In the figure below, $$P$$ and $$Q$$ are two equally intense coherent sources emitting radiation of wavelength $$20\,\text{m}$$. The separation between P and Q is $$5\,\text{m}$$ and the phase of P is ahead of that of Q by $$90^\circ$$. A, B and C are three distinct point of observation, each equidistant from the midpoint of PQ. The intensities of radiation at A, B, C will be in the ratio:

At point A:  $$\Delta x = PA - QA = d = 5\text{ m}$$

$$\Delta \phi_A = \phi_{\text{initial}} - \frac{2\pi}{\lambda}\Delta x = \frac{\pi}{2} - \frac{2\pi}{20}(5) = 0$$

$$I_A = 4I_0 \cos^2(0) = 4I_0$$

At point B:  $$\Delta x = PB - QB = 0$$

$$\Delta \phi_B = \phi_{\text{initial}} - 0 = \frac{\pi}{2}$$

$$I_B = 4I_0 \cos^2\left(\frac{\pi}{4}\right) = 2I_0$$

At point C:   $$\Delta x = QC - PC = d = 5\text{ m}$$

$$\Delta \phi_C = \phi_{\text{initial}} + \frac{2\pi}{\lambda}\Delta x = \frac{\pi}{2} + \frac{2\pi}{20}(5) = \pi$$

$$I_C = 4I_0 \cos^2\left(\frac{\pi}{2}\right) = 0$$

Ratio of intensities:   $$I_A : I_B : I_C = 4I_0 : 2I_0 : 0 = 2 : 1 : 0$$