The interference pattern is obtained by two coherent sources of same intensities $I_{0}$ . Find intensity at $y = \frac{D λ}{6 d}$ from central maximum.

2 I_{0}

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\frac{I_{0}}{3}

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3 I_{0}

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4 I_{0}

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Solution

The correct option is C $3 I_{0}$
$I_{n e t} = I_{0} + I_{0} + 2 I_{0} cos ϕ$
$= 2 I_{0} {1 + cos ϕ} = 4 I_{0} {cos}^{2} {\frac{ϕ}{2}}$
$ϕ = \frac{2 π}{λ} (\frac{d}{D} y) = \frac{2 π}{/ λ} . \frac{/ d}{/ D} . \frac{/ D λ}{6 / d} = \frac{π}{3} = 60^{\circ}$
$I_{n e t} = 4 I_{0} . {cos}^{2} 30 = 4 I_{0} \times \frac{3}{4} = 3 I_{0}$

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The interference pattern is obtained by two coherent sources of same intensities I0. Find intensity at y=Dλ6d from central maximum.

The correct option is C 3I0Inet=I0+I0+2I0 cos ϕ =2I0{1+cos ϕ}=4I0 cos2{ϕ2} ϕ=2πλ(dDy)=2π/λ./d/D./Dλ6/d=π3=60∘ Inet=4I0.cos2 30=4I0×34=3I0

The interference pattern is obtained by two coherent sources of same intensities $I_{0}$ . Find intensity at $y = \frac{D λ}{6 d}$ from central maximum.