Lower and upper bounds on extinction cross sections of arbitrarily shaped strongly absorbing or strongly reflecting nonspherical particles

The general belief that the sphere of equal volume provides a better approximation for the extinction cross section of a nonspherical particle than a sphere of equal surface area at small values of the size parameters is not correct. At some values of x, the equal volume sphere is a better approximation; at others, the equal surface area sphere is better. Details depend on the shape, size, and refractive index. For strongly absorbing particles at x > π, the extinction cross section of an equal volume sphere ’EV provides the lower bound, and σ_EVS_N/S_EV(where S_Nis the surface area of considered nonspherical particle, and SEV is the surface area of equal volume sphere) provides the upper bound on the extinction cross section of an arbitrarily shaped nonspherical particle.