Michelson Interferometer

Worked Example: Full Mirror Displacement

Consider a Michelson interferometer illuminated by light of vacuum wavelength λ = 600 nm. Initially, the path lengths are equal, leading to constructive interference at the detector (intensity I = 1). If we move one mirror by u = 8 eighth-wavelengths, we can calculate the new state.

The intensity at the detector returns to maximum, and the bright port remains bright.

Experiment: Gas Cell Delay

In this experiment, we explore how changing the optical medium affects the interference pattern.

Setup

1. Set the Vacuum wavelength lambda to 400 nm.
2. Set the Mirror displacement eighth-wavelengths u to 1.
3. Insert a gas cell by setting the Cell refractive index n to 1.25.
4. Set the Cell length wavelengths l to 1.
5. Observe the resulting Optical path difference and Normalized intensity in the results panel.

Observations

The mirror displacement alone creates an OPD of 2 · (1 · 400 / 8) = 100 nm. The gas cell has a physical length L = 1 · 400 = 400 nm. Because the light passes through it twice, the additional OPD is 2 · (1.25 - 1) · 400 = 200 nm. The total OPD is 100 + 200 = 300 nm. The signed fringe displacement is 300 / 400 = 0.75 cycles. The normalized intensity is (1 + cos(2π · 0.75)) / 2 = 0.5.

Limitations of the Model

This schematic model assumes perfect coherence, perfectly balanced beam-splitter reflections, and identical compensation in both arms. In a real Michelson interferometer, the light source has a finite coherence length. If the optical path difference exceeds this coherence length, the interference fringes will wash out and the intensity will average to 0.5 regardless of minor displacement.

Additionally, this model assumes perfectly collimated plane waves. Real instruments often use slightly diverging beams, which produce circular fringe patterns (Haidinger fringes) rather than a uniform intensity across the entire detector plane.

References

The following reference was consulted in the development of this interactive model:

• OpenStax University Physics Volume 3: 3.5 The Michelson Interferometer (Compensated arms, double path length, mirror displacement and gas-cell fringe changes)