= Etalon resolving power and order overlap
{title2=$d\mathcal F\ge Mc/(2\Delta\nu),\quad d<c/(2\Delta\nu)$}
For an ideal air-gap <Fabry–Pérot etalon> at <normal incidence>, the <free spectral range> is $\nu_{\rm FSR}=c/(2d)$ and the peak <full width at half maximum> is $\delta\nu=\nu_{\rm FSR}/\mathcal F$. To separate a pair of lines spaced by $\Delta\nu$ by at least $M$ peak widths, require $d\mathcal F\ge Mc/(2\Delta\nu)$. Putting both lines inside one unambiguous <free spectral range> additionally requires $d<c/(2\Delta\nu)$, so $\mathcal F>M$. In terms of their <vacuum> <wavelengths>, $c/\Delta\nu=\lambda_1\lambda_2/|\lambda_2-\lambda_1|$.
The strict order condition needs a margin if tails from adjacent periodic peaks are to be negligible. If every neighbouring peak in a scanned two-line periodic spectrum must be separated by $M$ widths, the stronger condition is $\min(\Delta\nu,\nu_{\rm FSR}-\Delta\nu)\ge M\nu_{\rm FSR}/\mathcal F$. Ordinary resolving power alone does not prevent ambiguous repeated orders. A fixed etalon's transmission as a function of <wavelength> is a periodic-in-frequency filter; it is not automatically a plot of the incident source's spectral lines.
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