In 1801, Thomas Young performed one of the most elegant experiments in the history of physics. He shone light through two narrow slits onto a screen — and instead of two bright bands, he saw a pattern of alternating bright and dark fringes. This could only happen if light behaved as a wave, with the two beams interfering constructively and destructively. Young's double-slit experiment settled, for a century, the question of whether light was a wave or a particle. (Quantum mechanics later showed it is both — but that understanding came only in the 20th century.)
When coherent light passes through two narrow slits separated by distance a, an interference pattern of bright and dark fringes appears on a screen at distance D. Fringe spacing (distance between adjacent bright fringes):
Δy = λD/a
where λ is the wavelength of light. Bright fringes occur where path difference = nλ (constructive interference); dark fringes where path difference = (n + ½)λ (destructive interference).
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:
Diagram — Young's double-slit: path difference and fringe formation
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.
Frequently Asked Questions
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.
Frequently Asked Questions
What does Young's double-slit experiment prove?
Young's double-slit experiment proves that light (and matter) has wave-like properties. When light passes through two narrow slits, the overlapping wavefronts produce an interference pattern of alternating bright and dark fringes — only possible for waves, not particles. The fringe spacing y = λD/d allows measurement of wavelength λ. When performed with single photons or electrons, the pattern still forms over time, proving each particle interferes with itself and travels through both slits simultaneously as a wave — a direct demonstration of quantum wave-particle duality.
What is the formula for Young's double-slit fringe spacing?
The fringe spacing (distance between adjacent bright or dark fringes) is y = λD/d, where λ is the wavelength of light (m), D is the distance from slits to screen (m), and d is the slit separation (m). This gives λ = yd/D — a way to measure wavelength from the fringe pattern. Wider slit separation → narrower fringes. Longer wavelength → wider fringes. Larger screen distance → wider fringes. The formula assumes D ≫ d (small angle approximation sin θ ≈ tan θ ≈ θ).
Why must the light be coherent for a double-slit experiment?
Coherent light has a fixed phase relationship between the two slits — each wavefront from one slit is in a definite phase relationship with the corresponding wavefront from the other. Without coherence, the phase difference between the slits varies randomly and rapidly — constructive and destructive interference regions average out, giving uniform illumination with no fringes. Lasers provide coherent light naturally. White light can be made coherent by passing through a single narrow slit first (as Young did) — this ensures both slits are illuminated by the same wavefront from the same source point.
What happens to fringe spacing if wavelength is increased?
From y = λD/d, fringe spacing is directly proportional to wavelength — if λ doubles, y doubles. Red light (λ ≈ 700 nm) produces wider fringe spacing than blue light (λ ≈ 450 nm). This is why white light (containing all wavelengths) produces coloured fringes: the central fringe is white (all colours in phase), but outer fringes spread out by wavelength, with red on the outside and blue on the inside of each bright fringe. This spectral splitting in the outer fringes was how Young identified that different colours correspond to different wavelengths.
What is the difference between constructive and destructive interference?
Constructive interference occurs where waves from both slits arrive in phase (path difference = nλ, n = 0, 1, 2…) — the amplitudes add, producing a bright fringe with intensity proportional to (2A)² = 4A² (four times a single slit's intensity). Destructive interference occurs where waves arrive exactly out of phase (path difference = (n+½)λ) — the amplitudes cancel, producing a dark fringe with zero intensity. Between these extremes, intermediate intensities occur. Total energy is conserved: the energy absent from dark fringes is redistributed into bright fringes.
What is Young's double-slit experiment?
Young's double-slit experiment passes coherent light through two narrow slits to produce an interference pattern of alternating bright and dark fringes on a screen. It proves light behaves as a wave. Fringe spacing Δy = λD/a, where λ is wavelength, D is slit-to-screen distance, and a is slit separation.
What is the fringe spacing formula?
Δy = λD/a, where Δy is the distance between adjacent bright (or dark) fringes, λ is the wavelength of light, D is the distance from slits to screen, and a is the slit separation. This allows wavelength to be measured: λ = aΔy/D.
Why do bright fringes form in a double-slit experiment?
Bright fringes occur where waves from both slits arrive in phase — constructive interference. This happens when the path difference from the two slits to the screen point is a whole number of wavelengths: δ = nλ. The path difference is zero at the central maximum (n=0) and increases moving away from centre.
What happens when white light is used in a double-slit experiment?
White light creates coloured fringes. The central fringe is white (all wavelengths have zero path difference). Moving outward, longer wavelengths (red) have their first-order bright fringe further from centre than shorter wavelengths (violet) — creating rainbow-coloured fringes. Further out, fringes from different colours overlap and merge into white/blurred bands.
What does Young's experiment show about the nature of light?
It shows light behaves as a wave — specifically that it can interfere with itself. Particles would produce two bright bands behind two slits; instead, light produces many bands. When performed with single photons or electrons, each individual particle still builds up an interference pattern over time — proving even single quanta have wave-like behaviour (wave-particle duality).
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