In a Young's double slit experiment, the separation between the two slits is 0.9 ~mm and the fringes are observed 1 ~m away. If it produces the second dark fringe at a distance of 1 ~mm from the central fringe, the wavelength of the monochromatic source of light used is

Step-by-step solution

Given, separation between two slits, d=0.9 ~mm =0.9 10⁻³ ~m Distance between slits and screen, D=1 ~m The distance between two consecutive dark or bright fringes is given as (fringe width) and that between central tringe and first dark fringe on either side is 2 . It is given that the spacing between second dark fringe and central fringe = + 2 = 3 2 As we know, = L d Hence, 3 2 D d =1 10⁻³ ~m aligned & 3 2 1 0.9 10⁻³ =1 10⁻³ ~m & = 2 3 10⁻³ 0.9 10⁻³ 1 =0.6 10⁻⁶ ~m aligned Wavelength of monochromatic source of light