Diffraction & Interference: Huygens' Wavelets Explain Both

Every point on a wavefront is a new source

Diffraction and interference both fall out of a single principle formulated by Christiaan Huygens in 1678: every point on an advancing wavefront can be treated as a source of a new, tiny secondary wavelet, and the wavefront a moment later is the envelope of all those wavelets added together. Where a wave passes through an obstacle or opening comparable in size to its wavelength, the wavelets spreading from different parts of the opening interfere with each other — reinforcing where they arrive in phase, cancelling where they arrive out of phase — and that interference pattern is what we see as diffraction.

Young's double slit: two sources, one pattern

Thomas Young's 1801 double-slit experiment sends light through two narrow, closely spaced slits and observes the pattern on a distant screen. Each slit acts as a Huygens source, and the two resulting wave trains overlap and interfere: at points where the path-length difference from the two slits is a whole number of wavelengths, the waves arrive in phase and add constructively into a bright fringe; where the difference is a half-integer number of wavelengths, they arrive out of phase and cancel into a dark fringe.

constructive (bright fringe):  d*sin(theta) = m * lambda        m = 0, ±1, ±2, ...
destructive (dark fringe):    d*sin(theta) = (m + 1/2) * lambda

  d      = slit separation
  theta  = angle from the centre line to the fringe
  lambda = wavelength

Young's experiment is historically important beyond optics: it was the decisive evidence that light behaves as a wave, settling (for over a century, until quantum mechanics complicated the picture again) a dispute with the particle theory of light Newton had favoured. Run the same experiment with single photons or electrons sent through one at a time, and the interference pattern still builds up dot by dot — one of the foundational demonstrations of wave-particle duality.

Single-slit diffraction: interference with itself

A single slit of finite width also produces a diffraction pattern, because different parts of the same slit act as separate Huygens sources that interfere with each other. Rather than the evenly spaced fringes of a double slit, a single slit produces one broad, bright central maximum flanked by progressively dimmer secondary fringes, with dark minima at:

single-slit minima:  a*sin(theta) = m * lambda        m = ±1, ±2, ±3, ...
  a = slit width
  narrower slit (smaller a) -> wider central maximum (more spreading)

This inverse relationship — a narrower opening produces a wider spread — is the same reason a small aperture blurs an image (diffraction-limited resolution) and why radio antennas and telescope mirrors need to be many wavelengths across to focus a beam tightly.

Diffraction gratings: many slits sharpen everything

A diffraction grating replaces two slits with hundreds or thousands of evenly spaced slits per millimetre. The bright-fringe condition is the same as for the double slit, d·sinθ = mλ, but with so many interfering sources the bright maxima become extremely narrow and intense while everything between them is driven toward near-total cancellation — which is what makes gratings, rather than a simple double slit, the practical tool for spectroscopy: each wavelength present in an incoming light beam is diffracted to its own precise angle, so a grating spreads white light into a sharp, well-separated spectrum the way a prism does through refraction instead.

The Fraunhofer intensity pattern

For diffraction observed far from the aperture (or equivalently, using a lens to project the pattern as if from infinity — the Fraunhofer regime, as opposed to the more complex near-field Fresnel regime), the intensity distribution from a single slit follows a closed-form sinc-squared curve:

I(theta) = I0 * [ sin(beta) / beta ]^2 ,   beta = (pi * a * sin(theta)) / lambda

  central maximum at theta = 0 is by far the brightest
  side lobes fall off rapidly: roughly 4.5%, 1.6%, 0.8% of the central peak's intensity

What the simulation shows

This simulation propagates real wavefronts through single-slit, double-slit and grating configurations using the Huygens construction directly, overlaying the theoretical Fraunhofer intensity curve so you can watch the interference pattern build up from individual wavelets and adjust wavelength, slit width, slit separation and grating line count to see how each parameter reshapes the fringe spacing and envelope in real time.

Frequently asked questions

Try it live

Everything above runs in your browser — open Diffraction & Interference and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.