Optical magnification as event information

The geometrical optics of approach events is delineated. It is shown that optical magnification provides information about distance and time until collision. An experiment is described in which two objects--white styropor spheres 10 cm in diameter, seen against a white plaster wall--were moved simultaneously at equal, constant speed along straight, converging paths at eye level towards a human observer and towards a common, virtual point of collision which either coincided with the observer's station point or was placed in front of, or behind, that point. Approach events differed with regard to trajectories, distances, velocities, and times-to-collision involved. Events were observed monocularly fixating and binocularly non-fixating, without head movements. The objects always stopped before colliding, and subjects had to respond to the virtual collisions. Most responses were too early, especially for impending collisions at, or behind the observers' station point. Responses for impending collisions in front of the observers tended to be too late, especially for larger total amounts of optical magnification and higher velocities, which together imply shorter times-to-collision. Relative errors were comparatively larger for very short and very long times-to-collision throughout, where events of the first kind were overshot, the latter ones undershot. Results are interpreted with reference to biological theories and the constraints imposed by geometrical optics. Special attention is focused on the issue of unavoidable, necessary confounding of variables in time-to-collision studies.