# Double-Slit Interference Calculator Δy = λL/d with first-order angle and the first four fringes each side — the ruler-measurable student bench classic. > Canonical page: https://elysiatools.com/en/tools/double-slit-interference - **Category:** Science & Education - **Keywords:** double slit, youngs experiment, interference fringes, fringe spacing, path difference, optics ## Overview The Double-Slit Interference Calculator computes interference fringe patterns produced in Young's classic double-slit experiment. By entering the light wavelength, slit separation, and screen distance, it determines the exact fringe spacing (Δy = λL/d), the first-order angular deflection, and the symmetrical positions of the first four bright maxima. ## Inputs - **Wavelength λ (nm)** (number): e.g. 550 - **Slit separation d (µm)** (number): e.g. 200 - **Screen distance L (m)** (number): e.g. 2 ## When to use - Preparing or validating undergraduate physics and optics laboratory experiments. - Designing optical benches to ensure interference fringes are wide enough to measure with a standard ruler or sensor. - Verifying theoretical homework problems involving Young's double-slit interference and fringe spacing equations. ## How it works - Specify the wavelength of the light source in nanometers (λ). - Enter the physical distance between the two slits in micrometers (d). - Input the distance from the slit aperture to the viewing screen in meters (L). - Review calculated values including fringe spacing (Δy), first-order diffraction angle (θ₁), and the linear offsets for maxima m = ±1 through ±4. ## Use cases - Physics educators calibrating bench demonstrations so students can measure fringes with standard millimeter scales. - Optics students cross-checking manual lab measurements of sodium lamp or laser interference patterns. - Lab technicians testing double-slit slide dimensions before conducting optical wavelength verifications. ## Frequently asked questions ### What equation is used to calculate fringe spacing? Fringe spacing is calculated using the small-angle approximation formula Δy = λL/d, where λ is wavelength, L is screen distance, and d is slit separation. ### How is the first-order maximum angle determined? The first-order angular position is computed using the exact grating condition θ₁ = arcsin(λ/d). ### What units must be used for inputs? Wavelength is entered in nanometers (nm), slit separation in micrometers (µm), and screen distance in meters (m). ### How many fringe positions are calculated? The tool outputs the symmetrical positions for the first four bright maxima (orders m = ±1, ±2, ±3, and ±4) relative to the central peak. ### Why are fringe spacing measurements useful in labs? Measuring visible fringe spacing with known slit geometry and screen distance allows direct experimental determination of the light's wavelength. ## 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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