$(a)\;10^{-7}\;m \\ (b)\;2 \times 10^{-7}\;m \\ (c)\;3 \times 10^{-7} \\ (d)\;5 \times 10^{-7}\;m $

The path difference between two reflected light from upper and lower surface of oil film is $2 \mu t$

Now for dark fringe to turn to bright fringe the change in the path difference should be minimum $\large\frac{ \lambda}{2}$

If $\Delta t$ is change in thickness

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

$\Delta t =\large\frac{\lambda}{4 \mu}$

$\qquad= \large\frac{9.6 \times 10^{-7}}{4 \times 1.2}$

$\qquad= 2 \times 10^{-7}\; m$

Hence b is the correct answer.

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