As shown in the figure, in Young’s double slit experiment, a thin plate of thickenss $\mathrm{t}=10\mathrm{\mu m}$  and refractive index $\mathrm{\mu }=1.2$ is inserted infront of slit S₁ . The experiment is conducted in air $(\mathrm{\mu }=1)$ and uses a monochromatic light of wavelength $\mathrm{\lambda }= 500 \mathrm{nm}$. Due to the insertion of the plate, central maxima is shifted by a distance of ${\mathrm{x\beta }}_0$. ${\mathrm{\beta }}_{\mathrm{o}}$ is the fringe-width before the insertion of the plate. The value of the x is ____.