In a Young's double slit experiment set up, the two slits are kept 0.4. mm apart and screen is placed at 1 m from slits. If a thin transparent sheet…

In a Young's double slit experiment set up, the two slits are kept $\displaystyle 0.4$ . mm apart and screen is placed at $\displaystyle 1$ m from slits. If a thin transparent sheet of thickness $\displaystyle 20 \mu \mathrm{~m}$ is introduced in front of one of the slits then center bright fringe shifts by $\displaystyle 20$ mm on the screen. The refractive index of transparent sheet is given by $\displaystyle \frac{\alpha}{10}$, where $\displaystyle \alpha$ is $\displaystyle \_\_\_\_$.