In this work, we analyze theoretically the frequency-dependent phase index np(ω) of a guided mode in photonic crystals from the photonic band structures. The np(ω) reveals a promising possibility for fabricating a chromatic prism using photonic crystals. We then investigate the superprisming effect of a photonic-crystal prism for both guided continuous-wave TM and TE modes. In addition to dielectric intuition, the effects of magnetic permeability of a magnetic photonic crystal on the photonic band structure, the phase index, and the superprisming effect are examined. It was found that magnetic intuition could enhance the resolution of a photonic-crystal prism for dividing TE modes of various wavelengths, but reduce the resolution for dividing TM modes.