Angular distributions for elastic scattering of alpha particles on 27Al, 28Si, 32S, Ti and 59Co nuclei have been measured in the angular range from about 20∘ to 179∘ (LAB). The experimental data were fitted with the optical model in full angular range. Many sets of four-parameter potentials, describing the elastic scattering, were found with the depths of the real part ranging from 40 to 450 MeV. A new discrete ambiguity in the optical model namely in r0 was observed