Relativistic Optics & Optical Navigation

Sagnac Effect

Simulate Georges Sagnac's 1913 optical rotation experiment. Counter-propagating laser beams in a rotating ring cavity experience a phase shift $\Delta\Phi = \frac{8\pi A \Omega}{\lambda c}$ proportional to rotation rate $\Omega$, powering modern ring laser gyroscopes (RLG).

Sagnac Phase Shift ΔΦ 0.84 rad

RLG Beat Frequency f_beat 254.8 kHz

Path Difference ΔL 84.5 nm

Cavity Rotation Controls

Rotation Speed Ω 2.5 rad/s

Ring Area A 0.10 m²

Visual Overlay

Show Counter-Propagating Laser Beams

Show Interference Fringe Shift

Show Cavity Mirror Badges

Controls

Sagnac Effect & Ring Laser Gyro Equations

Path Length Difference: ΔL = (4 A Ω) / c
Optical Phase Shift: ΔΦ = (8 π A Ω) / (λ c)
Ring Laser Beat Frequency: f_beat = (4 A Ω) / (λ L) (Independent of c!)

Developer Reference

Core Algorithm & Standalone Script

// Sagnac optical rotation & ring laser gyro solver
const canvas = document.getElementById('canvas');
const ctx = canvas.getContext('2d');
// delta_Phi = (8 * pi * A * Omega) / (lambda * c)