Understanding 2D projections on mirrors and on windows

Representational art tries to capture a 3D world on a 2D surface, and artists often discuss this in relation to the projected image on window panes and mirrors. But are 2D projections on transparent surfaces useful to learn about projections in general? Most people are unaware of the 2D projected size of objects on the surface of mirrors. They also incorrectly expect that these projections always get smaller with distance of the target object from the mirror, and do not change with distance of the observer (when the target is stationary). In this paper we extend this result about surfaces of mirrors to surfaces of windows, and we confirm that the errors that people make are not specific to Western culture by replicating the study in China. In contrast to their errors about projections, people are more accurate at predicting how field of view will vary depending on distance of the observer from a mirror or window. To explain how this pattern of (false) beliefs can stem from experience we argue that people do not perceive projections on transparent surfaces.