How this calculation works
An interferometer converts a changing optical path into a count of fringe passages. In a Michelson arm, moving one mirror changes the round-trip path, creating a factor of two between mirror travel and geometric arm-path change. This page converts a counted number of fringes into displacement magnitude for a uniform unchanged arm medium. It also reports the optical path change and displacement corresponding to a single fringe.
Mirror displacement = fringe count × vacuum wavelength/(2n)A worked example
At 632.8 nm vacuum wavelength in index-one medium, one fringe corresponds to 316.4 nm of mirror travel. One hundred fringe passages therefore correspond to 31.64 µm. The associated round-trip optical path change is 63.28 µm. Doubling the uniform refractive index halves the inferred physical mirror travel for the same count and vacuum wavelength.
Good to know
The index is constant during the measurement and the mirror displacement is collinear with the arm. Air-index changes can themselves shift fringes and cannot be separated from motion by this count-only formula. Vibration, wavelength drift, fringe-count errors and instrument calibration are not modeled. The displayed conversion precision is not an experimental uncertainty statement.
Reference: OpenStax — Michelson interferometer (opens in a new tab) ↗
What this calculation answers
An interferometer converts a changing optical path into a count of fringe passages. In a Michelson arm, moving one mirror changes the round-trip path, creating a factor of two between mirror travel and geometric arm-path change.
This page converts a counted number of fringes into displacement magnitude for a uniform unchanged arm medium. It also reports the optical path change and displacement corresponding to a single fringe.
The Plane parallel Fabry Perot FSR finesse and linewidth calculator uses repeated reflections to create resonances. Michelson mirror displacement instead changes the round-trip path difference between arms.
Use the right input conventions
Use vacuum wavelength in nanometres and the refractive index along the moving arm. The fringe count may include a measured fractional fringe if the instrument supports it. Enter a nonnegative magnitude rather than a signed direction.
The mirror is assumed to translate along the beam at normal incidence. Tilting a mirror, moving both arms or changing the refractive index requires a different path relationship and should not be represented as the same motion.
Interpret the result
A full fringe passage represents one wavelength of optical path difference. The moving mirror travels half that geometric amount in a medium of index one because the beam covers the changed arm length twice.
Fringe count alone does not reveal direction. A direction-sensitive measurement needs additional phase or quadrature information; this page therefore avoids attaching a positive or negative travel sign to the count.
Work through the example
At 632.8 nm vacuum wavelength in index-one medium, one fringe corresponds to 316.4 nm of mirror travel. One hundred fringe passages therefore correspond to 31.64 µm.
The associated round-trip optical path change is 63.28 µm. Doubling the uniform refractive index halves the inferred physical mirror travel for the same count and vacuum wavelength.
Where the model stops
The index is constant during the measurement and the mirror displacement is collinear with the arm. Air-index changes can themselves shift fringes and cannot be separated from motion by this count-only formula.
Vibration, wavelength drift, fringe-count errors and instrument calibration are not modeled. The displayed conversion precision is not an experimental uncertainty statement.
A few questions, answered
Where does the factor two come from?
The beam travels to the mirror and back, so a mirror displacement changes the geometric arm path twice.
What changes in the comparison?
Change the uniform arm medium while holding fringe count and vacuum wavelength fixed.