Which of the two vertical line segments is longer? Although your visual system tells you that the left one is longer, a ruler would confirm that they are equal in length. The Muller-Lyer illusion is one of the most famous of illusions. It was created by German psychiatrist Franz Muller-Lyer in 1889.

One role of an experimental psychologist is to find explanations for psychological phenomena like the Muller-Lyer illusion, and then to perform experiments to show whether or not the explanations are valid. Let us look at some possible explanations for the Muller-Lyer illusion and some ways to experimentally test their validity.


In the three-dimensional world, depth perception concerns judging distance. The closer an object is to the retina, the larger it is on the retina. However, in the two-dimensional world of the Muller-Lyer illusion, our brain makes assumptions about the relative depths of the two shafts based on monocular (pictorial) cues. We are used to seeing outside corners of buildings as near to us with the top and bottom of the corner sloping out and away (like the outward slanting fins of the Muller-Lyer illusion). We are used to seeing inside corners of buildings as farther from us with the top and bottom of the corner sloping in somewhat towards us (like the inward slanting fins of the Muller-Lyer illusion).

The retina is saying that the two shafts are the same length but the brain is interpreting the Muller-Lyer as a depth issue, with the shaft that looks like an outside corner being closer and the shaft that looks like an inside corner being farther away. In other words, the retina is saying "two shafts equal" and the brain is saying "outside shaft shorter than inside shaft". The brain usually wins differences like this. Thus, the brain seesas longer than.

Psychologists have attempted to support this theory that the Muller-Lyer illusion is caused by our experiences with outside and inside corners, by showing the illusion to an African tribe that lived in circular huts and therefore had no perceptual experiences with corners. People in this tribe didn't seem to be fooled by the illusion thus supporting the "experience with corners" explanation of the illusion.

A counter-study concerned a man who was completely blind (except for light sensitivity) from the of age 3. Recently this man received a successful corneal transplant. Studies have shown that he is impressively free from geometrical illusions that are associated with a suggestion of depth (such as the Shepard Tables illusion shown below -- the two table tops are the same size).

However, he shows roughly normal susceptibility to the Muller-Lyer illusion. This finding suggests that the Muller-Lyer illusion does not depend on processes associated with depth perception.

It should be noted that neither the "African tribe" study nor the "blind man" study are EXPERIMENTAL studies. To be experimental, you must have random assignment. It is not possible to randomly assign people to be "African tribe" or "blind".

Is an experimental test of the "depth" theory possible? For example, would doing the Muller-Lyer illusion by substituting circles or squares for the slanting fins be a proper experimental test of the illusion?

Some psychologists would argue "yes". Participants could be randomly assigned to either a Muller-Lyer with fins or a Muller-Lyer with circles. Then, the results could be compared to see if there was a difference in the performance of the two groups.

Some psychologists would argue "no". They would say that, even though the Muller-Lyer with the circles looks like the Muller-Lyer with the fins, they are not the same. For examples, circles are process by "curve" detectors while fins are processed by "angle" or "corner" detectors.

        Innate feature detectors have been found in the visual system
        Researchers (Hubel and Wiesel) in work on vision in frogs and cats
        have found innate feature detectors in the visual system. Detailed study
        revealed three basic kinds of feature-detecting cells. Simple cells respond
        to a particular stimulus appearing in a circumscribed area of the field
        (for example, a point of light in the upper-left quadrant). Thus, simple
        cells report location as well as feature. Complex cells respond to a
        particular stimulus (e.g., a point of light) appearing anywhere in the
        field; thus, they report only the presence of a feature, not its location.
        Hypercomplex cells respond to combinations of simple features, such as
        form corners, curves, and angles.

Experimental psychologists have to be careful that they are testing theory, and not just testing differences. On the other hand, would the "depth" theorists be logical in arguing that even though their theory is based on "learning", the most critical component of the theory is "unlearned" (biological feature detectors). It is required that experimental psychologists make logically consistent arguments in support of their point of view.

As an alternative, is it possible to experimentally test the depth theory by using only the fins and no shafts? Is the shaft an essential part of the learning experience? Is it an essential part of the experience of depth?

If you did this study, and you found that the illusion was the same for the group that did the illusion with the shaft present and for the group that did the illusion with the shaft absent, would this result invalidate the "depth" theory, or would it only show that shafts are not necessary for depth processing?

What ways can you think of to test the "depth" theory?


This explanation suggests that the shaft ending in the inward slanting fins causes people to perceive it as shorter because the perception of the shaft is pulled back by the "turning back" of the fins. In other words, our eyes go out toward the point and then come back as they follow the fin shafts back. This turning back of our eyes (or perception) makes the shaft seem shorter. Conversely, the outward slanting fins draw our perception on farther making that shaft seem longer.

One experimental way to test this theory is to see if flashing the illusion faster than our eyes can move will still produce the illusion.


Visual Acuity is our ability to distinguish details in the visual field. We have good visual acuity at the center of the fixation point, but in the peripheral region our sight is highly blurred. In a blurred image, neighboring points or line-segments appear to move closer together. According to this theory, when we look at the Muller-Lyer illusion, we tend to fixate on the center of the shaft between the two endpoints. Therefore, the fins are in our peripheral (or blurry) vision. This means that the fixation in the fins moves away from the center of the fins. As follows:

The result is that for the outward fins, the shaft looks longer and for the inward fins, the shaft looks shorter.

Since this theory appears to depend on the size and length of the fins (e.g. longer fins would move the illusion farther from the center of the fins)

and not on the distance separating the two fin heads, it is possible to experimentally test the theory by comparing short separation comparisons of of inward and outward fin heads with long separation comparisons (while keeping the head sizes the same).


The Intertip Disparity Theory says that the illusion is created because people perceptually measure the illusion from the ends of the tips of the fins. Therefore, for the inward fin part of the illusion, the maximal illusion should occur at zero intertip distance (where fins meet to form a diamond shape) and then decrease with increasing intertip distance. Research has shown this to be the case.


The there are two kinds of Averaging theory. The first concerns the fins, only, and claims that the fin pair affects the perceptual system's ability to measure the shaft (or space) distance. Specifically, it says that the Muller-Lyer judgment is based on the average of distances enclosed by the fin pair. The average distance enclosed by the inward fins is less than the average distance enclosed by the outward fins. Therefore, the inward fin space looks shorter than the outward fin space.

The second averaging theory claims that the ratio of fin length to shaft length determines the strength of illusion effect. Fin length would be subtracted from shaft length in the inward fin part of the illusion and added to the shaft length in the outward fin part of the illusion, thus creating the illusion.

One way to test this theory would be to have two inward half-fins on the same side (both right or both left) of the shaft, compared with two inward half-fins on opposite sides of the shaft (one left and one right). The ratio of fin length to shaft length would be the same in both cases. If these different configurations produced different magnitudes (amounts) of illusions when compared to some standard, then the averaging theory would not be supported.