The "multiple reflection error" - yet another way that we misunderstand mirrors

On her trolley! Janine, the mannequin

Considering the ubiquity of mirrors in everyday life, it's amazing how confused we are about them. For example, many of us are oblivious to the small size of our heads as they appear reflected in the mirror. A new study by Rebecca Lawson has provided a compelling demonstration of the "multiple reflection error" - yet another striking way that we misunderstand mirrors.

Imagine you're at the entrance to a narrow corridor and further down, several feet away, hanging on the right-hand wall, there are three rectangular mirrors (30cm x 45cm) at head height. At what point, as you proceed down the corridor, do you think you'll be able to see your face in the mirrors?

The correct answer is that your face will only be visible in each mirror when you are passing directly opposite. At no point will your face be visible in more than one mirror.

Lawson first tested people's understanding of this idea by having them stand at one end of a corridor and say in which of four positions in the corridor a mannequin "Janine" (moved about on a trolley) would be able to see herself in each of the three mirrors. Only two of the four positions in question were actually directly opposite one of the mirrors. So, of the 12 possible position/mirror combinations, the answer "yes, Janine can see her face" should only have been given twice. In fact, the 18 Liverpool University students answered yes an average of 6.1 times, grossly overestimating how often the mannequin could see herself in the mirrors. The errors weren't randomly distributed, they tended to be made when the mannequin was located near to the mirrors, but not directly opposite them.

The same errors were made when a single, larger mirror was divided up into three using duct tape (to ensure that participants realised the mirror surfaces were all flat against the wall and not angled like a dressing-table mirror), and also when the original three mirrors were arranged on the wall vertically, rather than horizontally.

Perhaps, Lawson reasoned, the participants were performing so poorly because it was confusing assuming the perspective of a mannequin. And also, perhaps because they were asked about each position and each mirror one at a time, so that they didn't realise the full implications of what they were saying: that the mannequin could see her face in multiple mirrors from a single position, and in the same mirror from different positions (an optical impossibility in the situation as described).

To avoid these issues, Lawson created another set-up in which more participants (prospective students and their parents) were shown a photograph of a person sat facing five mirrors arranged on the wall in the shape of a cross, with the central mirror at head height. The participants were given a piece of paper with five rectangles on it arranged in a cross shape, and they had to draw crudely what the person in the photo would be able to see of themselves in each mirror. Once again, there was a striking overestimation of where the person would be able to see reflections of their own head and face (participants should have indicated that the person's head/face would only be visible to them in the central mirror).

Finally, more participants actually sat in front of this set up of five mirrors in a cross shape. Half of them had just the central mirror uncovered then re-covered before they used the pencil and paper to indicate what they'd see in all the mirrors (the remaining mirrors were covered throughout). The other half of the participants had all the mirrors uncovered first, then re-covered before they gave their answers with the paper and pencil. In the first case, 58 per cent of the participants made multiple reflection errors - again, overestimating where they'd be able to see themselves in the mirrors. In the latter case, with the chance to experience the entire mirror set up, 24 per cent made such errors.
"This multiple reflection error is particularly surprising," Lawson said "because it directly contradicts our everyday experience that mirrors reflect a single coherent scene."

So why do people misunderstand mirrors in this way? Lawson said there are probably multiple reasons. One participant described her naive belief that whenever you turn your eyes towards a mirror, wherever it is, you will see yourself reflected in it - "mirrors look back at you," she said. No doubt this belief was held implicitly by many of the other participants.

"Almost nobody will have a clear, thought-through and self-consistent theory of optics which they use to guide their predictions," Lawson said. "Most people probably use a set of underspecified beliefs and heuristics, some of which are incompatible, leading them to make unsophisticated, noisy and inaccurate predictions. People rarely think explicitly about optics and what determines what they can see in a mirror or a window - or indeed, what they can see directly."
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Lawson, R. (2012). Mirrors, mirrors on the wall…the ubiquitous multiple reflection error. Cognition, 122 (1), 1-11 DOI: 10.1016/j.cognition.2011.07.001

Further reading:
Link to Mirrors and the mind (Psychologist magazine article).
Link to New York Times article on the psychology of mirrors.

Post written by Christian Jarrett for the BPS Research Digest. Thanks to Rebecca Lawson for providing images of her experiment.