YDSE: Film, Medium & Two Wavelengths question from JEE Main 2026 (21 Jan, Shift 2)

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 of thickness $20\ \mu\text{m}$ is introduced in front of one of the slits then center bright fringe shifts by 20 mm on the screen.

The refractive index of transparent sheet is given by $\frac{\alpha}{10}$, where $\alpha$ is ______.