text: The following example deals with a beam of light scattering off a circle with radius  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 units of length (e.g., meters). Let  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
  The reflection angle of this ray with respect to the incoming ray is , and the scattering angle is
  The differential relationship between incident and reflected intensity  is
  The differential cross section is therefore ()
  Its maximum at  corresponds to backward scattering, and its minimum at  corresponds to scattering from the edge of the circle directly forward. This expression confirms the intuitive expectations that the mirror circle acts like a diverging lens. The total cross section is equal to the diameter of the circle: