In Young's double slit experiment, the two slits are illuminated by a light beam consisting of wavelengths 4200 Å and 5040 Å . If the distance between the slits is 2.4 ~mm and the distance between the slits and the screen is 200 ~cm , the minimum distance from the central bright fringe to the point where the bright fringes due to both the wavelengths coincide is

Step-by-step solution

Let n₁ fringes of ₁=4200 Å and n₂ fringes of ₂=5040 Å wavelength are formed in a fixed distance on screen. So, n = constant or n₁ ₁=n₂ ₂ For minimum distance to be coincide, gathered n₁=n+1, n₂=n (n+1) 4200=n(5040) 4200 n+4200=5040 n n Required distance, x= n₁ ₁ D d Given, D=200 ~cm =2 ~m , d=2 4 10⁻³ ~m , n₁=5+1=6, ₁=4200 Å x= 6 4200 10⁻¹⁰ 2 24 10⁻³ x=2.1 10⁻³ ~m =2.1 ~mm gathered