Faradra

Faradra, a light-bending sorceress, holds a glass rod between two magnet poles, and the beam of light passing through it twists.

The Physics

In September 1845 Michael Faraday sent polarised light through a block of heavy lead-borate glass placed between the poles of a strong electromagnet, with the field along the beam. When the magnet was switched on, the plane of polarisation turned. It was the first experimental link between light and magnetism. He reported it in the Nineteenth Series of his Experimental Researches in Electricity (Phil. Trans. R. Soc. 136, 1, 1846). The rotation angle grows with the field and with the path length.

β = VBd

• β: rotation angle of the plane of polarisation (rad)
• V: Verdet constant of the material (rad T⁻¹ m⁻¹)
• B: magnetic flux density along the beam (tesla, T)
• d: path length through the material (m)

Faraday rotation is non-reciprocal: the rotation direction is set by the field, not by the beam's direction of travel. So light sent back through the glass rotates further, not back to where it started. Optical isolators use this to stop reflections travelling back into a laser.

Honest caveat: β = VBd holds for a uniform field along the beam. V depends strongly on wavelength and material, and only the field component along the beam counts.

On the sticker

Faradra steadies a glowing glass rod between two coils as a cyan beam runs along it. Printed text: FARADRA with the line β = VBd. Pixel-art kiss-cut vinyl sticker, white, in 2″, 3″, 4″ and 6″ sizes.