What is a Vergence?
Vergences describe the curvature of a wavefront. Geometric optics considers the propagation of spherical wavefronts - i.e. wavefronts emanating from point sources. A good two-dimensional analogy is the waves one observes on the surface of a pond after throwing a stone into the water.
The radius of curvature of a wavefront, r, is the distance from the source to the current position of the wavefront.
The curvature of the wavefront is then given as 1/r. Near the source, the curvature is very large. A long distance from the source, the wavefront is nearly straight - called a plane wave, and the curvature is zero.
A vergence is defined as V = n/r where n is the refractive index of the medium that the light is propagating through. A sign convention is also introduced-
- for light propagating away from a source (diverging), the vergence is negative i.e. V = -n/r
- for light propagating towards a focus (converging), the vergence is positive i.e. V = +n/r
The unit for vergences is the dioptre written as D which are equivalent to m-1.
The following diagram shows vergences for different locations of the wavefront propagating in a vacuum (n=1). After leaving the source, light rays are diverging and V<0. The grey centre area represents a changed from diverging to converging light (during which a plane wave is formed for which the radius of curvature is infinite). Thereafter the light converges to the focus with V>0.
