The Prism Illusion: A Function of Dislocated Equivalence Classes

Abstract

A mathematical analysis of the transformation of the direction of light rays passing through a wedge prism is presented. It is shown that if (x, y) is the angle of incidence and (x′, y′) the angle of emergence, y′ = y and x′ = f (x, y). The main properties of this function are displayed, and a numerical example is presented in tabular form. Looking through a prism gives the impression that, in general, y′ ≠ y, vertical dimensions being enlarged at the base end and contracted at the apex end of the prism. The function x′ = f (x, y) shows that horizontal dimensions are contracted at the base end and expanded at the apex. It is suggested that the perceptual process resists this deformation, so that horizontal dimensions are less contracted and less expanded than the function would indicate. Since this does not affect the dimensions of the retinal image, perceptual expansion (or contraction) of contracted (or expanded) horizontal dimensions entails expansion (or contraction) of vertical dimensions as well. The conclusion that y′ = y may be tested by looking through binocular prisms with bases on the temporal sides. If y′ ≠ y, vertical disparity will make binocular fusion difficult. No failure of fusion has been reported.