On immersing the apparatus in water, the speed of wave travelling in water decreases and hence it’s wavelength decreases as v ∝ λ

Thus the new wavelength is 1/n times the the original wavelength since n=λ1/λ2

The fringe width originally is given by β1=λD/2d

The new fringe width within water will be given by β2=λD/2nd or β2=β1/n

Thus the fringe width decreases by a factor of n when immersed in water.

Regards

Arun