A beam of light consisting of two wavelengths 7000   A o and 5500   A o is used to obtain interference pattern in Young's double slit experiment. The distance between the slits is 2 . 5   mm and the distance between the plane of slits and the screen is 150   cm . The least distance from the central fringe, where the bright fringes due to both the wavelengths coincide, is n × 10 – 5

Step-by-step solution

The given data is λ 1 = 7000   A o λ 2 = 5500   A o d = 2 . 5 × 10 - 3   m D = 1 . 5   m The path difference is given by n λ 1 = m λ 2 7 n = 5 . 5   m ⇒ 14 n = 11   m ⇒ n = 11 and m = 14 The formula for the distance of a bright fringe is y = n λ 1 D d ⇒ y = 11 × 7 × 10 - 7 × 1 . 5 2 . 5 × 10 - 3 = 46 . 2 × 10 - 4 = 462 × 10 - 5 It is given that n × 10 - 5 = 462 × 10 - 5 ⇒ n = 462