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Differential cross sections ofα-elastic scattering have been measured for the target nuclei¹¹B,¹²C,¹³C,¹⁴N,¹⁵N, and¹⁶O atE=48.7 and 54.1 MeV and for the nuclei¹⁷O,¹⁸O, and²⁰Ne atE=54.1 MeV. The experimental results were analysed in terms of the optical model using different complex potentials. Special emphasis is given to the application of the double-folding approach for the real part of the potential. The imaginary part is expressed in terms of Fourier-Bessel functions. Differential cross sections for theα-¹⁶O scattering over a wide energy range and for the elasticα-scattering for nuclei in the mass rangeA=11 up toA=24 atE=54.1 MeV are analysed by this method. A close correlation between the absorptive part of the potential and nuclear deformation is observed.