A beam of light consisting of wavelengths 650 nm and 550 nm illuminates the Young's double slits with separation of 2 mm such that the interference fringes are formed on a screen, placed at a distance of 1.2 m from the slits. The least distance of a point from the central maximum, where the bright fringes due to both the wavelengths coincide, is _ _ _ _ 10⁻⁵ ~m .

Step-by-step solution

Given wavelengths are ₁ = 650 nm and ₂ = 550 nm. Slit separation d = 2 mm = 2 10⁻³ m. Distance to screen D = 1.2 m. For the bright fringes of both wavelengths to coincide at a distance y from the central maximum, we have: y = n₁ ₁ D d = n₂ ₂ D d where n₁ and n₂ are integers representing the order of the fringes. This simplifies to n₁ ₁ = n₂ ₂ . n₁ n₂ = ₂ ₁ = 550 650 = 11 13 The least values for coincidence are n₁ = 11 and n₂ = 13 . The least distance y is given by: y = n₁ ₁ D d = 11 650 10⁻⁹ 1.2 2 10⁻³ y = 11 650 0