In the YDSE shown below, two slits are covered with thin sheets having a thickness $t$ and $2t$ and refractive indices $2\mu$ and $\mu$ respectively. The position of central maxima is shifted by a distance of $N$ (in $\mathrm{cm}$) from the central position of the screen. Find the value of $N$.
$[d = 1 \mathrm{mm}; D = 1 \mathrm{m}; t = 2 \times {10}^{-2} \mathrm{mm},$$\mu =\frac{3}{2}$ ]