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(D) For coherent sources,the resultant intensity at the center (where path difference is zero) is given by $I_{max} = (A_1 + A_2)^2$. Assuming equal a

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$\frac{I_0}{2}$

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(D) For coherent sources,the resultant intensity at the center (where path difference is zero) is given by $I_{max} = (A_1 + A_2)^2$. Assuming equal amplitudes $A_1 = A_2 = A$,we have $I_0 = (A + A)^2 = 4A^2$.Since intensity $I$ of a single source is $A^2$,we have $I_0 = 4I$,which implies $I = \frac{I_0}{4}$.For incoherent sources,the interference term averages to zero over time. Therefore,the resultant intensity is simply the sum of the individual intensities: $I_R = I_1 + I_2$.Substituting $I_1 = I_2 = I = \frac{I_0}{4}$,we get $I_R = \frac{I_0}{4} + \frac{I_0}{4} = \frac{2I_0}{4} = \frac{I_0}{2}$.

Resultant intensity at the centre of the screen due to two coherent sources is $I_0$. If the sources are incoherent,then the intensity at the same point will be

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