What is the single-slit diffraction minima formula?

Dark fringes (minima) occur where a·sin(θ) = m·λ, with m = ±1, ±2, ±3, … Here a is the slit width, λ is the wavelength, and θ is the angle from the center. The screen position is y = L·tan(θ).

Why is there no m = 0 minimum?

The m = 0 direction is the central maximum — the brightest point directly ahead of the slit. Minima start at m = ±1 on either side.

What is the central maximum width?

The central maximum spans from the first minimum on one side to the first minimum on the other side. Its half-width is y₁ = L·tan(arcsin(λ/a)), so the full width is 2y₁.

How does slit width affect diffraction?

A narrower slit (smaller a) spreads the pattern wider — the first minimum moves farther from the center. A wider slit concentrates light closer to the axis. When a >> λ, diffraction becomes negligible.

What approximation does this calculator use?

For small angles (θ < ~15°), sin(θ) ≈ tan(θ) ≈ θ, so y ≈ mλL/a. This tool uses the exact formula (arcsin + tan) for accuracy across all angles, including large-angle cases.

Does this apply to sound or water waves too?

Yes — the formula a·sin(θ) = mλ applies to any wave diffraction through a single aperture. Just substitute the correct wavelength and slit/aperture width for your wave type.

Single Slit Diffraction Calculator

Enter slit width, light wavelength, and screen distance to compute diffraction minima angles, positions, and the central maximum width.

Slit Parameters

Slit Width (a) μm

Typical lab slit: 10–500 μm

Wavelength (λ) nm

Visible light: 380–700 nm

Screen Distance (L) m

Show minima ±5 orders

Diffraction Minima

Dark fringe positions where a·sin(θ) = m·λ

Order (m)	Angle θ (°)	sin(θ)	Position y (mm)

Enter parameters above and click Calculate.

Summary

Enter slit width, light wavelength, and screen distance to compute diffraction minima angles, positions, and the central maximum width.

How it works

Enter the slit width (a) in micrometers — the physical opening the light passes through.
Enter the light wavelength (λ) in nanometers (visible range: 380–700 nm).
Enter the screen distance (L) in meters — how far the observation screen is from the slit.
Select how many minima orders to display using the slider (up to ±10).
Click Calculate to see each minimum's angle, screen position, and central maximum width.

Use cases

Solve single-slit diffraction problems in university optics courses.
Verify lab measurements of dark fringe positions against theory.
Explore how slit width affects the spread of the diffraction pattern.
Compare patterns produced by different wavelengths of light.
Design optical setups where diffraction spread must be controlled.
Understand the resolution limit imposed by aperture size in imaging systems.

Frequently Asked Questions

Last updated: 2026-09-22 · Reviewed by Nham Vu