In a Young’s double slit experiment set up, the two slits are kept 0.4. mm apart and screen is placed at 1 m from slits. If a thin transparent sheet of thickness 20 μm is introduced in front of one of the slits then centre bring fringe shifts by 20 mm on the screen. The refractive index of transparent sheet is given by α/10, where α i s ________.
Physics · Wave Optics · Young's Double Slit Experiment
JEE Mains 2026 21 January Evening Shift

Question

In a Young’s double slit experiment set up, the two slits are kept 0.4. mm apart and screen is placed at 1 m from slits. If a thin transparent sheet of thickness 20 μm is introduced in front of one of the slits then centre bring fringe shifts by 20 mm on the screen. The refractive index of transparent sheet is given by α/10, where α i s ________.

Physics · Wave Optics · Young's Double Slit Experiment

JEE Mains 2026 21 January Evening Shift

G1 Physics · Accepted Answer

The shift of the central bright fringe due to a thin transparent sheet is y(shift) = (μ - 1)tD/d. Given, y(shift) = 20 mm = 20 × 10⁻³ m, t = 20 μm = 20 × 10⁻⁶ m, D = 1 m, d = 0.4 mm = 0.4 × 10⁻³ m. Therefore, 20 × 10⁻³ = (μ - 1)(20 × 10⁻⁶)(1)/(0.4 × 10⁻³). Hence, μ - 1 = (20 × 10⁻³)(0.4 × 10⁻³)/(20 × 10⁻⁶) = 0.4. Thus, μ = 1.4. The question gives μ = α/10. Therefore, α/10 = 1.4, so α = 14. Therefore the answer is 14.