Arago

Arago raises a round shield against the beam. Dead centre of its shadow, a star still burns.

The Physics

Light waves bending around the edge of a round, opaque disk all arrive in step on the axis behind it. In ideal Fresnel (paraxial) theory, with a point source, the centre of the shadow is about as bright as if the disk were not there. The Fresnel number tells you which regime you are in.

N_F = a² / (λ L) and, on axis, I ≈ I₀

• N_F: Fresnel number (dimensionless)
• a: disk radius (m)
• λ: wavelength (m)
• L: disk-to-screen distance (m)
• I₀: unobstructed intensity at the same point (W/m²)

In 1818 Fresnel submitted his diffraction memoir; Poisson, judging it, derived the "absurd" bright spot as an objection, Arago put a disk in the beam and saw it, and Fresnel won the 1819 prize.

Honest caveat: Real disks need very round, smooth edges, hence the ≈. The spot had been seen earlier and passed unnoticed: Delisle (1715), Maraldi (1723).

On the shirt

Front: Arago, the pixel-art character, with the title. Back: the Fresnel number, the on-axis result, the 1818–1819 prize story and the earlier sightings. Printed on a unisex tee.