How this calculation works
A plane-parallel Fabry–Perot cavity transmits a repeating set of resonant frequencies. Mirror spacing sets their separation, while mirror reflectivity controls the width of each ideal transmission peak. This page reports free spectral range, intensity full width at half maximum and reflectivity-limited finesse. It uses the exact Airy half-maximum expression rather than assuming the high-reflectivity approximation is always exact.
FSR = c/(2nL); FWHM = 2 FSR/π × asin[(1−R)/(2√R)]; finesse = FSR/FWHMA worked example
A 100 mm air cavity has free spectral range 1.49896229 GHz and round-trip time about 0.667128 ns. At mirror intensity reflectivity 0.9, the high-reflectivity approximate finesse is about 29.8038. The exact Airy width gives a slightly different finesse near 29.79. The page reports both so that the approximation can be compared rather than silently used outside its most accurate range.
Good to know
Mirrors are identical and the cavity has no absorption or scattering loss. Alignment, surface defects, finite beam divergence and scan calibration can broaden real resonances. The result does not predict a complete laser linewidth, photon lifetime with arbitrary losses or a confocal spectrum. It is an ideal plane-parallel intensity-transfer calculation.
Reference: MIT — optics and interferometry (opens in a new tab) ↗
What this calculation answers
A plane-parallel Fabry–Perot cavity transmits a repeating set of resonant frequencies. Mirror spacing sets their separation, while mirror reflectivity controls the width of each ideal transmission peak.
This page reports free spectral range, intensity full width at half maximum and reflectivity-limited finesse. It uses the exact Airy half-maximum expression rather than assuming the high-reflectivity approximation is always exact.
The Michelson fringe count and mirror displacement calculator relates a counted phase cycle to path change. Cavity peak spacing additionally uses the optical round-trip time and a specified plane-parallel geometry.
Use the right input conventions
Length is mirror separation in millimetres. Reflectivity is the intensity fraction for each of two identical lossless mirrors, not an electric-field amplitude coefficient. The supported range begins at 0.5 so the stated peak-width interpretation remains well defined.
Enter a frequency-independent real index. The cavity is plane parallel: do not substitute a confocal instrument’s c/(4L) transverse-mode spacing for the c/(2nL) longitudinal spacing used here.
Interpret the result
Finesse is the ratio of adjacent-peak spacing to linewidth. A narrower ideal peak increases finesse without changing the spacing when length and index stay fixed. Neither result is automatically the measured finesse of an aligned instrument.
The round-trip optical time is the reciprocal of the free spectral range in this nondispersive model. In a dispersive medium, group index affects frequency spacing and requires a different treatment.
Work through the example
A 100 mm air cavity has free spectral range 1.49896229 GHz and round-trip time about 0.667128 ns. At mirror intensity reflectivity 0.9, the high-reflectivity approximate finesse is about 29.8038.
The exact Airy width gives a slightly different finesse near 29.79. The page reports both so that the approximation can be compared rather than silently used outside its most accurate range.
Where the model stops
Mirrors are identical and the cavity has no absorption or scattering loss. Alignment, surface defects, finite beam divergence and scan calibration can broaden real resonances.
The result does not predict a complete laser linewidth, photon lifetime with arbitrary losses or a confocal spectrum. It is an ideal plane-parallel intensity-transfer calculation.
A few questions, answered
Is reflectivity an amplitude or power value here?
It is intensity reflectivity, the fraction of incident power reflected by each mirror.
What changes in the comparison?
Increase mirror reflectivity and compare linewidth at unchanged free spectral range.