Vergence (optics)

A convex lens or concave mirror will cause parallel rays to focus, converging toward a point.

The simple ray model fails for some situations, such as for laser light, where Gaussian beam analysis must be used instead.

[1] Vergence is defined as where n is the medium's refractive index and r is the distance from the point source to the wavefront.

[2] The light can also be pictured as consisting of a bundle of lines radiating in the direction of propagation, which are always perpendicular to the wavefront, called "rays".

Thus, in this case the convergence of the rays transmitted by a lens is equal to the radius of the light source divided by its distance from the optics.

This limits the size of an image or the minimum spot diameter that can be produced by any focusing optics, which is determined by the reciprocal of that equation; the divergence of the light source multiplied by the distance.

The only way to achieve a smaller spot is to use a lens with a shorter focal-length, or expand the beam to a larger diameter.

In this case, the diffraction of the light starts to play a very active role, often limiting the spot size to even larger diameters, especially in the far field.

[7] For non-circular light sources, the divergence may differ depending on the cross-sectional position of the rays from the optical axis.

Vergence of a beam. The vergence is inversely proportional to the distance from the focus in metres. If a (positive) lens is focussing the beam, it has to sit left of the focus, while a negative lens has to sit right of the focus to produce the appropriate vergence.
A simple telescope . Collimated (parallel) light waves converge through a lens, then diverge to be collimated by another lens, converging again through the lens of the eye.