Does the Fabry Perot spectrometer's free spectral range change with distance?

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The discussion focuses on the use of a Fabry-Pérot (FP) cavity for spectrometry, specifically regarding the relationship between cavity distance and the free spectral range (FSR). It is noted that the maxima of the FP cavity occur at intervals of λ/2, and the FSR, defined as c/2d, varies with the cavity distance d. The participant expresses concern about whether this variation affects the spacing between the maxima during spectroscopy. Ultimately, the participant confirms their understanding and successfully derives the relevant concepts. The conversation highlights the complexities of using FP cavities in spectrometry and the importance of understanding FSR dynamics.
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Hi

I have a question regarding doing spectrometry using a FP-cavity. For a fixed wavelength, the successive maxima of the FP-cavity occur when the distance of the cavity is changed by a multiple of λ/2. This we can use to look at the spectrum of light in the cavity by changing the distance. In my book it is stated that these maxima are separated by the free spectral range (FSR), which in frequency is given by c/2d.

However, the FSR naturally changes with the distance d of the cavity. Does that mean that the spacing between the maxima changes when doing spectroscopy? The reason why I ask is because I have not seen a reference mentioning this, so I am worried that I might be wrong.Niles.
 
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I understand it now, I figured out how to derive it. Finally some success.
 
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