Fresnel

Augustin-Jean Fresnel (1788–1827) was a French engineer and physicist whose work significantly advanced the wave theory of light. Building on Huygens’ principle, he developed a rigorous mathematical framework for interference, diffraction, and polarization, helping to establish light as a wave phenomenon and addressing a range of optical phenomena from fringes to shadow diffraction.

One of Fresnel’s major contributions is the set of Fresnel equations, which describe how light is reflected and transmitted at the interface between two media with different refractive indices. The equations depend on the polarization of the incident light (s and p components) and the angle of incidence, and they account for phenomena such as partial reflection, partial transmission, total internal reflection, and Brewster’s angle. These results were instrumental in refining optical design and interpretation of experimental data.

Fresnel also introduced mathematical tools for describing diffraction, notably the Fresnel integrals, which define the Cornu spiral. This formalism explains near-field (Fresnel) diffraction patterns and complements the Fraunhofer (far-field) description of diffraction.

In addition to his theoretical work, Fresnel devised the Fresnel lens, a compact, efficient refracting lens using concentric zones to focus light. The lens became widely used in lighthouses and later in various optical instruments and stage lighting.

Fresnel’s legacy includes concepts and tools bearing his name—Fresnel equations, Fresnel integrals, the Cornu spiral, Fresnel diffraction, Fresnel zones, and the Fresnel lens—foundational to wave optics and practical optics alike.