Wave Interference & Young's Slits Calculator

Wave Interference Guide

Young's Double-Slit Formula

Fringe spacing: w = λD/d. Where w = fringe spacing (m), λ = wavelength (m), D = distance from slits to screen (m), d = slit separation (m). Example: sodium light λ = 589nm, d = 0.5mm, D = 1.5m. w = (589×10⁻⁹ × 1.5) / (0.5×10⁻³) = 8.835×10⁻⁷/5×10⁻⁴ = 1.77×10⁻³ m = 1.77 mm. Young's experiment (1801) provided the first compelling evidence for the wave nature of light — two coherent sources produce alternating bright (constructive) and dark (destructive) interference fringes.

Constructive and Destructive Interference

Path difference Δ = d sin θ ≈ d × (y/D) for small angles. Constructive interference (bright fringe): Δ = nλ, where n = 0, 1, 2... Destructive interference (dark fringe): Δ = (n + ½)λ, where n = 0, 1, 2... The central bright fringe: Δ = 0. First bright fringes either side: Δ = λ. Superposition principle: where two waves meet, the resultant displacement equals the sum of the individual displacements. Constructive: both waves in phase (crest meets crest) — amplitudes add. Destructive: waves exactly

Single-Slit Diffraction

A single slit of width a produces a central maximum and minima at angles: sin θ = nλ/a. Where n = ±1, ±2... (not zero — central maximum). Position of first minimum from centre on screen: y = λD/a. A 0.1mm slit with 589nm light at 1.5m: y = (589×10⁻⁹ × 1.5)/(0.1×10⁻³) = 8.84mm from centre. The single-slit pattern envelope modulates the double-slit fringes — missing orders appear where the single-slit minimum coincides with a double-slit maximum (when d/a is an integer). Narrower slit → wider diff

Coherence and Interference

Two sources must be coherent (constant phase relationship) to produce stable interference fringes. A single laser beam split by two slits is coherent. Two separate lamps: not coherent — fringes would average out. Laser light: highly coherent (long coherence length), monochromatic (narrow wavelength range). White light: very short coherence length — only the central fringe (Δ=0) is white; other fringes show colour fringing (different wavelengths interfere constructively at different positions). A