CORNU’S SPIRAL UVic（回旋曲线维多利亚大学）.pdfVIP

1 CORNU’S SPIRAL If a parallel beam of light from a distant source encounters an obstacle, the shadow of the obstacle is not a simple geometric shadow but is, rather, a diffraction pattern. For example, it is well known that the diffraction pattern formed by a slit looks like the function shown in figure 1. FIGURE 1 Such diffraction is called Fraunhofer diffraction. If, however, the source of light is not distant, but is close to the diffracting obstacle so that the incident waves are not plane waves, the diffraction pattern will look somewhat different. Such diffraction is called Fresnel diffraction, and its theory is, unsurprisingly, a little more difficult than the theory for Fraunhofer diffraction. If the source of light is a point source, so that the incident wavefronts are spherical, the detailed quantitative theory is not at all easy. If the incident wavefronts, however, are cylindrical (say from a linear source) the analysis, which is two dimensional, is a little more tractable. Cornu’s spiral is a graphical device that enables us to compute and predict the Fresnel diffraction pattern from various simple obstacles. “Cornu”, by the way, is French for “horned”, and can also mean “spiral” - i.e. like the horns of a bighorn sheep or of an ibex. Because of this I wondered, when I first heard about Cornu’s spiral, whether it should really be called a “cornu spiral”, rather than Cornu’s spiral. However, it is correctly named Cornu’s spiral after a real nineteenth 2 century French scientist, Marie Alfred Cornu. The mathematical properties of the spiral had been examined by various mathematicians (for example, Euler) before Cornu, but it has acquired the name of Cornu because of its application by Cornu to the theory of Fresnel diffraction. Let us look, in f