Young’s Double-Slit Experiment
In 1801, Thomas Young performed one of the most elegant experiments in the history of science: he passed light through two narrow, closely spaced slits and observed a pattern of alternating bright and dark bands — called fringes — on a distant screen. This was extraordinary because, if light were simply a stream of particles, you would expect two bright patches and nothing more. Instead, the banded pattern was unmistakable evidence that light behaves as a wave, capable of interfering with itself in the same way that ripples on a pond overlap and either reinforce or cancel each other. The experiment works because the two slits act as two coherent sources of light waves — meaning they emit waves with a constant phase relationship. As these waves spread out (diffract) from each slit, they meet and overlap across the screen. Where a crest from one slit meets a crest from the other, constructive interference occurs and a bright fringe appears. Where a crest meets a trough, destructive interference occurs and a dark fringe appears. The result is a regular, repeating pattern of light and dark bands whose spacing depends on the wavelength of the light, the slit separation, and the distance to the screen. Young's double-slit experiment remains central to physics today because it demonstrates wave–particle duality. Even single photons fired one at a time through the slits eventually build up the same interference pattern — a fact that lies at the heart of quantum mechanics. Understanding fringe formation and spacing gives students a precise, quantitative window into the wave nature of light.
- Setting Up the Geometry
- Condition for Bright Fringes (Constructive Interference)
- Condition for Dark Fringes (Destructive Interference)
- Deriving the Fringe Spacing Formula
- What Affects Fringe Visibility?
Setting Up the Geometry
Imagine two slits, S₁ and S₂, separated by a distance d, illuminated by a monochromatic (single-wavelength) coherent light source. A screen is placed a distance D away, where D ≫ d. A point P on the screen is at perpendicular distances r₁ and r₂ from the two slits. The key quantity is the path difference Δ = r₂ − r₁: the extra distance that the wave from one slit travels compared with the wave from the other slit.
Condition for Bright Fringes (Constructive Interference)
When the path difference is a whole number of wavelengths, the two waves arrive in phase — crest meets crest — and reinforce each other: Δ = mλ, where m = 0, ±1, ±2, … The central bright fringe (m = 0) sits at the midpoint of the screen where the path difference is zero. The first bright fringe on either side corresponds to m = ±1 (one full wavelength of path difference), and so on.
Condition for Dark Fringes (Destructive Interference)
When the path difference is a half-integer number of wavelengths, the two waves arrive exactly out of phase — crest meets trough — and cancel: Δ = (m + ½)λ, where m = 0, ±1, ±2, … This produces the dark bands between successive bright fringes. The symmetry of the conditions means bright and dark fringes alternate uniformly across the screen.
Deriving the Fringe Spacing Formula
For a point P at height y above the centre of the screen, the path difference (using the small-angle approximation, valid when D ≫ d) is Δ ≈ yd/D. Setting this equal to mλ for constructive interference gives y_m = mλD/d. The spacing between adjacent bright (or dark) fringes is therefore Δy = λD/d. This elegant formula tells us: fringes are wider when light has a longer wavelength, when the screen is farther away, or when the slits are closer together.
What Affects Fringe Visibility?
The fringes are only sharp and clearly visible if the light is coherent (constant phase relationship between slits) and approximately monochromatic (single wavelength). White light produces overlapping coloured fringes because each wavelength has a different spacing. Increasing the slit width broadens each single-slit diffraction envelope, which modulates the overall brightness of the pattern. In practice, a laser is the ideal light source because it is both coherent and monochromatic.
The Key Equation
- \Delta y — Fringe spacing (m): The perpendicular distance between the centres of two adjacent bright (or dark) fringes on the screen.
- \lambda — Wavelength (m): The wavelength of the monochromatic light used. Visible light ranges from approximately 400 nm (violet) to 700 nm (red).
- D — Slit-to-screen distance (m): The perpendicular distance from the plane of the slits to the screen. Must be much larger than d for the small-angle approximation to hold.
- d — Slit separation (m): The distance between the centres of the two slits. Typically of the order of tenths of a millimetre in school experiments.
Worked Example
Problem. A student shines a red laser of wavelength 632 nm through a double slit with slit separation 0.25 mm. The screen is placed 1.80 m away. Calculate the fringe spacing and state whether the fringes would be closer together or farther apart if the same experiment were repeated with green light (λ = 520 nm).
Answer. The fringe spacing with red light is approximately 4.55 mm. With green light (520 nm) the fringes would be closer together at approximately 3.74 mm, because fringe spacing is directly proportional to wavelength.
Origins · 1 minThomas Young and how this was discovered
Thomas Young conducted his famous double-slit experiment in 1801, demonstrating conclusively that light exhibits wave-like behaviour through interference. He also established the principle of superposition for waves and introduced the concept of the wavelength of light. His results were initially controversial, as Newton's corpuscular (particle) theory of light was the dominant view at the time, but Young's wave interpretation was eventually vindicated. Young was a polymath of extraordinary breadth: in addition to his wave theory of light, he made major contributions to the decipherment of Egyptian hieroglyphics (working on the Rosetta Stone), established the elastic modulus in materials science (now called Young's modulus), and was fluent in thirteen languages by age fourteen.
Related Concepts
- Wave Superposition — Interference in the double-slit experiment is a direct consequence of the principle of superposition — the resultant displacement at any point is the sum of the displacements of the individual waves.
- Diffraction — Each slit in Young's experiment diffracts the incoming light, spreading it out so that wavefronts from both slits overlap and can interfere across the whole screen.
- Wave Properties: Wavelength, Frequency and Speed — The fringe spacing formula depends directly on wavelength λ, so a solid understanding of wave properties — particularly the meaning and measurement of wavelength — is essential for interpreting double-slit results.
- Thin-Film Interference — Thin-film interference (e.g. colours on a soap bubble) is another application of the same constructive and destructive interference principles first demonstrated by Young's experiment.