In Young's double slit experiment, the slits are 2 mm apart and are illuminated by photons of two wavelengths λ 1 = 12000 Å and λ 2 = 10000 Å . At what minimum distance from the common central bright fringe on the screen 2 m from the slit will a bright fringe from one interference pattern coincide with a bright fringe from the other?

Step-by-step solution

Given, λ 1 = 12000 Å  and λ 2 = 10000 Å  D = 2   cm d = 2   mm = 2 × 10 - 3   m We have, λ 1 λ 2 = n 2 n 1 = 12000 10000 = 6 5 as X = n 1 λ 1 D d n 1 = 5 = 5 × 12000 × 10 - 10 × 2 2 × 10 - 3 = 5 × 1 . 2 × 10 4 × 10 - 10 × 10 3 = 6   mm