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A monochromatic light source of wavelength $λ$ is placed at S. Three slits $S_{1}, S_{2} a n d S_{3}$ and are equidistant from the source S and the point P on the screen. $S_{1} P - S_{2} P = λ / 6$ and $S_{1} P - S_{3} P = 2 λ / 3$ . If I be the intensity at P when only one slit is open, how many times the intensity at P is increased when all the three slits are open

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answer is 3.

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$Φ_{12} = \frac{λ}{3} \times \frac{2 π}{λ} = 120^{\circ} Φ_{13} = \frac{4 λ}{3} \times \frac{2 π}{λ} = 480^{\circ} (A_{R} = \sqrt{2} A_{0}) I_{e} = 2 I_{0}$

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