Prove that the law of conservation of energy is obeyed during interference of light.

Explanation

Consider that the two sources of light are emitting light waves of intensities `I_(1)` and `I_(2)` respectively.
If there is no interference between the light waves from the two sources, then intensity of light at point on screen will be
`I = I_(1) + I_(2)`.....(i)
In case of interference between two sources of intensities `I_(1)` and `l_2`, the resultant intensity is given by:
`I = I_(1) + I_(2) + 2sqrt(I_(1) I_(2)) cos phi`
`I_("max") = I_(1) + I_(2) + 2sqrt(I_(1) I_(2)), [therefore cos phi = +1]`
`I_("min") = I_(1) + I_(2) -2sqrt(I_(1) I_(2)) [therefore cos phi =-1]`
`I_("average") =(I_("max") + I_("min"))/2 = I_(1) + I_(2)`......(ii)
Although Imgx is greater than sum of individual intensities (`I_(1) + I_(2)`) and Imin is less than sum of individual intensities `(I_(1) + I_(2))` but the average intensity is just equal to sum of individual intensities in accordance with eq.
Actually the light energy which disappears at dark region will appear at bright region but the total energy remains same. So we can say that during interference of light waves, law of conservation of energy is obeyed.