Hatched-line Illusions

Related to the convergence-divergence concept are the illusions produced by hatched lines.  These illusions excited much interest and discussion over the last century.  The earliest of them is the Zollner illusion, which dates back to 1860, and can be considered as one of the main figures which triggered off the study of optical illusions.  Shown below is Zollner’s illusion in its simplest form. 

Fig. 64 – The Zollner illusion.  The long horizontal lines are parallel to each other.

It has been suggested that assessing acute angles set in different directions produced the illusion.  Zollner himself discovered that the illusion is the strongest when the hatching lines are inclined at 45° to the main lines.  It has already been shown that convergence and divergence can affect our judgement of lengths, as shown in the Muller-Lyer illusions.  Perhaps they account for the seemingly unequal distances between different portions of the main lines.