JEE Main 2026 — 4 April, Evening Shift — Question 24

In a double slit experiment, when one of the slits is covered by a transparent mica sheet of refractive index 1.56, the central fringe shifts to the position of $7^{\mathrm{th}}$ bright fringe, obtained with both slits uncovered. If the light source wavelength is $450\ \mathrm{nm}$, the thickness of mica sheet is $\alpha \times 10^{-9}\ \mathrm{m}$. The value of $\alpha$ is