Double-slit diffraction

Double-slit diffraction — Young's 1801 experiment — demonstrates both interference and diffraction simultaneously. Light of wavelength λ illuminates two parallel slits each of width a, separated by centre-to-centre distance d. On a distant screen, the intensity pattern is I(θ) = I₀ · [sin(πd sin θ/λ)]² / [sin(π(d/N) sin θ/λ)]² · [sin(πa sin θ/λ)/(πa sin θ/λ)]² — for two slits, an interference cosine-squared pattern multiplied by the single-slit sinc² envelope. Bright fringes occur at d sin θ = mλ (integer m) within the envelope; the envelope's first zero at sin θ = λ/a determines how many bright fringes are visible before the single-slit diffraction kills the pattern.

Young's 1801 experiment was the decisive evidence for the wave theory of light against Newton's corpuscular theory: no particle picture could produce alternating bright/dark fringes, but the wave-superposition picture produced them immediately, and the predicted fringe spacing λL/d (for screen distance L) matched measurement. The same setup, performed a century and a quarter later with electrons, photons one at a time, and eventually heavy molecules, established the wave–particle duality that defines quantum mechanics. "The heart of quantum mechanics," Feynman called the double-slit — "the only mystery." In optical laboratories today the double slit is a standard teaching tool; in quantum foundations, it remains the setup of choice for illustrating measurement and superposition.