How does the fringe width in Young's double-slit experiment change when the distance of separation between the slits and screen is doubled?

Fringe width, β = λD/d where all the symbols have their usual meanings.
Now the distance between the slit and screen is doubled i.e D' = 2D
∴New fringe width β' = λ(2D)/d = 2β
Thus fringe width gets also doubled.