The wavelength of the waves arriving at $P$ from two coherent sources $S_{1}$ and $S_{2}$ is $4 m$ , while intensity of each wave is $I_{0}$ . The resultant intensity at P is $2 I_{0}$ . Find the minimum value of $S_{2} P$ in metres.

\frac{x \sqrt{5}}{2}

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2 x

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(x + 1)

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(x + \sqrt{2})

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Solution

The correct option is C $(x + 1)$
$I = I_{o} + I_{o} + 2 \sqrt{I_{o} . I_{o}} c o s ϕ = 2 I_{o}$
So,
$c o s ϕ = 0$
$ϕ = \frac{n π}{2} = \frac{π}{2}$
$(n = 1)$ for) $S_{2} P$ to be minimum

$ϕ = \frac{2 π Δ x}{λ} = \frac{π}{2}$
$⟹ Δ x = 1 m$

We know,
$Δ x = S_{2} P - S_{1} P = 1$
$⟹ S_{2} P = S_{1} P + 1 = (x + 1) m$

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