 Solution

For normal incidence, adjacent grating lines have optical path difference $s\sin \theta$. Constructive interference at order $m$ requires $s\sin {\theta }_m=m\lambda$. Differentiating at fixed $m$ yields the angular dispersionIt is zero in the zero order and increases in magnitude toward grazing diffraction. An order exists only if $|m\lambda |\le s$. The number of illuminated lines controls peak width and resolving power, but does not alter this angle-versus-wavelength relation.