Abstract
A homothetic conformal transformation of the metric tensor is both necessary and sufficient to ensure that a source-free non-null electromagnetic field in four dimensions undergoes a duality rotation leaving its energy-momentum tensor invariant. For null electromagnetic fields the condition is sufficient but not necessary. The result suggests that vacuum Einstein-Maxwell space-times exist which admit groups of homothetic motions. If the order of such a group is greater than unity it must be associated with isometry transformations of the metric tensor other than those obtained as a special case of the conformal group.