(a) Let S be the illuminated portion of a conductor. If r̂ is the local unit normal vector to S and k = k₀ k̂ is the propagation direction of the backscattered wave, show that the cross section for backscattering in the physical optics approximation is

(b) Specialize to a flat, rectangular plate with negligible thickness that lies in the z = 0 plane. The side parallel to the x-axis has length a and the side parallel to the y-axis has length b. If the center of the plate coincides with the origin of spherical coordinates and the plate area is A, show that

Transcribed Image Text:

OR = k² 47² S ds' k ' exp(-2ik r') 2