Grating dispersion
= Grating dispersion
{title2=$d\beta/d\lambda=m/(d\cos\beta)$}
At fixed incidence angle, differentiating the <grating equation> gives $d\beta/d\lambda=m/(d\cos\beta)$. A camera with <focal length> $f$ therefore has local focal-plane dispersion $q=fm/(d\cos\beta)$ near its optical axis. With coordinate $X=f\tan(\beta-\beta_0)$, the full derivative is $q=f\sec^2(\beta-\beta_0)m/(d\cos\beta)$.