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A spectrometer that resolves spectral lines using the angular dispersion of a diffraction grating. A narrow slit at a collimator focal plane supplies nearly parallel illumination; a telescope or focusing lens forms separate images for different outgoing angles. At normal incidence, the grating equation is $d\sin \theta =m\lambda$. The slit width, illuminated groove count, aberrations and detector sampling jointly determine whether a calculated angular separation is actually resolved.

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.