As shown in the figure, in Young's double slit experiment, a thin plate of thickness t =10 μ m and refractive index μ=1.2 is inserted infront of slit…

As shown in the figure, in Young's double slit experiment, a thin plate of thickness $\displaystyle \mathrm{t}=10 \mu \mathrm{~m}$ and refractive index $\displaystyle \mu=1.2$ is inserted infront of slit $\displaystyle \mathrm{S}_1$. The experiment is conducted in air ( $\displaystyle \mu=1$ ) and uses a monochromatic light of wavelength $\displaystyle \lambda=500 \mathrm{~nm}$. Due to the insertion of the plate, central maxima is shifted by a distance of $\displaystyle x \beta_0$. $\displaystyle \beta_0$ is the fringe-width befor the insertion of the plate. The value of the $\displaystyle x$ is $\displaystyle \_\_\_\_$.