In the figure there are two coherent point sources S 1 and S 2 located in a certain plane. They are separated by a distance 'd'. The radiation wavelength is equal to λ . Taking into acco

Question

In the figure there are two coherent point sources $S_{1}$ and $S_{2}$ located in a certain plane. They are separated by a distance 'd'. The radiation wavelength is equal to $λ$ . Taking into account that oscillation of source $S_{2}$ lag in phase behind the oscillations of source $S_{1}$ by $ϕ (ϕ < π)$ then the angle $θ$ at which the radiation intensity can be maximum will be (Given: the observation point distance from the centre of $S_{1} S_{2}$ is much greater than d)

Two coherent sources S1 and S2 and the angle theta measured from the line S1S2

Options:

Answer:

A

Solution:

Path to a far point: $r_{2} - r_{1} = d cos θ$

$S_{2}$ lags by $ϕ$ , so net phase difference: $\frac{2 π}{λ} d cos θ + ϕ$

For maximum: $\frac{2 π}{λ} d cos θ + ϕ = 2 πn$

$θ = cos^{- 1} [(n - \frac{ϕ}{2 π}) \frac{λ}{d}]$

Option (A)

TestHub · Accepted Answer

Path to a far point: r 2 ​ − r 1 ​ = d cos θ S 2 ​ lags by ϕ , so net phase difference: λ 2 π ​ d cos θ + ϕ For maximum: λ 2 π ​ d cos θ + ϕ = 2 πn θ = cos − 1 [ ( n − 2 π ϕ ​ ) d λ ​ ] Option (A)

Physics - Wave Optics Question with Solution | TestHub

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