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 before the insertion of the plate. The value of the $x$ is $\_\_\_\_$ .