= 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 dispersion>
$$
\boxed{\frac{d\theta_m}{d\lambda}=\frac{m}{s\cos\theta_m}.}
$$
It 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.
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