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In young's double slit experiment performed using a monochromatic light of wavelength $λ$ , when a glass plate ( $μ$ =1.5) of thickness x $λ$ is introduced in the path of the one of the interfering beams, the intensity at the position where the central maximum occurred previously remains unchanged. The value of x will be :

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1.5

0.5

answer is B.

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Detailed Solution

Path difference at $O = (μ - 1) t$ .

If the intensity at O remains (maximum) unchanged, path difference must be n $λ$ .

$\begin{array}{l} \Rightarrow (μ - 1) t = nλ \\ (1 .5 - 1) xλ = nλ \\ \Rightarrow x = 2 n \end{array}$

For $n = 1, x = 2$

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