We study the detection theory of polydispersities for dilute suspension of optical and size polydisperse spherical particles， for which the Rayleigh-Gans-Debye (RGD) approximation is valid.To develop the theory a concentric core-shell hard sphere model is adopted,in which particles possess a continuous variation in the core size and shell thickness,the latter is directly proportional to the radius of core,thus giving rise to a distribution in the particle refractive indices.We assume the shell thickness to be L=αR,where αm(K) is derived. We analyse the dependence of the average scattered intensity I(q) and the effective diffusion coefficient De(q) which is obtained from the first cumulant measured by dynamic light scattering in the case that the refractive index of the solvent and that of the shell are matched,i.e.,nm=ns, on the scattering vector q.A linear relation between the extreme point of the effective diffusion coefficient and the polydispersity δ is obtained, which gives a method to detect the small size polydispersities of a disperse system.