What to do: Grab the central arrow with your mouse and drag its tip to the centre between the outer arrowheads. Now you may press “Show result” and learn how you fared…
I hope you have enjoyed the “Müller-Lyer Illusion” (1889). When one bisects the horizontal line, it is quite normal that large errors are made, so don’t be annoyed or disappointed (I err by ≈ 10%).
This phenomenon is placed in the category “size constancy” because I find the perspective explanation (see further down) very convincing. Müller-Lyer's original figure showed two double-ended arrows, here I used the Brentano variant.
The German satirical magazine ‘Pardon’ published in ≈1970 an article on this illusion. It was accompanied by the two neighbouring pictures, demonstrating a Müller-Lyer effect on enclosed objects ;-). [The right elephant not only looks larger, but also happier…]
The picture on the right (from Amazingart) demonstrates the perspective explanation (Gregory 1968): When you place the mouse pointer over the picture, the blue lines indicate that the two red arrows are of equal length. The arrow configuration “angles in” (near the ticket counter) is always the front side of an object, the “angles out” configuration occurs at the far end of a room, for instance (here next to the door). So, given no further information (as in the Müller-Lyer arrangement at top), the brain assumes the “angles in” configuration to be closer, computes size constancy on it, and –given identical retinal size of the two angle arrangements– concludes that the “angle in”-line is shorter.
[Thanks to Michael Birnbaum for pointing out that the green ruler mark had, at some time, not really been centered…]
Müller-Lyer FC (1889) Optische Urteilstäuschungen. Archiv für Physiologie Suppl. 263–270
Brentano F (1892) Über ein optisches Paradoxen. Zeitschrift für Psychologie 3:349–358
Müller-Lyer FC (1894) Über Kontrast und Konfluxion. Zeitschrift für Psychologie IX p 1 / X p 421
Lewis EO (1909) Confluxion and contrast effects in the Mueller-Lyer illusion. Brit J Psychol 3:21–41
Rudel R & Teuber HL (1963) Decrement of visual and haptic Müller-Lyer illusion on repeated trials: A study of cross-modal transfer. Quarterly Journal of Experimental Psychology 15:125–131
Segall HH, Campbell DT, Herskovits MJ (1966) The Influence of Culture on Visual Perception. Bobbs-Merrill, Indianapolis
Dewar RE (1967) Stimulus determinants of the magnitude of the Mueller-Lyer illusion. Perceptual and Motor Skills, 24 , 708–710
Gregory RL (1968) Perceptual illusions and brain models. Proc R Soc Lond B Biol Sci 171:24279–296Christie PS (1975) Asymmetry in the Mueller-Lyer illusion: Artifact or genuine effect? Perception 4:453–457
Restle F & Decker J (1977) Size of the Mueller-Lyer illusion as a function of its dimensions: Theory and data. Perception & Psychophysics 21:489–503
Adam J & Bateman L (1983) A correlational analysis of symmetry between the arrowhead and featherhead Mueller-Lyer illusions. Perception 12:119–129
Pressey AW & Martin NS (1990) The effects of varying fins in Mueller-Lyer and Holding illusions. Psychol Res 52:46–53