The intensity of the radiation from a source of electric waves when the electric constants of the medium in the neighbourhood of the source are different from the electric constants at a distance from it

If a simple oscillator is close to a perfectly conducting plane, with its axis perpendicular to the plane, the magnetic force at the point (r , θ), wherer is the distance of the point from the oscillator, and θ is its angular distance from the axis of the oscillator, is the real part of 2Ae3πι/4 + ικVt r-½ K3/2 (ικr ) sinθ, and the real part of Ae3πι/4 + ικVt r-½ K3/2 (ικr ) sinθ is the magnetic force due to the oscillator alone. The rate of transfer of energy across the surface of a sphere enclosing the oscillator is 2πA2 /3Kκ V, and the rate of transfer of energy from an oscillator A1 , when there is no conducting plane, is πA1 2 /3Kκ V, and therefore, if the energy supplied is the same in both cases, A1 2 = 2A2 , that is, the effect of the conducting plane is to increase the amplitude of the waves at any point in the ratio √2 to 1, or to double the intensity.