In a YDSE bi-chromatic light of wavelengths, 400 nm and 560 nm are used. The distance between the plane of the slits is 0 . 1 mm and the distance between the slits and the screen is 1 m . The minimum distance between two successive regions of complete darkness is

Step-by-step solution

Let n th minimum of 400nm coincides with m th minimum of 560 nm, then For n th minima δ = 2 n - 1 λ 2 2 n - 1 4 0 0 2 = 2 m - 1 5 6 0 2 2 n - 1 2 m - 1 = 7 5 = 1 4 1 0 = 2 1 1 5 i.e., 4 th minimum of 400 nm coindes with 3rd minimum of 560 nm. Distance of n th minima from center = 2 n - 1 λD 2 d Location of this minimum is, Y 1 = 2 × 4 - 1 1 0 0 0 4 0 0 × 1 0 - 6 2 × 0 · 1 = 1 4 mm Next 11th minimum of 400 nm will coincide with 8th minimum of 560 nm. Location of this minimum is, Y 2 = 2 × 1 1 - 1 1 0 0 0 4 0 0 × 1 0