Several discrete sets of optical potentials which fit the data on the elastic scattering of medium-energy $\ensuremath{\alpha}$ particles are examined. It is shown that the usual criterion for equivalence of these potentials is valid only if little variation is allowed in the diffuseness parameter, and that a more widely applicable criterion is obtained by considering the magnitudes of the potentials at the strong-absorption radius. It is also shown that, because of the ambiguities in the optical potential for $\ensuremath{\alpha}$ particles, the half-way radius and the equivalent radius of the potentials are functions of the depth and therefore cannot be regarded as significant nuclear size parameters. The strong-absorption radius, however, is shown to be a very significant size parameter, which can be related not only to the reflection coefficients but also to the optical-model wave function.