At fixed incident and central outgoing angles, the <grating equation> gives $m\lambda_m=K=d(\sin\alpha+\sin\beta_0)$. Adjacent central wavelengths are separated by
$$
\lambda_m-\lambda_{m+1}=\frac K{m(m+1)}\sim\frac{\lambda_m}m.
$$
This is the usual adjacent-order <free spectral range>. A detector width of approximately $q\Delta\lambda_{\rm FSR}$, where $q$ is the <grating dispersion>, covers one such interval.


Free spectral range of an echelle grating

{title2=$\Delta\lambda_{\rm FSR}$}
{wiki}

The free spectral range is the wavelength or frequency spacing between adjacent orders or resonances of an optical instrument. It identifies when different orders can overlap.


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 Incoming links: Free spectral range