In this paper,effect of geometric parameters and grazing incidence on excitation of magnetic polaritons(MPs)in a 1D multi-groove grating with different groove depths made of silver was studied.Numerical results reveal that when the distance between grooves is sufficiently small,the resonance wavelengths of MPs excited in the grooves of unequal depths exhibit red shift with decrease of the distance,contrary to the case with equal groove depths.The shift of the MP resonance wavelengths was explained with the LC circuit model.Furthermore,it was found that the resonance wavelengths of MPs depend linearly on the groove depths except when the difference between the groove depths is small.When the grooves have equal depths,a large drop of the absorptance can occur due to the interaction and cancellation of the electric field vectors in the region between the grooves.Finally,the results show that when a TM wave is at grazing incidence,MPs can be excited simultaneously in the grooves at a blue-shifted wavelength due to reduction of the effective capacitance,resulting in a dramatic enhancement of the absorptance.Therefore,the results in this work may provide useful guidance in the design of wavelength-selective absorbers based on MPs.