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(B) When a glass plate of refractive index $\mu$ and thickness $t$ is introduced in the path of one of the beams,the additional path difference introd

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$2$

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(B) When a glass plate of refractive index $\mu$ and thickness $t$ is introduced in the path of one of the beams,the additional path difference introduced is $\Delta p = (\mu - 1)t$.For the intensity at the original central position $O$ to remain unchanged (i.e.,to remain a maximum),the path difference must be an integral multiple of the wavelength $\lambda$.Therefore,$\Delta p = n \lambda$,where $n = 1, 2, 3, \dots$Given $\mu = 1.5$ and $t = x \lambda$,we have:$(\mu - 1)t = n \lambda$$(1.5 - 1) (x \lambda) = n \lambda$$0.5 x \lambda = n \lambda$$0.5 x = n$$x = 2n$For the smallest non-zero value of $x$,we take $n = 1$,which gives $x = 2(1) = 2$.

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