Interference fringes are obtained in a Young double slit experiment using beam of light consisting two wavelengths 500   nm and 600   nm . Bright fringes due to both wavelengths coincide at 2 . 5   mm from the central maximum. If the separation between the slits is 3   mm , then the distance between the screen and plane of the slits is

Step-by-step solution

We know, y = n 1 λ 1 D d = n 2 λ 2 D d ⇒   n 1 λ 1 = n 2 λ 2 ⇒   n 1 500 nm = n 2 600 nm ⇒   5 n 1 = 6 n 2 ∴   n 1 = 6 ,   n 2 = 5           ∴     n 1 ≠ 0 ,   n 2 ≠ 0 Consider; y = n 1 λ 1 D d ⇒   2 . 5   mm = 6 × 500 nm 3 mm × D ⇒   D = 2 . 5 × 3 × 10 - 6 6 × 500 × 10 - 9 ∴   D = 2 . 5   m