As shown in the figure, in Young's double slit experiment, a thin plate of thickness $t=10 \mu \mathrm{m}$ and refractive index $\mu=1.2$ is inserted infront of slit $S_{1}$. The experiment is conducted in air $(\mu=1)$ and uses a monochromatic light of wavelength $\lambda=500 \mathrm{~nm}$. Due to the insertion of the plate, central maxima is shifted by a distance of $x \beta_{0} . \beta_{0}$ is the fringe-width befor the insertion of the plate. The value of the $x$ is _____________.