Asymptotic approximations to the Mie efficiency factors for extinction, absorption, and radiation pressure, derived from complex-angular-momentum theory and averaged over $\Delta \beta \sim \pi$ ($\beta =\mathrm{size}\mathrm{parameter}$), are given and compared with the exact results. For complex refractive indices $N=n+ik$ with $1.1<~n<~2.5$ and $0<~k<~1$, the relative errors decrease from ∼(1-10)% to ∼(${10}^{-2\mathrm{}}$-${10}^{-3\mathrm{}}$)% between $\beta =10\mathrm{}$ and $\beta =1000\mathrm{}$, and computing time is reduced by a factor of order $\beta$, so that the Mie formulae can advantageously be replaced by the asymptotic ones in most applications.

• Received 22 May 1980

DOI:https://doi.org/10.1103/PhysRevLett.45.1490