Single-Slit Diffraction Calculator
Calculate the positions of diffraction minima from a single slit.
Find angles and positions on a screen for the first 3 dark fringes.
When light passes through a narrow slit, it diffracts (spreads out). Dark fringes (minima) appear at angles where waves from different parts of the slit cancel each other:
Minima: sin(θ) = mλ/a where m = ±1, ±2, ±3…
Position on screen: y_m = D × tan(θ_m) ≈ D × mλ/a (small angle approximation)
Where:
- θ = Angle to the minimum
- m = Order of minimum (±1, ±2, …)
- λ = Wavelength of light (m)
- a = Slit width (m)
- D = Distance from slit to screen (m)
- y = Position of minimum on the screen (m)
Central maximum width: The central bright fringe spans from m = −1 to m = +1, so its half-width is: Δy = Dλ/a
A narrower slit produces wider diffraction → more spreading.
Why single-slit diffraction matters:
- It sets the diffraction limit for optical instruments — the smallest feature a lens can resolve
- Telescope resolving power is limited by the aperture diameter (which acts like a single slit)
- Radio telescopes need huge diameters to achieve good angular resolution because radio wavelengths are much longer than visible light
- The Airy disk (circular aperture diffraction) is described by the same physics: θ_min = 1.22λ/D
Color and diffraction: Shorter wavelengths (violet, 400 nm) diffract less than longer wavelengths (red, 700 nm). This causes chromatic dispersion in diffraction gratings and explains why prisms separate colors.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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