Question

White light is used to illuminate the two slits in Young’s double slit experiment. The separation between the two slits is b and the screen is at a distance d (>>b) from the slits. At a point on screen directly opposite one of the slits certain waves lengths are missing. Some of the missing wave lengths are

(a) λ = \(\frac{b^2}{d}\)

(b) λ = \(\frac{2b^2}{d}\)

(c) λ = \(\frac{b^2}{3d}\)

(d) λ = \(\frac{2b^2}{3d}\)

Answer 1

 (a) λ = \(\frac{b^2}{d}\) /  (c) λ = \(\frac{b^2}{3d}\)

The wave lengths that are missing at the point P, considered, are the ones undergoing destructive interference. The path difference, Δ ; between the two interferring beams at P is

For destructive interferrence

For different allowed values of n; λ is

The missing wave length is given by (a) and (c).