Question

A system illustrated in Fig. 5.12 consists of two coherent point sources 1 and 2 located in a certain plane so that their dipole moments are oriented at right angles to that plane. The sources are separated by a distance d, the radiation wavelength is equal to λ. Taking into account that the oscillations of source 2 lag in phase behind the oscillations of source 1 by φ (φ < π), find:

(a) the angles θ at which the radiation intensity is maximum;

(b) the conditions under which the radiation intensity in the direction θ = π is maximum and in the opposite direction, minimum.

Answer 1

(a) With dipole moment ⊥r to plane there is no variation with θ of individual radiation amplitude. then the intensity variation is due to interference only.

In the direction given by angle θ the phase difference is

We have added φ to 2π/λ because the extra path that the wave from 2 has to travel K in going to P (as compared to 1) makes it lag more than it already is (due to φ).