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 \( \dfrac{\alpha}{10} \), where \( \alpha \) is ___________.
