In a Young's double slit experiment, an angular width of the fringe is $0.35^{\circ}$ on a screen placed at 2 m away for particular wavelength of 450 nm. The angular width of the fringe, when whole system is immersed in a medium of refractive index $\frac{7}{5}$, is $\frac{1}{\alpha}$. The value of $\alpha$ is \_\_\_\_.