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Home/Optics & Light/Michelson Interferometer

Michelson Interferometer

The Michelson interferometer is a foundational optical instrument that splits a light beam into two paths and recombines them to produce an interference pattern. This simulator visualizes the core principle of interference by modeling the intensity of light observed at the detector as a function of the optical path difference (Δ) between the two arms. The primary equation governing the output intensity for monochromatic light of wavelength λ is I(Δ) = I₀ cos²(πΔ/λ), where I₀ is the maximum intensity. This pattern arises from the superposition of electromagnetic waves, governed by the principle of linear superposition, and demonstrates constructive interference when Δ is an integer multiple of λ and destructive interference when it is a half-integer multiple. The simulator also introduces the concept of tilt fringes, which are circular or curved interference fringes formed when the mirrors are not perfectly perpendicular, creating a wedge of air between the two virtual images of the source. A crucial extension models the effect of finite spectral bandwidth through the concept of temporal coherence. Here, the sharp cos² interference pattern is multiplied by a coherence envelope function, typically a sinc or Gaussian, which decays over the coherence length. This shows how interference contrast (visibility) diminishes as Δ exceeds the coherence length of the light source. Key simplifications include treating the light source as a perfect point source or an extended source with perfect flatness, ignoring polarization effects, and modeling the beamsplitter as ideal with 50/50 splitting and no absorption. By manipulating mirror positions, tilt, and source wavelength/bandwidth, students directly explore the relationship between path difference, fringe formation, and the limits imposed by the coherence properties of light.

Who it's for: Undergraduate physics and engineering students in courses covering wave optics, interferometry, and optical metrology. It is also valuable for advanced high school students in specialized STEM programs.

Key terms

  • Optical Path Difference
  • Interference Fringes
  • Coherence Length
  • Monochromatic Light
  • Beamsplitter
  • Superposition Principle
  • Fringe Visibility
  • Temporal Coherence

Live graphs

Light

633 nm

Paths

320 nm
0.35 nm/px

Coherence (schematic)

80 µm

Visibility V ≈ exp(−(Δ/L_c)²) with Δ in µm; set L_c ≥ 500 µm for essentially full coherence.

Measured values

Visibility V(Δ)1.0000
I at center0.0003norm.
Δ / λ0.506

How it works

In a Michelson interferometer the beam splitter sends light along two arms; mirrors return the beams and they recombine. The detected intensity varies with the optical path difference Δ as cos²(πΔ/λ) for monochromatic light. A slight tilt between the returning wavefronts produces straight fringes; moving a mirror sweeps Δ and shifts the pattern. A finite coherence length (e.g. from bandwidth) reduces fringe contrast at large Δ.

Key equations

I ∝ V cos²(π Δ / λ)
V(Δ) ≈ exp(−(Δ / L_c)²) (Gaussian envelope, schematic)

Frequently asked questions

Why do the fringes sometimes appear as concentric circles?
Circular fringes, or 'fringes of equal inclination,' appear when there is a slight tilt between the mirrors. This creates a virtual air wedge, and light rays entering at different angles experience different path differences. Points of equal path difference lie on circles centered on the optical axis, producing the characteristic bullseye pattern.
What does the coherence length represent, and why does the fringe contrast fade?
Coherence length is the maximum optical path difference over which light waves remain capable of producing clear interference. Real light sources are not perfectly monochromatic; they contain a range of wavelengths. Each wavelength produces its own interference pattern, and these patterns shift relative to each other as the path difference increases. Beyond the coherence length, they smear out, reducing the overall contrast (visibility) to zero.
How is this interferometer used in real-world applications?
The Michelson interferometer is a versatile tool. It was famously used in the Michelson-Morley experiment to test for the luminiferous aether. Today, its principles are used in Fourier-transform infrared (FTIR) spectroscopy to analyze material composition, in gravitational wave detectors (like LIGO) to measure infinitesimal length changes, and in optical coherence tomography (OCT) for medical imaging of tissues.
Does the simulator's equation I(Δ) = I₀ cos²(πΔ/λ) always hold true?
This specific form assumes ideal conditions: a perfectly monochromatic point source, a 50/50 lossless beamsplitter, and equal intensity in both interfering beams. In practice, factors like source size, polarization, beamsplitter efficiency, and detector response modify the exact intensity function. The simulator's core model isolates the fundamental wave interference effect from these practical complexities.