A beam of light consisting of wavelengths 7000 Å and 5500 Å is used in Young's double slit experiment. Slit separation is 2.5 mm and screen distance is 150 cm. The least distance from the central fringe where bright fringes of both wavelengths coincide is n × 10⁻⁵ m. Find n.
Physics · Wave Optics · Young's Double Slit Experiment
JEE Mains 6 April 2023 Shift 2 Evening Shift

Question

A beam of light consisting of wavelengths 7000 Å and 5500 Å is used in Young's double slit experiment. Slit separation is 2.5 mm and screen distance is 150 cm. The least distance from the central fringe where bright fringes of both wavelengths coincide is n × 10⁻⁵ m. Find n.

Physics · Wave Optics · Young's Double Slit Experiment

JEE Mains 6 April 2023 Shift 2 Evening Shift

G1 Physics · Accepted Answer

For bright fringes of the two wavelengths to coincide: m₁λ₁ = m₂λ₂ Here: λ₁ = 7000 Å λ₂ = 5500 Å The smallest integers satisfying the condition are 11×7000 = 14×5500 = 77000 Å Equivalent path wavelength: 77000 Å = 7.7×10⁻⁶ m Fringe position: y = λD/d = (7.7×10⁻⁶)(1.5)/(2.5×10⁻³) = 4.62×10⁻³ m = 462×10⁻⁵ m Final value: 462