In a Young’s double-slit arrangement, the screen is turned through a small angle β (β≪1rad) about a vertical axis so that it is no longer parallel to the plane of the slits. The slit separation is d and the distance from the mid-point of the slits to the screen remains D (D≫d).
(i) Show that, to first order in small quantities, the path difference between the two waves reaching a point on the screen at a transverse distance y from the central line is approximately Δx≈d(Dy+β).
(ii) Hence write the condition for the m-th bright fringe on the tilted screen.