Michelson interferometer mirror displacement

What Michelson fringe counting measures and what the response contains

This calculator returns the normalized fringe_count and wavelength you supplied, the computed mirror_displacement rounded to the requested precision, the optical_path_change Nλ (equal to 2ΔL), the precision used, a short formula string, a concrete equation with substituted numbers, the method tag michelson_mirror_displacement, and a one-line message. There is no ray-trace path and no random sampling of intensities: the engine either builds exact floating-point ΔL inside the supported magnitude range or rejects the input with invalid_input. Rejected cases include missing N or λ, non-finite values, magnitudes above the documented ceiling, a negative fringe count, and any wavelength that is zero or non-positive, because the displacement formula is undefined when λ is not a positive length.

How fringe count and wavelength are read and how ΔL stays reproducible

Optional leading plus signs and scientific notation on numeric strings are allowed when they parse as finite decimals; embedded spaces, hex prefixes, and non-numeric tokens are rejected with a clear message so a bad cell does not become a wrong displacement. Fringe count must be non-negative: a negative N is rejected because “number of fringes counted” is not a signed counter in this contract (use a signed convention in your own post-processing if you track direction of motion separately). The engine does not convert nanometres for you: enter λ in the same unit you want for ΔL—metres yield metres, micrometres yield micrometres. The preferred fields are fringe_count for N and wavelength for λ, but aliases N, n, fringes, fringeCount, and m for the fringe tally, and lambda, the Greek letter λ, wl, and wavelength_m for the wavelength, are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. Wavelength must be strictly positive; zero and negative values fail with invalid_input because division of path change by two still requires a meaningful positive λ. An optional precision field, with aliases decimals and dp, chooses how many decimal places to expose for the numeric fields, defaulting to twelve and capped at fifteen so JSON goldens stay stable. Computation multiplies N by λ, halves the product for mirror_displacement, and also reports optical_path_change as N times λ so you can cross-check the round-trip identity 2ΔL equals Nλ without re-deriving it. Pair the free browser run on this page with the priced API when you need the identical mathematical result inside an automated pipeline.

Where Michelson displacement checks fit in labs, study, and software

On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split—free interactive exploration and a priced, identical API—matches the rest of the KIT tier-A catalog and lets you move from a lab bench demo to an automated pipeline without changing the mathematical result. Pair it with other optics endpoints when you are building a small lab of free, deterministic helpers for interference, diffraction, and introductory wave physics.