In this study, the Angstrom exponent of the polydispersed aerosol size distribution was theoretically studied. The Angstrom exponent was represented using a harmonic mean type analytic approximation. A log-normal aerosol size distribution was assumed and a sensitive analysis of the Angstrom exponent was performed. The change in the Angstrom exponent was estimated for a range of values of the real and imaginary parts of the refractive index. The result of the approximate analytic solution was comparable with that obtained by numerical integration, although there exists some discrepancy, especially for the intermediate range of particle sizes. Subsequently, this study quantitatively shows how the refractive index and particle size distribution are crucial in estimating the Angstrom exponent, and that an analytic type approximation can be applied for the estimation of the Angstrom exponent, especially for the limiting ranges of particle size (i.e., for the Rayleigh and geometric mean dominant size ranges).