Does the principle of conservation of energy hold for interference and diffraction phenomena? Explain briefly.

Suppose the two interfering waves from two coherent source have the same amplitude. Let I_o be the intensity of each wave. If $\mathrm{\varphi }$ is the phase difference between the two waves on arriving at any point P on the screen, then resultant intensity at P is given by
${\mathrm{I}}_{\mathrm{R}}=4{\mathrm{I}}_0{\cos }^2\frac{\mathrm{\phi }}{2}$
The intensity of the bright fringe is 4I₀ while the intensity of dark fringe is zero. The intensity of interference pattern as a function of phase difference $\mathrm{\varphi }$ between the two waves on arriving at the screen.
The average value of ${\cos }^2\frac{\mathrm{\phi }}{2}$ over a cycle is $1/2{\mathrm{I}}_{\mathrm{av}}=4{\mathrm{I}}_0\times \frac{1}{2}=2{\mathrm{I}}_0$
In interference and diffraction, light energy is redistributed. If it reduces in one region, producing a dark fringe, it increases in another region, producing a bright fringe. There is no gain or loss of energy, which is consistent with the principle of conservation of energy.