Single-Slit Diffraction Simulator
Explore Fraunhofer diffraction through a single slit. Adjust slit width and wavelength to see how the diffraction pattern changes.
Single-Slit Diffraction
When light passes through a single narrow slit of width a, it spreads out (diffracts) and produces a characteristic pattern on a screen: a bright central maximum flanked by weaker secondary maxima separated by dark minima. This is Fraunhofer (far-field) diffraction.
Dark Fringes (Minima)
The minima occur where the contributions from the top and bottom halves of the slit exactly cancel. The condition is a sinθ = mλ for integers m ≠ 0. For small angles, the position of the m-th minimum on the screen is y_m = mλL/a.
Central Maximum Width
The central bright maximum spans from the first minimum on one side to the first minimum on the other. Its half-width is θ ≈ λ/a. A narrower slit (smaller a) diffracts more, spreading the central peak wider. A wider slit gives a narrower, more intense central peak.
Intensity Formula
The intensity at position y on the screen follows the sinc-squared function: I = I₀(sinα/α)² where α = πay/(λL). The secondary maxima have intensities roughly 4.7%, 1.6%, and 0.8% of the central maximum.
| Order m | Position y_m | Intensity (relative) |
|---|---|---|
| 0 (central max) | 0 | 100% |
| 1 (1st minimum) | λL/a | 0% |
| 1.5 (1st secondary max) | ≈1.43λL/a | ≈4.7% |
| 2 (2nd minimum) | 2λL/a | 0% |
| 2.5 (2nd secondary max) | ≈2.46λL/a | ≈1.6% |
Single-Slit Diffraction Formulas
Intensity Distribution (Fraunhofer)
Minima Condition
Minimum Position on Screen
Central Maximum Half-Width
| Symbol | Name | Unit |
|---|---|---|
| a | Slit width | m (or mm) |
| λ | Wavelength | m (or nm) |
| L | Screen distance | m |
| m | Diffraction order (nonzero integer) | — |
| α | Phase parameter πa sinθ/λ | rad |
| I₀ | Central intensity | W/m² |
Frequently Asked Questions
Why does a narrower slit produce a wider diffraction pattern?
This is a consequence of the uncertainty principle and Fourier theory. The slit constrains the transverse position of photons (Δx = a). A smaller Δx requires a larger spread in transverse momentum (Δp_y), corresponding to a wider angular spread. Mathematically, the pattern width scales as λ/a.
What is the difference between single-slit diffraction and double-slit interference?
Double-slit interference produces equally-spaced fringes of roughly equal brightness (cos² pattern). Single-slit diffraction produces a broad central peak with weaker, unequally-spaced secondary maxima (sinc² pattern). In practice, double-slit patterns are modulated by the single-slit envelope of each slit.
Why is there no minimum at m = 0?
At m = 0 (the centre), all path differences are zero — every wavelet from the slit arrives in phase. The waves add completely constructively, giving the bright central maximum. Minima only occur for m ≠ 0 where path differences produce cancellation.
How does wavelength affect the pattern?
Longer wavelengths diffract more, so the pattern spreads further: Δy = λL/a. Red light (700 nm) produces a wider central maximum than blue light (450 nm) with the same slit. White light produces coloured fringes outside the white central peak.
What is Fraunhofer diffraction?
Fraunhofer (far-field) diffraction applies when the screen is far enough from the slit that the wavefronts arriving at any screen point are essentially plane waves. The condition is L ≫ a²/λ. For visible light and mm-scale slits this is typically satisfied at distances > 1 m.