there is more than one complete spectrum formed by a diffraction grating, because a grating separates wavelength by different pathways, which produces several orders. Therefore, there is more than one interference- taking place creating a large number of maxima and minima. This shows that a diffraction grating is based on interference, thus light reflecting from near by groves of the grating with be in-phase. However, when you increase the angle, waves coming from neighboring grooves will become in step, thus they will interfere constructively, furthermore, producing a brighter light intensity and creating multiple spectrum.
