(a) Show that for arbitrary initial polarization, the scattering cross section of a perfectly conducting sphere of radius a, summed over outgoing polarizations, is given in the long-wavelength limit by

Where n0 and n are the directions of the incident and scattered radiations, respectively, while N?0 is the (perhaps complex) unit polarization vector of the incident radiation (N?0* ?c N?0 = 1; n0 ?c N?0 = 0).
(b) If the incident radiation is linearly polarized, show that the cross section is

Where n ?c n0 = cos ? and the azimuthal angle N? is measured from the direction of the linear polarization.