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Triple-Slit Interference

Beyond Double-Slit: Three-Way Interference​

Adding a third slit creates a richer interference pattern with subsidiary maxima between the principal peaks. This demonstrates how multiple coherent sources combine to create complex wave patterns.

The Physics​

With three slits, the interference pattern becomes more structured:

  • Principal maxima: Occur where all three waves constructively interfere
  • Subsidiary maxima: Smaller peaks between principals where two waves reinforce
  • Minima: More complex pattern of destructive interference

Intensity Pattern​

For three equally-spaced slits, the intensity distribution follows: I(θ) = I₀ (sin(3φ/2)/sin(φ/2))²

Where φ = 2πd sin(θ)/λ is the phase difference between adjacent slits.

Pattern Characteristics​

Triple-Slit vs Double-Slit Pattern:

Double-Slit:
████    ████    ████    ████    ████    ████
 (simple, evenly-spaced peaks)

Triple-Slit:
██████   ██   ██████   ██   ██████   ██   ██████
 (main)  (sub) (main)  (sub) (main)  (sub) (main)

 └─────────────────────────────────────────────┘
         More structure, sharper peaks

Key differences:

  1. Sharper principal maxima - peaks are narrower
  2. Subsidiary maxima - small peaks between main peaks
  3. Better resolution - useful for spectroscopy

The Simulation​

Grid: 512 × 512 points
Slit width: 5.0 units
Slit separation: 25.0 units
Number of slits: 3
Initial momentum: kx = 3.0

Animation​

The video above shows the wavepacket evolution in real-time, revealing the complex three-way interference pattern.

Run It Yourself​

claude -p "Simulate triple-slit interference: Create a barrier at x=85 with three slits \
  (separation=20, height=10), use an elliptical wavepacket with width=[15,50] \
  (vertical long axis), show potential overlay, add sensor line at x=220, \
  and save to /tmp/triple_slit.gif" --allowedTools "mcp__quantum-mcp__*"

From Slits to Gratings​

The triple-slit experiment is a step toward the diffraction grating:

N SlitsPattern Characteristics
1Broad central maximum, weak side lobes
2Regular interference fringes
3Sharper peaks with 1 subsidiary maximum
NVery sharp peaks with N-2 subsidiary maxima
∞Delta-function peaks (perfect diffraction grating)

The Grating Equation​

For N slits, principal maxima occur at: d sin(θ) = mλ (m = 0, ±1, ±2, ...)

And the peak width decreases as 1/N, making diffraction gratings excellent for spectroscopy.

Applications​

  • Spectroscopy: Gratings with thousands of lines separate wavelengths
  • X-ray crystallography: Crystal lattices act as 3D gratings
  • Holography: Interference patterns encode 3D information
  • Quantum computing: Multi-path interference is fundamental

Side-by-Side Comparison​

Triple-Slit Potential