In Young's double slit experiment, the slits are 2 mm apart and are illuminated by photons of two wavelengths ₁ = 6000 Å and ₂ = 5000 Å one after the other. 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: d = 2 mm = 2 10⁻³ m D = 2 m ₁ = 6000 = 6 10⁻⁷ m ₂ = 5000 = 5 10⁻⁷ m Let the n₁ -th bright fringe of ₁ coincide with the n₂ -th bright fringe of ₂ . The position of the n -th bright fringe from the central maximum is given by y = n D d . For coincidence: n₁ ₁ D d = n₂ ₂ D d n₁ ₁ = n₂ ₂ n₁ n₂ = ₂ ₁ = 5000 6000 = 5 6 For the minimum distance from the central maximum, we take the smallest integer values for n₁ and n₂ , which are n₁ = 5 and n₂ = 6 . Substituting n₁ = 5 into the position formula: y = 5 6 10⁻⁷ 2 2