Double-Slit Interference Simulator
Visualize Young's double-slit interference. Adjust slit separation, wavelength, and screen distance to see fringe spacing change in real time.
Young's Double-Slit Experiment
In 1801, Thomas Young demonstrated the wave nature of light by passing it through two narrow slits separated by a distance d. The two emerging wavefronts superpose on a distant screen, producing alternating bright (constructive interference) and dark (destructive interference) fringes.
Constructive and Destructive Interference
A point on the screen at height y from the centre receives light from both slits. The path difference between the two rays is Δ = d sinθ ≈ dy/L for small angles. When Δ equals a whole number of wavelengths (mλ) the waves add constructively; when Δ equals a half-integer number ((m+½)λ) they cancel.
| Condition | Path difference Δ | Result |
|---|---|---|
| Constructive (bright) | mλ (m = 0, ±1, ±2, …) | Bright fringe |
| Destructive (dark) | (m + ½)λ (m = 0, ±1, ±2, …) | Dark fringe |
Fringe Spacing
The distance between adjacent bright fringes (fringe spacing) is constant across the central region of the pattern and depends only on wavelength, slit separation, and screen distance. Wider slits (larger d) produce narrower fringes; longer wavelength or greater screen distance produces wider fringes.
Intensity Distribution
The intensity at point y on the screen is given by I = 4I₀ cos²(πdy/(λL)), where I₀ is the intensity from a single slit. The pattern has a cos² envelope modulated by the single-slit diffraction envelope, though for wide slits the modulation is significant.
Double-Slit Formulas
Condition for Bright Fringes
Fringe Position (small angle)
Fringe Spacing
Intensity Pattern
| Symbol | Name | Unit |
|---|---|---|
| d | Slit separation | m (or mm) |
| λ | Wavelength of light | m (or nm) |
| L | Screen distance | m |
| m | Fringe order (integer) | — |
| Δy | Fringe spacing | m (or mm) |
| θ | Angle from centre | rad |
Frequently Asked Questions
Why must the two slits be coherent sources?
Interference requires a stable phase relationship between the two waves. If the phase difference changes randomly (incoherent sources), the bright and dark fringes wash out and the screen shows uniform illumination. Two slits illuminated by a single coherent source share the same phase.
What happens to the fringe pattern if one slit is covered?
Covering one slit removes the interference. The pattern becomes a broad single-slit diffraction envelope, with no sharp fringes — just a central bright maximum that fades toward the edges.
Why does increasing slit separation make fringes closer together?
Fringe spacing Δy = λL/d. When d increases, the denominator grows, so Δy decreases. Wider slit separation means the path difference changes more rapidly with angle, creating more fringes in the same angular range.
Can double-slit interference occur with electrons?
Yes. In the famous Davisson–Germer and electron double-slit experiments, electrons build up exactly the same cosine-squared interference pattern, one electron at a time. This demonstrates wave-particle duality: each electron interferes with itself.
What is the role of wavelength in the experiment?
Longer wavelengths spread out more (Δy = λL/d), giving wider fringe spacing. Shorter wavelengths (UV, X-ray) produce finer fringes. White light produces a white central fringe flanked by coloured fringes because each wavelength has a different Δy.