Michelson Interferometer Explained Simply with Easy Examples

The Michelson interferometer is a precision instrument that splits a beam of light into two parts, sends them along perpendicular arms to mirrors and recombines them to form interference fringes. A tiny movement of one mirror by half a wavelength changes the fringe pattern noticeably, so extremely small distances can be measured.

This instrument matters because it produced one of the most famous results in physics: the Michelson-Morley experiment that showed no ether wind and supported relativity. Today it is used in length standards, spectroscopy and the giant LIGO detectors that observed gravitational waves.

Key Concepts

A beam splitter is a half-silvered plate that reflects half and transmits half of the light. Mirrors M1 and M2 are plane and perpendicular. Their virtual images produce an effective air film whose thickness difference gives circular fringes when arms are equalised. Moving M1 by distance x changes path difference by 2x. Each fringe shift corresponds to lambda divided by 2 movement.

• Division of amplitude creates coherence.
• Circular fringes form with extended source and equal inclination.
• Compensating plate equalises glass path in both arms.

Formulas

If N fringes shift when mirror moves by delta L, then delta L equals N lambda divided by 2. So lambda equals 2 delta L divided by N. Path difference equals 2 times difference in arm lengths for normal round trip. Units: delta L in metres, lambda in metres. Assumptions: monochromatic light, mirror movement slow and vibration free. Limit: coherence length restricts maximum arm difference.

Worked Example

When mirror M1 is moved by 0.15 mm, 500 fringes cross the centre. Find wavelength of light.

delta L equals 0.15 mm equals 0.15 times 10 to power minus 3 m equals 1.5 times 10 to power minus 4 m.

lambda equals 2 delta L divided by N equals 2 multiplied by 1.5 times 10 to power minus 4 divided by 500.

Numerator equals 3.0 times 10 to power minus 4. Divide by 500 gives 6.0 times 10 to power minus 7 m equals 600 nm. The light is orange-red in colour.

Common Misconceptions

• Moving mirror by one wavelength shifts one fringe: Wrong. Light makes a round trip, so movement lambda divided by 2 gives path change lambda and one fringe shift.
• Interferometer measures absolute distance directly without counting: Wrong. It measures change in distance by counting fringes relative to a starting position.
• Any source will give fringes for large arm difference: Wrong. Path difference must lie within coherence length; white light needs near-zero difference.

Real-World Applications

Michelson interferometers calibrate gauges, measure refractive indices of gases and determine spectral line wavelengths in Fourier transform spectroscopy. LIGO uses kilometre-scale Michelson interferometers with Fabry-Perot arms to detect length changes smaller than a proton diameter due to gravitational waves. Optical coherence instruments test lens surfaces and flatness to fractions of a wavelength.

Michelson interferometer splits amplitude, recombines beams from two perpendicular mirrors and counts fringes. Mirror movement of N lambda divided by 2 shifts N fringes, enabling wavelength and tiny length measurements.