Crossed-bar Illusions

The crossed-bar illusions were invented over a century ago by the well-known physicist Poggendorff.  They are sometimes referred to as Poggendorff’s illusions, and were the subject of much discussion in the late nineteenth century.

Fig. 68 – Poggendorff’s illusion.  The lines A and X are actually continuous.

The lines B and X in Fig. 68 appear to be continuous, and it appears that the line A is placed below the line BX.  However, if a ruler is placed on A, it is discovered that A and X actually form a continuous line. 

It is not well understood why the illusion arises, but we do know that the degree of illusion is strongly related to the degree of obliquity, as shown in Fig. 69. 

Fig. 69 – The degree of obliquity strongly affects Poggendorff’s illusion. 

Fig. 69 clearly shows that as the inclination of the lines is diminished, the illusion progressively weakens.  It disappears when the lines are perpendicular to the bar.  Hence, to produce a convincing crossed-bar illusion, a steep crossing angle is required.  Furthermore, a steeper inclination will tolerate a greater separation distance between the two lines, as shown in Fig. 70. 

 Fig. 70 – The steeper the inclination the greater the separation tolerated.