Diffraction & Interference — When Light Bends Around Corners

1. Huygens-Fresnel Principle

Every point on a wavefront acts as a secondary point source of spherical wavelets. The amplitude at any point P is the coherent superposition of all secondary wavelets from the previous wavefront:

2. Single-Slit Diffraction

3. Double-Slit Interference (Young)

4. Diffraction Grating

5. Airy Disk and Resolution Limit

6. Fresnel vs Fraunhofer Regimes

7. JavaScript Diffraction Simulator

// Fraunhofer diffraction intensity for arbitrary 1D aperture
// using numerical DFT (or analytically for standard shapes)

function singleSlitIntensity(theta, lambda, a) {
  const beta = (Math.PI * a * Math.sin(theta)) / lambda;
  if (Math.abs(beta) < 1e-10) return 1;
  const sinc = Math.sin(beta) / beta;
  return sinc * sinc;
}

function doubleSlitIntensity(theta, lambda, a, d) {
  const envelope = singleSlitIntensity(theta, lambda, a);
  const delta = (Math.PI * d * Math.sin(theta)) / lambda;
  const interference = Math.cos(delta) ** 2;
  return envelope * interference;
}

function gratingIntensity(theta, lambda, a, d, N) {
  const envelope = singleSlitIntensity(theta, lambda, a);
  const delta = (Math.PI * d * Math.sin(theta)) / lambda;
  let multi;
  if (Math.abs(Math.sin(delta)) < 1e-10) {
    multi = N * N;
  } else {
    const r = Math.sin(N * delta) / Math.sin(delta);
    multi = r * r;
  }
  return envelope * multi / (N * N); // normalise
}

// Generate intensity pattern on screen at distance L
function diffractionPattern(type, params, screenW = 0.05, L = 1, nPoints = 2000) {
  const pts = [];
  for (let i = 0; i < nPoints; i++) {
    const y = (i / nPoints - 0.5) * screenW;
    const theta = Math.atan(y / L);
    let I;
    if (type === 'single')
      I = singleSlitIntensity(theta, params.lambda, params.a);
    else if (type === 'double')
      I = doubleSlitIntensity(theta, params.lambda, params.a, params.d);
    else
      I = gratingIntensity(theta, params.lambda, params.a, params.d, params.N);
    pts.push({y: y * 1000, I}); // y in mm
  }
  return pts;
}

// Example: 600-line/mm grating, λ=589nm, N=200 illuminated slits
const pattern = diffractionPattern('grating', {
  lambda: 589e-9,
  a: 0.8e-6,    // slit width 0.8 μm
  d: 1/600000,   // 600 lines/mm → d in m
  N: 200
}, 0.1, 1);
const peak = Math.max(...pattern.map(p => p.I));
console.log(`Peak at I = ${peak.toFixed(3)}`);

8. Applications