Physics Question from JEE Main 2026 · 21 January, Shift 2

In a Young's double slit experiment set up, the two slits are kept $0.4 \, \text{mm}$ apart and screen is placed at $1 \, \text{m}$ 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 $20 \, \text{mm}$ on the screen. The refractive index of transparent sheet is given by $\frac{\alpha}{10}$, where $\alpha$ is _____.