Calculate diffraction patterns for single slit, double slit, diffraction grating, and circular aperture. Includes angle, fringe spacing, and order tables.
Diffraction is the bending and spreading of waves when they encounter obstacles or pass through apertures. It is a fundamental wave phenomenon that limits the resolution of all optical instruments and creates the characteristic fringe patterns observed in laboratory optics experiments. The four most important diffraction configurations — single slit, double slit, diffraction grating, and circular aperture — each produce distinct, mathematically predictable patterns.
In a single-slit experiment, light passing through a narrow slit produces a central bright maximum flanked by increasingly dim secondary maxima, separated by dark minima at angles where a·sin(θ) = mλ. Young's double-slit experiment creates an interference pattern of equally spaced bright fringes modulated by the single-slit envelope. Diffraction gratings with hundreds or thousands of slits produce extremely sharp spectral lines used in spectroscopy. Circular apertures create the Airy disk pattern that defines the diffraction limit of telescopes, microscopes, and cameras.
This comprehensive calculator handles all four diffraction types, computing angles, fringe positions, order tables, angular dispersion for gratings, and Airy ring data for circular apertures. An interactive intensity profile visualization helps students and researchers understand the pattern structure intuitively.
Use this calculator to move from wavelength and aperture geometry to diffraction angles, fringe spacing, and resolution limits without re-deriving each pattern from scratch. It keeps the same setup visible across slits, gratings, and apertures so you can compare the patterns directly. That is especially helpful when you are checking which opening size or grating spacing best matches the wavelength you are using.
Single Slit minima: a·sin(θ) = mλ. Double Slit maxima: d·sin(θ) = mλ. Grating maxima: d·sin(θ) = mλ. Circular Aperture (Airy): θ = 1.22 λ/D.
Result: 0.315° (5.50 mm on screen)
A single slit of 0.1 mm width illuminated by 550 nm light produces the first minimum at sin(θ) = 550e-6/0.1 = 0.0055, θ = 0.315°, which is 5.50 mm from center on a screen 1 m away.
Most diffraction calculations reduce to a simple relationship between wavelength and aperture spacing. Once wavelength becomes a non-negligible fraction of the opening size, wave spreading is no longer a small correction and the angular structure becomes obvious.
A single slit emphasizes the envelope created by the aperture width, a double slit highlights interference between two paths, and a grating sharpens the allowed directions by repeating the geometry many times. A circular aperture produces the Airy pattern that sets the diffraction limit of imaging systems.
These formulas are useful for optics labs, grating selection, and quick resolution estimates, but real instruments also include finite source size, imperfect coherence, aberrations, and detector limits. Treat the result as the clean theoretical baseline.
Diffraction is the bending of waves around obstacles. Interference is the superposition of waves from multiple sources. In practice, most diffraction patterns involve both effects simultaneously.
For a single slit, the path difference across the slit ranges from 0 to a·sin(θ). The central maximum spans from −λ/a to +λ/a, giving it twice the angular width of higher-order maxima.
With many slits, constructive interference only survives in very narrow angular bands where all paths line up together, so the bright maxima become much sharper than in a simple double-slit pattern. That is why gratings are so useful for spectroscopy.
The Airy disk is the diffraction pattern from a circular aperture — a bright central disk surrounded by concentric dark and bright rings. Its radius defines the resolution limit.
The formulas apply to any electromagnetic wave. Enter the X-ray wavelength (typically 0.01–10 nm) and the crystal lattice spacing in place of slit dimensions.
Longer wavelengths produce wider diffraction patterns because the ratio λ/a (or λ/d) determines the angle. Red light produces wider patterns than blue light for the same aperture.