: 20-Jul-2006
Peer-reviewed: PENDING

Topics in Particle and Dispersion Science