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In a Young's double slit experiment, using unequal slit widths, the intensity at a point midway between a bright and dark fringes is 4I. If one slit is covered by an opaque film, intensity at that point becomes 2I. If the other is covered instead, then the intensity at that point is

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$(5 + 2 \sqrt{2}) I$

$(5 + 4 \sqrt{2}) I$

answer is A.

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Detailed Solution

Location of the point, $y = \frac{ω}{4} = \frac{λ D}{4 d}$

$\Rightarrow Δ x = \frac{y d}{D} = \frac{λ}{4}$

From the given data it can be observed that intensity of each source is equal to 2I

$\Rightarrow ϕ = \frac{2 π}{λ} \cdot Δ x = \frac{π}{2}$

$∵ I_{R} = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}} \cos ϕ$

$∴ 4 I = 2 I + I_{2} + 0$

$\Rightarrow I_{2} = 2 I$

when one of the slits is covered then intensity will be due to general illumination that is 2I

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