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…

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