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 $n_{\text{IR}}=1.5307\pm 0.0003$ and the value of the characteristic wavelength ${\lambda }_0=(164.5\pm 0.4)\hspace{0.17em}\text{nm}$ of the oscillator responsible for the dispersion.

中文翻译：

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白光下的海丁格-迈克尔逊环

我们使用相干理论来解释为什么有必要修改迈克尔逊干涉仪的传统设置以获得具有扩展白光源的海丁格环。修改包括将载玻片引入干涉仪的两个臂之一。这种插入避免了白光的低时间相干性所施加的严格限制，这阻止了对传统设置的干涉环的观察。为了理解这个限制，我们制定并实施了一个观察干涉条纹的标准。修改后的设置还可以进行光谱干涉实验，以分析干涉仪的输出并确定整个可见光谱内载玻片的折射率。使用 Sellmeier' 对测量数据进行拟合$n_{\text{红外线}}=1.5307\pm 0.0003$ 和特征波长的值 ${\lambda }_0=(164.5\pm 0.4)\hspace{0.17em}\text{纳米}$ 负责色散的振荡器。