Why does rotation break the symmetry between the two directions?

In a rotating frame the effective transit times for clockwise vs counter-clockwise beams around the loop differ slightly: one beam travels a bit farther in space-time than the other before they recombine. That tiny time difference becomes a measurable phase shift at the detector.

How do fiber gyros get large sensitivity from a small coil?

Many fiber turns multiply the effective optical area: N loops contribute roughly N times the single-loop phase shift, so a compact coil can rival a large free-space loop for the same Ω.

Is the formula on the page exact for any shape?

The compact scalar form quoted assumes a planar loop and the usual textbook approximations. Real devices account for non-planar paths, source spectrum, and noise; the simulator emphasizes scaling (Δφ ∝ Ω A / λ) rather than engineering-grade calibration.

Does the Sagnac effect depend on the medium’s refractive index?

In the standard derivation for light guided in a medium, n enters the phase shift because the optical path length changes with the slowing of the wave. The page exposes n as a slider to remind that fiber cores are not vacuum.

Sagnac (Ring) Interferometer

Δφ ∝ Ω·A/λ for counter-propagating beams in a rotating loop — optical gyro idea.

About this model

A Sagnac interferometer sends two light beams around the same closed path in opposite directions. When the platform rotates, the effective path lengths differ slightly, producing a phase shift proportional to the enclosed area A, the angular velocity Ω, the refractive index n of the medium, and inversely to wavelength λ (Δφ = 8π Ω A n / (λ c) for the textbook planar-loop scalar form used on this page). Fiber-optic gyroscopes wrap many turns to multiply the effective area. The visualization is schematic: an ellipse stands in for the loop and a slow rotation hints at the phase bias. The model is non-relativistic and does not treat general relativity or detailed shot-noise limits; it is meant to connect rotation, area, and fringe shift qualitatively and in order of magnitude.

Who it's for: Students in optics, inertial navigation, and rotational sensing who need a clear link between geometry, rotation rate, and interferometric phase.

Key terms

Sagnac effect
Ring interferometer
Optical gyro
Enclosed area
Angular velocity
Phase shift
Fiber gyro
Counter-propagating beams

How it works

A ring interferometer compares counter-propagating beams; rotation breaks symmetry and produces a phase shift proportional to angular velocity — the optical gyro principle.

Frequently asked questions

Why does rotation break the symmetry between the two directions?: In a rotating frame the effective transit times for clockwise vs counter-clockwise beams around the loop differ slightly: one beam travels a bit farther in space-time than the other before they recombine. That tiny time difference becomes a measurable phase shift at the detector.
How do fiber gyros get large sensitivity from a small coil?: Many fiber turns multiply the effective optical area: N loops contribute roughly N times the single-loop phase shift, so a compact coil can rival a large free-space loop for the same Ω.
Is the formula on the page exact for any shape?: The compact scalar form quoted assumes a planar loop and the usual textbook approximations. Real devices account for non-planar paths, source spectrum, and noise; the simulator emphasizes scaling (Δφ ∝ Ω A / λ) rather than engineering-grade calibration.
Does the Sagnac effect depend on the medium’s refractive index?: In the standard derivation for light guided in a medium, n enters the phase shift because the optical path length changes with the slowing of the wave. The page exposes n as a slider to remind that fiber cores are not vacuum.

Other simulators in this category — or see all 50.

View category →

NewSchool

Brewster Angle

Launch Simulator

tan θ_B = n₂/n₁; R_p→0; θᵢ+θₜ=90°; Fresnel R_s, R_p vs θᵢ.

NewSchool

Fermat's Principle

Launch Simulator

OPL = n₁AP+n₂PB vs hit point; minimum = Snell path.

NewSchool

Chromatic Aberration

Launch Simulator

Cauchy n(λ); thin-lens f(λ); paraxial rays R/G/B.

School

Diffraction

Launch Simulator

Single and double slit with interference patterns.

Kids

Color Mixing

Launch Simulator

Additive (RGB) and subtractive (CMY) interactive color mixing.

NewSchool

Polarization (Malus)

Launch Simulator

Two polarizers. Rotate θ, see I = I₁ cos²θ and extinction.

Sagnac (Ring) Interferometer

About this model

How it works

Frequently asked questions

More from Optics & Light

Brewster Angle

Fermat's Principle

Chromatic Aberration

Diffraction

Color Mixing

Polarization (Malus)

Sagnac (Ring) Interferometer

About this model

How it works

Frequently asked questions