The following example deals with a beam of light scattering off a circle with radius r and a perfectly reflecting boundary. The beam consists of a uniform density of parallel rays, and the beam-circle interaction is modeled within the framework of geometric optics. Because the problem is genuinely two-dimensional, the cross section has unit of length (e.g., metre). Let α be the angle between the light ray and the radius joining the reflection point of the ray with the center point of the mirror. Then the increase of the length element perpendicular to the beam is