In Young's double-slit experiment, a thin plate of thickness t = 10 μm and refractive index μ = 1.2 is inserted in front of one slit. The light wavelength is λ = 500 nm. The central maximum shifts by xβ₀, where β₀ is the original fringe width. Find x. Image
Physics · Wave Optics · Fringe shift due to thin plate
JEE Mains JEE Advanced

Question

In Young's double-slit experiment, a thin plate of thickness t = 10 μm and refractive index μ = 1.2 is inserted in front of one slit. The light wavelength is λ = 500 nm. The central maximum shifts by xβ₀, where β₀ is the original fringe width. Find x. Image

Physics · Wave Optics · Fringe shift due to thin plate

G1 Physics · Accepted Answer

Fringe shift due to a thin plate: Δx = [(μ − 1)t/λ] β₀ Hence: x = (μ − 1)t/λ = (1.2 − 1)(10 × 10⁻⁶)/(500 × 10⁻⁹) = (0.2 × 10 × 10⁻⁶)/(5 × 10⁻⁷) = 4 Final answer: 4.