Young's Double-Slit Experiment: Proof & Applications

In 1801, Thomas Young shone light through two narrow slits onto a screen — and instead of two bright bands, he got dozens: alternating bright and dark fringes stretching across the screen. That pattern is only possible if light waves from the two slits interfere with each other, adding where they arrive in phase and cancelling where they arrive out of phase. It was the first definitive proof that light is a wave — and it remained the definitive proof for over a century, until quantum mechanics complicated the picture spectacularly.

The complication: if you repeat Young's experiment with single photons — or single electrons — sent through one at a time, the interference pattern still builds up. Each particle somehow "knows about" both slits. That's not a theoretical puzzle; it's an experimental result. The double-slit experiment is the cleanest demonstration of wave-particle duality in existence.

How the Experiment Works

A coherent light source (one with consistent phase relationship — a laser is ideal) illuminates two narrow slits separated by distance a. Each slit acts as a secondary source of Huygens wavelets. The two sets of waves spread out and overlap in the region beyond the slits.

At any point on the screen, the waves from the two slits have travelled different distances — this difference is the path difference δ. Whether they arrive in phase or out of phase determines whether that point is bright or dark.

Constructive interference (bright fringe): waves arrive in phase — path difference is a whole number of wavelengths:

Destructive interference (dark fringe): waves arrive perfectly out of phase — path difference is a half-integer number of wavelengths:

The Fringe Spacing Formula

For a screen at distance D from the slits (with D ≫ a), the fringe spacing (distance between adjacent bright or dark fringes) is:

This formula allows the wavelength of light to be measured precisely: rearranging, λ = aΔy/D. By measuring the slit separation a, the screen distance D, and the fringe spacing Δy with a ruler, Young measured the wavelength of light for the first time.

Fringe spacing increases when:

• λ increases (longer wavelength light → wider fringes: red wider than blue)

• D increases (screen further away → wider fringes)

• a decreases (slits closer together → wider fringes)

Worked Examples

Example 1: Finding wavelength

Two slits separated by a = 0.5 mm = 5 × 10⁻⁴ m are placed 2.0 m from a screen. Fringe spacing Δy = 2.4 mm = 2.4 × 10⁻³ m. Find the wavelength of light.

600 nm — orange-red visible light. ✓

Example 2: Fringe spacing with blue light

Blue light (λ = 450 nm) passes through slits 0.3 mm apart, screen 1.5 m away.

Example 3: Path difference to dark fringe

Light of wavelength 500 nm illuminates double slits. What path difference produces the 2nd dark fringe?

Conditions for Clear Interference Fringes

Coherence: the two sources must be coherent — maintaining a constant phase relationship. A laser provides perfect coherence; ordinary light sources must have light from a single source divided by the two slits (so they remain phase-correlated). Incoherent sources produce overlapping, randomly-phased patterns that wash out the fringes.

Monochromatic light: a single wavelength gives sharp, clearly separated fringes. White light produces overlapping fringe patterns for each wavelength, creating coloured fringes near the centre with the central white maximum, then a blurred pattern further out.

Slit width: slits must be narrow enough to produce diffraction (spreading of light through the slit), allowing overlap of the two beams. Wider slits produce a single-slit diffraction envelope that modulates the double-slit pattern.

Young's Experiment and Quantum Mechanics

Young's experiment became even more profound in the 20th century. When performed with single photons — fired one at a time — the interference pattern still builds up on the screen over thousands of photon detections. Each photon hits the screen at a single point (particle-like), yet the statistical distribution over many photons creates the interference pattern (wave-like). The same experiment with single electrons, neutrons, and even atoms gives the same result.

This is the core of wave-particle duality: each quantum object interferes with itself, following a probabilistic wave description, but is detected as a discrete particle. And if you add a detector to determine which slit each photon/electron goes through, the interference pattern disappears — the act of measurement collapses the wave behaviour. Young's simple experiment thus sits at the very heart of quantum mechanics.

The Young's Double-Slit Setup

Two narrow slits, separated by distance d, are illuminated by coherent monochromatic light of wavelength λ. A screen is placed at distance D from the slits. Each slit acts as a secondary point source (by Huygens' principle), and the two sets of circular wavefronts overlap and interfere on the screen.

The Fringe Formula

Constructive interference (bright fringes) occurs where path difference = nλ (n = 0, 1, 2, …). Destructive interference (dark fringes) occurs where path difference = (n+½)λ. For small angles (D ≫ d), the fringe spacing y between adjacent bright fringes is:

Rearranged to find wavelength: λ = yd/D. This is how Young measured the wavelength of light in 1801 — before any other method existed.

Derivation

The path difference from two slits to a point P at height x on the screen is Δ = xd/D (for small angles, where sin θ ≈ tan θ ≈ θ). Bright fringes: xd/D = nλ → x_n = nλD/d. Fringe spacing: y = x_{n+1} − x_n = λD/d. The central bright fringe (n = 0, path difference = 0) is at the centre; intensity falls off toward the edges due to single-slit diffraction modulation.

Worked Example

Light of λ = 589 nm passes through slits d = 0.4 mm apart, screen at D = 1.5 m. Find fringe spacing.

What the Experiment Proves

The double-slit experiment proves the wave nature of light — only waves can interfere. Particles would produce two bright strips, not a spread pattern. When performed with individual photons fired one at a time, the interference pattern still builds up — each photon interferes with itself, going through both slits simultaneously as a wave (wave-particle duality). When a detector is placed at the slits to determine which slit the photon went through, the interference pattern disappears — the act of measurement collapses the wavefunction.

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