In this paper, we study the asymptotic behaviour of the scattering phase
s(λ) of the Dirichlet Laplacian associated with obstacle Ω, where Ω is a bounded open subset of IR
n (
n≥2) with non-smooth boundary ∂Ω and connected complement Ω
e =IR
n \Ω. We can prove that if Ω satisfies a certain geometrical condition, then
, where
depending only on
n, and |·|
j (
j/ =
n-1,
n) is a
j-dimensional Lebesgue measure.