Questions about what is visible in a mirror are difficult. Sometimes this is because the relationship between the real and the virtual world is hard to imagine, but in some cases it is hard to see what happens on the surface of a mirror even when standing in front of it (e.g. Bertamini & Parks, 2005; Bertamini, Spooner & Hecht, 2003).
Whether we are looking at a mirror or a window with a glass pane, what we see is on the other side of a surface that we perceive as transparent. We have found that it is difficult to make judgments about the projection of the transparent surface (Bertamini, Lawson & Liu, in press; Lawson, Bertamini & Liu, in press).
We believe that the source of the difficulty is the fact that it is difficult, or indeed impossible, to perceive the 2D properties of a projection of the 3D world that we are looking at. Naively, one may think that having the visual information in front of us should help: after all a projection is what takes place inside our eyes. This is not so.
Details of several experiments are in our publications, but consider here a very simple study.
Observers were given either the upper, face diagram or the lower, body diagram and were told that the diagram showed them standing facing a wall. They drew a rectangle to show what height a mirror on the wall would need to be for them to see all of their face or all of their body in it. A typical (incorrect) response is illustrated beside each diagram. To check if people had understood this drawing task, they were also asked to mark on a scale what height of mirror they would need to see the full length of their face or of their body. This scale, which ranged from 25% to 150% in 25% steps, was in proportion to their own height, so 25% meant a mirror that was a quarter of their height.
Almost everybody indicated that a mirror the same height as their face (or body) would be needed to see all of their face (or body) in it, whereas the correct response is a mirror of half that height. The 20 observers given the face diagram drew a mirror 102% of the depicted height of their face and marked a height 91% of their full face height on the scale. Four people drew mirrors 49%, 51%, 51% and 66% of their face height; the range for the remaining 16 people was 80%-166%. The 20 observers shown the body diagram drew a mirror 107% of the depicted height of their body and marked a height 104% of their full body height on the scale. One person drew a mirror 44% of their body height; the range for the remaining 19 people was 87%-146%.
References:
Bertamini, M. Lawson, R. & Liu, D. (2008). Understanding 2D projections on mirrors and on windows. Spatial Vision, 21, 273 -289. file
Bertamini, M., & Parks, T.E. (2005). On what people know about images on mirrors. Cognition. 98, 85-104.
Bertamini, M., Spooner, A., & Hecht, H. (2003). Naive optics: Predicting and perceiving reflections in mirrors. Journal of Experimental Psychology: Human Perception and Performance, 29, 5, 982-1002.
Lawson, R. & Bertamini, M. Liu, D. (2007). Overestimation of the projected size of objects on the surface of mirrors and windows. Journal of Experimental Psychology: Human Perception and Performance, 33, 1027-1044 file