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The intensity of each of the two slits in Young's double slit experiment is I₀ , Calculate the minimum separation between the two points on the screen where intensities are 2I₀ and I₀ , (Given, fringe width = $α$ )

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$\frac{α}{12}$

$\frac{α}{4}$

$\frac{α}{3}$

None of these

answer is C.

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Detailed Solution

Intensity, $I = 4 I_{0} \cos^{2} \frac{ϕ}{2}$

$∵ I = I_{0}$

$I = 4 I_{0} C O S^{2} (\frac{π Y}{λ})$

$∴$ $ϕ = \frac{2 π}{3} = \frac{2 π}{λ} \cdot Δ x = \frac{2 π}{λ} (\frac{y d}{D})$

$∴$ $y = \frac{λ D}{4 d}$

Further, $I_{0} = 4 I_{0} \cos^{2} \frac{ϕ}{2}$

$\Rightarrow ϕ = \frac{2 π}{3} = \frac{2 π}{λ} Δ x = \frac{2 π}{λ} (\frac{y_{2} d}{D})$

$∴ y_{2} = \frac{λ D}{3 d}$

Minimum separation, $Δ y = y_{2} - y_{1} = \frac{1}{12} (\frac{λ D}{d}) = \frac{α}{12}$

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