Single-Slit Diffraction Calculator
Enter wavelength, slit width and screen distance to compute the single-slit diffraction pattern: dark fringes at a·sinθ=mλ (m=1,2,3…), central maximum width 2Lλ/a. λ=550 nm, a=0.1 mm, L=1 m → central width 11 mm.
Input Data
Results
At a glance:Single-slit diffraction: when a plane wave of wavelength λ passes a slit of width a, Huygens' principle makes every point in the slit act as a secondary source, and their interference on a distant screen produces a diffraction pattern — a bright central maximum with dark and bright fringes on both sides, described by I(θ)=I₀·sinc²(πa·sinθ/λ). Dark fringes (intensity zero) satisfy a·sinθ=mλ (m=±1,±2,±3,…); the central maximum is the region between the two first minima (m=±1), and its width is 2Lλ/a (small-angle, L screen distance). Term by term: λ is the wavelength; a the slit width — the wider the slit, the more the light goes straight and the narrower the pattern; L the screen distance. Physical meaning: diffraction is the wave nature of light bending at an edge — the narrower the slit (closer to λ), the more it spreads. The central maximum carries most of the light (about 90%), and its width sets the resolution limit (related to the Rayleigh criterion). History: Grimaldi first observed diffraction in 1665; Fresnel's 1818 wave theory explained it rigorously. Classic example: λ=550 nm, a=0.1 mm=1e-4 m, L=1 m → first dark angle sinθ=λ/a=5.5e-7/1e-4=0.0055, θ≈0.315°, distance y=L·tanθ≈0.0055 m=5.5 mm; central width 2y=11 mm. Applications: (1) optical resolution and the Airy disk; (2) diffraction gratings (many slits); (3) spectroscopy; (4) laser beam shaping; (5) X-ray diffraction (crystal lattice as the 'slit').
Formula
Dark fringes: a·sinθ = m·λ (m=1,2,3,…)
First dark angle: sinθ₁ = λ/a
Central width: W = 2L·λ/a
Intensity: I(θ) = I₀·sinc²(πa·sinθ/λ)
Small angle: θ ≈ sinθ ≈ tanθ = y/L
$$a\sin\theta = m\lambda, \quad W = \frac{2L\lambda}{a}, \quad I(\theta) = I_0\operatorname{sinc}^2\!\left(\frac{\pi a\sin\theta}{\lambda}\right)$$How to Use
- Enter wavelength λ (nm; visible ~550).
- Enter slit width a (mm; 0.05–0.5).
- Enter screen distance L (m).
- The tool gives the central width, first/second dark angles and distances.
Case Studies
Slit width and pattern size
λ=550 nm, L=1 m: a=0.1 mm → central width 11 mm; a=0.05 mm → 22 mm (narrower slit spreads more).
a=0.5 mm → central width 2.2 mm (wider slit, narrower pattern).
The pattern width scales inversely with slit width — diffraction broadens as the slit narrows.
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.