In a Young's double slit experiment, the distance between the slits is 2 mm and the screen is placed at a distance of 2 m from the slits. A beam of light consisting of two wavelengths, ₁ = 600 nm and an unknown shorter wavelength ₂ , is used. It is observed that the n^ th bright fringe of ₁ coincides with the (n+1)^ th bright fringe of ₂ at a distance of 2.4 mm from the central maximum. The value of ₂ (in nm ) is ___

Step-by-step solution

The position of the n^ th bright fringe for wavelength ₁ is given by y = n ₁ D d Given y = 2.4 mm = 2.4 10⁻³ m , D = 2 m , d = 2 mm = 2 10⁻³ m , and ₁ = 600 nm = 600 10⁻⁹ m . Substituting the values: 2.4 10⁻³ = n 600 10⁻⁹ 2 2 10⁻³ 2.4 10⁻³ = n 600 10⁻⁶ n = 2.4 10⁻³ 6 10⁻⁴ = 4 It is given that the n^ th bright fringe of ₁ coincides with the (n+1)^ th bright fringe of ₂ . n ₁ = (n+1) ₂ 4 600 = 5 ₂ ₂ = 2400 5 = 480 nm Answer: 480