If Young's double slit experiment is performed in water

If Young's double slit experiment is performed in water instead of air, then. Since frequency remains the same, therefore the wavelength must decrease. 
The fringe width will decrease.
Fringe width, β = D λ d Dλd or β ∞ λ If the experiment is performed in water, wavelength λ decreases, so fringe width also decreases.
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