In water, wavelength of light decreases by a factor μ, the refractive index of water. In Young's double slit experiment, let screen is placed at a distance D,d is the distance between coherent sources.
The fringe width is given by W=dDλ
where, λ is wavelength of light used.
When the whole setup is dipped in water, wavelength is λw=μλa hence, it decreases.
Therefore, fringe width decreases and hence, fringe pattern shrinks.