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 $7^{\text {th }}$ bright fringe, obtained with both slits uncovered. If the light source wavelength is 450 nm , the thickness of mica sheet is $\alpha \times 10^{-9} \mathrm{~m}$. The value of $\alpha$ is $\_\_\_\_$ .