Chapter 13 of 50

Right on Spot

“Truth is stranger than fiction, but it is becauseFiction is obliged to stick to possibilities; Truth isn’t.”

Mark Twain, 1897

Poisson’s spot, also called the Arago spot, demonstrates wave diffraction through the unexpected appearance of a bright point at the center of a circular object’s shadow. When Augustin-Jean Fresnel proposed light as a wave phenomenon in 1818, Siméon Poisson derived this counterintuitive prediction in an attempt to disprove the theory. The effort backfired when François Arago experimentally confirmed the spot, which corpuscular optics could not explain, providing decisive support for the wave model of light.

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Topics

Newton’s Corpuscular Theory
Huygens’s Wave Theory
Young’s Double Slit
Fresnel’s Diffraction Theory
Poisson’s Absurd Prediction
Arago Spot Experiment
1818 Grand Prix
Wave Theory Vindication
Predictive Precision
Scientific Method Evolution
QED Modern View

Sidenote

Model Comparison: Three theoretical models are applied to two classic experiments: the double slit and the photoelectric effect. The goal is to highlight where predictions agree with the observed.

Top (Corpuscular): Double-slit: no interference, $I(x) \sim e^{-(x - x_1)^2} + e^{-(x - x_2)^2}$ . Photoelectric: emission occurs only if photon energy exceeds the threshold, $R \sim \Theta(\omega - \phi)$ .

Middle (Wave): Double-slit: interference arises from wave superposition, $I(x) \sim \cos^2(x)$ . Photoelectric: continuous energy absorption incorrectly predicts emission at all $\omega$ , $R \sim 1$ .

Bottom (QED): Double-slit: coherent paths interfere, $I(x) \sim |\Psi_1 + \Psi_2|^2 \sim \cos^2(x)$ . Photoelectric: decoherent transition amplitudes yield $R \sim |\mathcal{M}|^2 \sim \Theta(\omega - \phi)$ . The same path integral formalism applies, but coherence conditions differ.

Green frames highlight where predictions match experimental outcomes.