Chapter 37, Problem 38AP

Two wavelengths λ and λ + Δλ (with Δλ << λ) are incident on a diffraction grating. Show that the angular separation between the spectral lines in the mth-order spectrum is

$\Delta \theta =\frac{\Delta \lambda }{\sqrt{{(d/m)}^2-{\lambda }^2}}$

where d is the slit spacing and m is the order number.