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Q.

The path difference between two interfering waves at a point on the screen is $λ$ /6 from central maximum. The ratio of intensity at this point and that at the central fringe will be

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a

0.75

b

853

c

7.5

d

85.3

answer is A.

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Detailed Solution

$\begin{array}{l} ϕ = \frac{2 π}{λ} (Δx) = \frac{2 π}{λ} \times \frac{λ}{6} = \frac{Π}{3} \\ I = 4 I_{0} \cos^{2} \frac{ϕ}{2} = 4 I_{0} {(\frac{\sqrt{3}}{2})}^{2} \\ = 4 I_{0} \frac{3}{4} and I_{central maximum} = 4 I_{0} \\ \frac{I}{I_{central maximum}} = \frac{3}{4} = 0 .75 \end{array}$

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