# Single-Slit Diffraction Calculator a·sinθ = mλ minima with the double-wide central maximum and optional screen positions. > Canonical page: https://elysiatools.com/en/tools/single-slit-diffraction - **Category:** Science & Education - **Keywords:** single slit diffraction, diffraction minima, central maximum, slit width, airy pattern, optics ## Overview The Single-Slit Diffraction Calculator computes the angular and linear positions of diffraction minima using the single-slit equation a·sinθ = mλ. By entering the slit width, light wavelength, fringe order, and optional screen distance, you can instantly determine diffraction angles, the double-wide central maximum spread, and exact fringe coordinates on a screen. ## Inputs - **Slit width a (µm)** (number): e.g. 100 - **Wavelength λ (nm)** (number): e.g. 550 - **Minimum order m** (number): e.g. 1 - **Screen distance L (m, optional)** (number): e.g. 2 ## When to use - Analyzing optics lab experiments to verify single-slit diffraction minima and central fringe widths. - Designing optical apertures and laser setups where beam spreading and diffraction limits must be quantified. - Solving physics problem sets involving Fraunhofer diffraction angles and fringe displacement on observation screens. ## How it works - Specify the slit aperture width a in micrometers (µm) and the incident light wavelength λ in nanometers (nm). - Set the target diffraction minimum order m (e.g., 1, 2, 3) and optionally enter the distance to the observation screen L in meters. - The tool applies the condition a·sinθ = mλ to compute sinθ, exact diffraction angles θ, the total central maximum angular width 2θ₁, and linear fringe positions y = L·tanθ. ## Use cases - Physics undergraduate students verifying diffraction lab measurements against theoretical predictions. - Optical engineers determining spatial beam spread through narrow rectangular slits or apertures. - Educators generating theoretical reference values and fringe spacing charts for lecture demonstrations. ## Frequently asked questions ### What equation does this calculator use for single-slit minima? It uses the Fraunhofer diffraction condition a·sinθ = mλ, where a is the slit width, θ is the angle to the m-th dark minimum, and λ is the light wavelength. ### Why is the central maximum twice as wide as secondary maxima? The central bright peak spans from the m = -1 minimum to the m = +1 minimum, giving it an angular width of 2θ₁, which is double the angular spacing between subsequent adjacent minima. ### What units should be entered for slit width and wavelength? Enter the slit width in micrometers (µm) and the light wavelength in nanometers (nm). Distance to the screen is specified in meters (m). ### Is the small-angle approximation used to calculate screen positions? The calculator determines the exact angle via arcsin(mλ/a) and computes linear position using y = L·tanθ rather than relying strictly on the small-angle approximation y ≈ L·mλ/a. ### What happens to the diffraction pattern if the slit width is decreased? Decreasing slit width increases diffraction spreading, causing the angular spacing of minima and the central maximum width to widen proportionally. ## Related tools - [Bohr Model Calculator](https://elysiatools.com/en/tools/bohr-model-calculator): Hydrogen level n: r_n = n²a₀, E_n = −13.605693/n² eV, v_n = αc/n, orbital period, plus optional transition energies with named series lines. - [de Broglie Wavelength Calculator](https://elysiatools.com/en/tools/de-broglie-wavelength): Matter-wave λ = h/p via particle & speed (γmv optional), direct momentum, or electron voltage (relativistic + h/√(2mE) comparison). 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