A thin large film having refractive index  $\mu =\frac{3}{2}$, is placed in front of slits $S_1$ and  $S_2$ of Young's double slit experiment such that its thickness varies according to the equation  $t=t_0{\cos }^2\left(\frac{5\pi y}{4d}\right)$ where y = 0 is taken at  $S_1$. Find the value of $t_0$  such that there is central maxima at P (refer diagram) $\left(AssumeD>>d\right)$