To make the central fringe at the center O. A mica sheet of refractive index 1.5 is introduced. Choose the correct statements(s)

To make path difference 0 at O.
Mica sheet has to be introduce in front of  $S_1$
Geometrical path difference before entering slits should be balanced by optical path difference due to mica sheet.

Before entering slits $∆x_{Geom}=S{S}_2-S{S}_1=\sqrt{2}d-d=\left(\sqrt{2}-1\right)d$

After passing through slits $∆x_{optical}=S_{1}O-S_{2}O=\left(\mu -1\right)t$

$\begin{array}{l}(\sqrt{2}-1)d=(\mu -1)t\\ \Rightarrow t=\frac{(\sqrt{2}-1)d}{(\mu -1)}\\ \Rightarrow t=2(\sqrt{2}-1)d\end{array}$