In Young's double slit experiment, Let $β$ be the fringe width and $I_{o}$ be the intensity at the central bright fringe. At a distance 'x' from the central bright fringe, the intensity will be

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$I_{0} \cos^{2} (\frac{x}{β})$

$I_{0} \cos^{2} (\frac{πx}{β})$

$\frac{I_{0}}{4} \cos^{2} (\frac{πx}{β})$

$I_{0} \cos (\frac{x}{β})$

answer is C.

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Detailed Solution

$Δx = \frac{dx}{D} = \frac{λ}{2 π} (ϕ); ϕ = \frac{2 πdx}{Dλ} = \frac{2 πx}{β}$
$I = 4 I_{i} \cos^{2} θ / 2$ and $4 I_{i} = I_{0} given$
$∴ I = I_{0} \cos^{2} (\frac{πx}{β})$

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