Consider the scattering of light by an opaque particle with size a >> 1/k. Neglect any scattering via excitation of electrons in the particle. Then the scattering is solely due to diffraction of light around the particle. With the aid of Babinet’s principle, do the following.

(a) Explain why the scattered light is confined to a cone with opening angle △θ ∼ π/(ka) ≪1.

(b) Show that the total power in the scattered light, at very large distances from the particle, is P_S = FA, where F is the incident energy flux, and A is the cross sectional area of the particle perpendicular to the incident wave.

(c) Explain why the total “extinction” (absorption plus scattering) cross section is equal to 2A independent of the shape of the opaque particle.