Vergence (optics)

In geometrical optics, the vergence is the reciprocal of the curvature radius of a wave front. It is measured in diopters ( 1 / m).

For a point of outgoing ( divergent ) beam of rays the wave fronts are spherical and the vergence is the negative reciprocal of the distance r from the starting point:

Meets this beam to a converging lens, and is the starting point at the focal point of the lens, as is the vergence immediately before the lens

Through the lens, the light is collimated, the rays are parallel, the wave fronts precisely, the vergence zero.

The change of the vergence of on, the refractive power D of the lens. It is positive for converging lenses, negative for diverging lenses and is also expressed in diopters.

True conversely a plane wave ( parallel rays ) to a converging lens, the beam obtains the positive refractive power D of the lens as a vergence: immediately after the lens is considered

Positive means vergence Convergence: The rays of the beam to a focus to run. Which is in the distance behind the lens.

When approaching the focus of the vergence increases faster and faster. The concept of vergence is only useful in dimensions far above the wavelength. At one focus the vergence has calculated a pole, that is, it diverges and changes its sign: Against the focusing point they would have a positive infinity, then negative infinity. When Gaussian beam of wave optics, however, the curvature of the wave fronts initially increases with the vergence, but is close to the focus smaller again. During passage through the focus of the curvature continuously changes from positive to negative, that is, directly at the intersection of the rays of the geometrical optics, the wave fronts are plane. Sufficiently far behind the focus vergence is right again with the curvature of the wave fronts coincide ( both negative).

• Paraxial optics