Fresnel Integrals and Wave Optics

Augustin-Jean Fresnel (1788–1827) developed the wave theory of light mathematically, proving that light diffracts and interferes. The Fresnel integrals — ∫₀ˣ sin(t²)dt and ∫₀ˣ cos(t²)dt — cannot be computed in closed form but trace the 'Cornu spiral,' a curve that appears in the analysis of diffraction through a slit. Fresnel also designed the Fresnel lens — concentric rings that achieve the focusing power of a thick glass lens in a thin, lightweight form. All lighthouse lenses, overhead projectors, and many camera lenses use his design.