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Single-Slit Diffraction Calculator

Enter slit width, wavelength, order and screen distance to get the fringe.

How it is calculated

The tool locates the dark fringes (minima) of single-slit diffraction. It solves a·sin θ = m·λ for the angle: sin θ = m × λ / a, then θ = arcsin(sin θ). Units matter: the slit width a is in millimetres, the wavelength λ in nanometres, the order m is 1 or more, and the screen distance L is in metres. The distance of that dark fringe from the centre of the pattern is y = L × tan θ, shown in millimetres, with the angle in degrees; both are rounded to two decimals. If m × λ / a is greater than 1, no such minimum exists and no result is given. Order 0 is not accepted because the centre is the bright maximum.

Worked example

A red helium-neon laser (633 nm) shines through a slit 0.1 mm wide onto a screen 1.5 m away. We want the second dark fringe, m = 2. First sin θ = 2 × 633 × 10⁻⁹ / (0.1 × 10⁻³) = 0.01266, so θ = arcsin(0.01266) = 0.73°. Then y = 1.5 m × tan θ = 0.01899 m, which is 18.99 mm from the centre of the pattern, so the second dark band sits about 19 mm from the middle of the bright central band.

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Common mistakes

  • Entering the slit width in micrometres or metres; the field is millimetres, so a 100 µm slit is 0.1, not 100.
  • Giving the wavelength in metres or micrometres; it must be in nanometres (633, not 0.633 or 633e-9).
  • Reading the answer as the position of a bright fringe; the formula gives the dark minima, and the bright secondary maxima lie roughly between them.
  • Entering the screen distance in millimetres or centimetres; it is in metres and the result is multiplied by 1000 to give millimetres.
  • Using a slit narrower than the wavelength (or a high order) and getting nothing; when m·λ is larger than a there is no minimum at all, so the tool returns no result. The tool also does not round a fractional order to a whole number, so keep m an integer.

About this calculator

When light passes through a narrow single slit, it spreads out and produces a pattern of bright and dark fringes on a screen rather than a sharp shadow — a direct demonstration of light's wave nature. The dark fringes (diffraction minima) occur where a sin θ = mλ, with a the slit width, λ the wavelength, θ the angle from the central axis, and m the integer order (1, 2, 3...); the position on the screen follows from θ and the slit-to-screen distance.

Physics students verify this relationship in the classic single-slit lab, while optical engineers and spectroscopists use it to predict how narrow apertures, laser beams, and spectrometer slits will spread light — critical when designing instruments that need to resolve fine spectral or spatial detail.

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Comments (1)

  • Editorial team

    This tool returns the dark fringes, so it suits a laser demonstration where you need to know where to put the pencil marks on the screen. A quick sanity check: a 0.1 mm slit with 500 nm light puts the first dark band at about 0.29 degrees. Make the slit narrower and that angle grows until no minimum exists at all. Which slit width and light source are you working with in your lab?

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