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.