Coherent sources are needed to ensure that the positions of maxima and minima do not change with time.
Alternate Answer
Coherent sources have constant phase difference and, therefore, produce a sustained interference pattern.
For path difference $\lambda,$ phase difference
$\Phi = 2\pi$
$\text{Hence}, \text{k} = 4\text{I}_{0}\cos^{2}\pi =4 \text{ I}_{0}$
For path difference $\lambda\big/3$
Phase difference $\Phi = 2\pi\big/3$
Intensity
$\text{I}' = 4\text{I}_{0}\cos^{2}\pi\big/3$
$ = 4\text{I}_{0}\bigg(\frac{1}{2}\bigg)^{2} = \text{I}_{0}$
Therefore, $\text{I}' = \frac{\text{k}}{4}.$
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