Horocycles of Light in a Ferrocell

Abstract

We studied the effects of image formation in a device known as Ferrocell, which consists of a thin film of a ferrofluid solution between two glass plates subjected to an external magnetic field in the presence of a light source. Following suggestions found in the literature, we compared the Ferrocell light scattering for some magnetic field configurations with the conical scattering of light by thin structures found in foams known as Plateau borders, and we discuss this type of scattering with the concept of diffracted rays from the Geometrical Theory of Diffraction. For certain magnetic field configurations, a Ferrocell with a point light source creates images of circles, parabolas, and hyperboles. We interpret the Ferrocell images as analogous to a Möbius transformation by inversion of the magnetic field. The formation of circles through this transformation is known as horocycles, which can be observed directly in the Ferrocell plane.

Keywords

• ferrofluid
• magnetism
• magneto-optics
• hyperbolic geometry
• optics