Haidinger-Michelson rings in white light

TL;DR

This paper explains how modifying a Michelson interferometer with a glass slide allows observation of Haidinger rings in white light and enables spectral analysis of the glass's refractive index across the visible spectrum.

Contribution

It introduces a modified Michelson interferometer setup that overcomes coherence limitations, enabling the observation of Haidinger rings with white light and spectral refractive index measurements.

Findings

Successful observation of Haidinger rings in white light using the modified setup.

Determination of the glass slide's refractive index spectrum across visible wavelengths.

Identification of the oscillator wavelength responsible for dispersion via Sellmeier's law fit.

Abstract

We use coherence theory to explain why it is necessary to modify the conventional setup of a Michelson interferometer to obtain Haidinger rings with an extended source of white light. The modification consists of introducing a glass slide into one of the two arms of the interferometer. This insertion circumvents the drastic restriction imposed by the low temporal coherence of white light, which prevents the observation of interference rings with the conventional setup. In order to understand this restriction, we developed and implemented a criterion for observing interference fringes. The modified setup also makes it possible to perform a spectral interferometry experiment to analyze the output of the interferometer and determine the refractive index of the glass slide over the whole visible spectrum. The fit of measured data using Sellmeier's law gives the extrapolated value of the refractive index to the IR $n_\mathrm{IR}=1.5307\pm0.0003$ and the value of the characteristic wavelength $\lambda_0=(164.5\pm0.4)\;\mathrm{nm}$ of the oscillator responsible for the dispersion.