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Three coherent point sources S(1),S(2) a...

Three coherent point sources `S_(1),S_(2) and S_(3)` are placed on a line perpendicular to the screen as shown in the figure. The wavelength of the light emitted by the sources is lambda. The distance between adjacent sources is `d=3lambda` The distance of `S_(2)` from the screen is D`(gtgt lambda)`. Find the minimum (non zero) distance x of a point P on the screen at which complete darkness is obtained.

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