Hence, phase difference between $S_{1}$ and $S_{2}, \phi=\frac{\lambda}{6} \times \frac{2 \pi}{\lambda}=\frac{\pi}{3}$
So intensity between $S_{1}$ and $S_{2}$ is,
$I^{\prime}=I \cos ^{2}\left(\frac{\pi}{6}\right)^{2}=\frac{3 I}{4}$ $............(i)$
Given, $S_{1} P-S_{3} P=\frac{2 \lambda}{3}$
Hence, phase difference between $S_{1}$ and $S_{3}, \phi=\frac{2 \lambda}{3} \times \frac{2 \pi}{\lambda}=\frac{4 \pi}{3}$
So intensity between $S_{1}$ and $S_{2}$ is,
$I^{\prime \prime}=I \cos ^{2}\left(\frac{2 \pi}{3}\right)^{2}=\frac{I}{4} \quad \ldots \ldots \ldots(i i)$
The intensity at P when all the three slits are open is, $I \frac{I^{\prime}}{I^{\prime \prime}}=3 I$
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