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

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$2\lambda$

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(A) When a glass plate of thickness $t$ and refractive index $\mu$ is introduced in the path of one of the beams,the path difference introduced is $\Delta x = (\mu - 1)t$.The condition for the intensity to remain unchanged at the position of the original central maximum is that the new path difference must be an integer multiple of the wavelength $\lambda$,such that the phase difference is a multiple of $2\pi$.For the intensity to remain the same (i.e.,constructive interference),the path difference must be $\Delta x = n\lambda$,where $n = 1, 2, 3, ...$.Setting the path difference equal to the first order of constructive interference $(n = 1)$:$(\mu - 1)t = \lambda$Given $\mu = 1.5$:$(1.5 - 1)t = \lambda$$0.5t = \lambda$$t = 2\lambda$Thus,the minimum thickness is $2\lambda$.

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