Evidence for the Formal Equivalence between Emmert’s Law and Size-Distance Invariance Hypothesis

Abstract

Emmert’s law and the size-distance invariance hypothesis have been said to be equivalent formally if Emmert’s law can be assumed to state that perceived size of an afterimage is proportional to perceived distance of the projected surface of the afterimage. However, there have been very few studies that attempted to verify this formal equivalence empirically. We measured perceived sizes and distances of an afterimage and real objects. Nineteen participants projected afterimages of 1 deg in visual angle on the wall located at 1m to 23m away from the participants, and also observed real objects of 1 deg in visual angle, which were located at the same physical distances as those of the afterimage. Each participant reproduced apparent sizes of the afterimages or real objects using the reproduction method and estimated apparent distances using the magnitude estimation method. When the mean apparent sizes of the afterimage and real objects represented as a function of apparent distance were fitted to linear functions, the slopes did not differ between afterimage and real object. These results were interpreted as evidence for the formal equivalence of Emmert’s law and the size-distance invariance hypothesis.