The Green reciprocation theorem also attached. it take from " Classical Electrodynamic 3rd by Jackson"
Two infinite grounded parallel conducting planes are separated by a distance d. A point charge q is placed between the planes.
Use the reciprocation theorem of Green to prove that the total induced charge on one of the planes is equal to (-q) times the fractional perpendicular distance of the point charge from the other plane.
(Hint: As your comparison electrostatic problem with the same surfaces choose one whose charge densities and potential are known and simple.)