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

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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.
 
I understand it now, I figured out how to derive it. Finally some success.
 

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