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Q.

In the Young’s double slit experiment using a monochromatic wavelength $(λ)$ , the path difference (in terms of an integer n) corresponding to any point having half the peak intensity is

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a

$(2 n + 1) \frac{λ}{4}$

b

$(2 n + 1) (\frac{λ}{8})$

c

$(2 n + 1) \frac{λ}{2}$

d

$(2 n + 1) \frac{λ}{6}$

answer is B.

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Detailed Solution

$\begin{array}{l} I = I_{0} \cos^{2} \frac{ϕ}{2} \\ \frac{I_{0}}{2} = I_{0} \cos^{2} \frac{ϕ}{2} \\ \cos^{2} \frac{ϕ}{2} = \frac{1}{2} \\ ϕ = \frac{π}{2}, \frac{3 π}{2}, \frac{5 π}{2} ..... \frac{(2 n + 1) π}{2} \\ ϕ = \frac{2 π}{λ} (△ x) \\ △ x = (2 n + 1) \frac{λ}{4} \end{array}$

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