The Rayleigh Wood anomalies refer to an unexpected repartition of the electromagnetic energy between the several interference orders of the light emerging from a grating. Since Hessel and Oliner (Appl. Opt. 4, 1275-1297 (1965)), several studies have been dedicated to this problem, focusing mainly on the case of metallic gratings. In this paper, we derive explicit expressions of the reflection coefficients in the case of dielectric gratings using a perturbative approach. This is done in a multimodal description of the field combined with the use of the admittance matrix, analog to the so-called electromagnetic impedance. Comparisons with direct numerical calculations show a good agreement with our analytical prediction.