In Young's two-slit experiment, the fringe width denoted by β and given by

\(\beta=\frac{\lambda D}d\)

Where, λ = wavelength of the light in air, D = distance between slits and screen, and d be the distance between two slits. When the whole apparatus is kept in water, the wavelength of light changes. So, \(\beta_w=\frac{\lambda_wD}d\)

Here, 

\(\frac{\beta_w}\beta=\frac{\lambda_w}\lambda=\frac1{\mu_w}\)      \(\left[\because\mu_w=\frac c{v_w}=\frac{\lambda\cdot f}{\lambda_w\cdot f}=\frac\lambda{\lambda_w}\right]\)

Or, \(\beta_w=\frac1{\mu_w}\cdot\beta\)

The fringe width decreases to a factor of \(\frac1{\mu_w}\) times that in the air.