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Two coherent narrow slits emitting light...

Two coherent narrow slits emitting light of wavelength `lambda` in the same phase are placed parallel to each other at a small separation of `2lambda`. The light is collected on a screen S which is placed at a distance D(gtgt`lambda`) from the slit `S_1` as shown in figure. Find the finite distance x such that the intensity at P is equal to intensity O.
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Text Solution

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Path difference at O,
` S_1O = S_2O = 2lambda`
i.e. maximum intensity is obtained at O. Next maxima will be obtained at point P where,

or ` S_1P-S_2P = lambda`
or `d cos theta = lambda`
or `2lambda cos theta = lambda`
or `cos theta = 1/2 `
`:. theta = 60^@`
Now in `DeltaS_1PO`, `(PO)/(S_1O)= tan theta or x/D = tan 60^@ = sqrt3`
`:. x = sqrt 3 D`.
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