Franz Muller-Lyer (1889) first studied the figures that have become known as the Muller-Lyer Illusion. He discovered that the line with outgoing tails is almost always seen as longer than the line of the same length with inward tails. Since the first discovery many theories have been discussed as to why this occurs.

Krueger (1972) found that increasing the tail length would increase the intensity of the illusion to a certain point, at which the strength of the illusion will decrease. In a previous experiment on the effects of the tail length we (Smith, Sexton and Hall, 2003) found that there was no substantial difference in the strength of the illusion based upon the tail lengths we presented to our subjects. thus it may have been that our experimental lengths had already reached the point at which the illusion is at its strongest and was already declining in strength. The purpose of this particular experiment is to explore the effects of tail length and to attempt to discover at which point the length of the tails stops strengthening the illusion. To find this point, subjects were shown a control figure, along with ten figures with varied tail lengths. In addition the subjects looked at ten one-tailed figures, with the same varied tail tail lengths. Beagley (1985) discusses the fact that eliminating one tail will decrease the strength of the illusion a great deal. so by presenting both one and two tailed figures we are hoping to find the exact amount of increase or decline in illusion strength that is created by tail length.

Methods

The subjects of this experiment were 23 Alma College students.

The experiment was created on the computer program Eye Lines and viewed on Mac Computers. The control stimuli was a straight, 131mm, tail-less line. The other figures were ten lnes with one outward pointing tail and ten lines with two outward pointing tails (See Figure 1) with the lengths of 5mm, 10mm, 15mm, 25mm, 30mm, 50mm, 70mm, 90mm and 100mm.

Figure 1: The One and Two-Tailed Stimuli Used in This Experiment

Each subject was asked to sit directly in front of the computer screen. Upon entering their identifying initials they viewed a cycle of twenty-one images. They were then asked to use the mouse or arrow keys to manipulate a line until they felt it matched the image line (with or without tails). Once they felt they had achieved a match, they were asked to push any key on the keyboard. Each image was presented once, in a varied order.

Results

For the two-tailed line there was a steady increase in the strength of the illusion until the subjects reached the tail length of 90mm. At this point there was rather large decrease in illusion strength of almost 8.8 mm. (See Figure 2).

Figure 2: Effects of Increased Tail Length on Two-Tailed Mueller-Lyer Illusion.

The one-tailed created a general decrease in the strength of the illusion when compared to the two-tailed error. There also remained a general increase in the strength of the illusion, though not as steady as the two-tailed version. The illusion strength begins a steady decline after hitting its strongest point at 70mm. (See Figure 3).

Figure 3: Effects of Increased Tail length on the One-tailed Mueller-Lyer Illusion

Discussion

The results were much like what was expected. The strength of the Mueller-Lyer illusion lost strength when it was viewed with only one tail. It also seems to increase in strength when the line length is increased, to a certain point, and then proceeds to lose strength after this point. the problem comes with deciding at which length the strength of the illusion has reached its highest point. While both the one and two-tailed versions of the illusion appear to have such a point, the points are not of the same length. There may be no way to find an exact length at which the tails are no longer a factor in the illusion. But a number of things can be said with a good deal of confidence by looking at the results of this experiment. Tail-length has an effect on the strength of the illusion, one-tailed lines create a weaker illusion than that of two-tailed lines. And finally in both cases, there is a point at which the lines are too long and the illusion is thus weakened.

Beagley, Walter K (1985). Interaction of Muller-Lyer with filled-unfilled space illusion: An explanaition of Muller-Lyer asymmetry. Perception and Psychophysics,37, (45-49).

Krueger, Lester E. (1972). Gregory's Theory of Illusions: Some Disconfirming Evidence in the case of the Muller-Lyer Illusion.Psychological Review, 79, (538-539).

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