In Young’s double–slit experiment the separation between the slits is doubled and the distance between the slit and the screen is halved. The fringe–width becomes

Distance between the two slits d'=2d Distance between the slit and the screen D'=D2 Fringe width β=λDd   and                     β'=λD'd'                           =λ(D/2)2d                            =λD4d                   ∴  β'=β4