$(a)\;4.5 \times 10^{-7}\;m \\ (b)\;9 \times 10^{-7}\;m \\ (c)\;1.5 \times 10^{-8}\; m \\ (d)\;4.5 \times 10^{-4}\;m $

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Path difference produced by a plate of thickness t and refractive index $\mu$ is

$(\mu-1)t$

This path difference must be minimum equal to $\large\frac{\lambda}{2}$

$ (\mu-1)t =\large\frac{\lambda}{2}$

$t= \large\frac{\lambda}{2} \times \large\frac{1}{\mu-1}$

$t= \large\frac{900 \times 10^{-9}}{2} \times \frac{1}{-5}$

$\qquad= 900 \times 10^{-9}\;m$

$\qquad= 9 \times 10^{-7}\;m$

Hence b is the correct answer.

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