## Sunday, May 21, 2006

### Vergence

Vergence is defined as the reciprocal of the distance from a reference point (in meters) to the point of focus.

• Vergence is measured in diopters. (1 diopter = 1/1m = 100/100cm)

• The vergence of the light rays coming from an object is directly related to the distance from the object.

In Figure 1, the divergence of rays of light emanating from point O is, at A, 1/-0.25 = -4.00D; at B, 1/-0.50 = – 2.00D; at C, 1/-1 = –1.00D; at D, 1/-2 = –0.50D and at E, 1/-3 = –0.33D.

click on image to enlarge

In Figure 2, the convergence of the rays of light, converging to the point I is, at A, 1/4 = +0.25D; at B, 1/3 = +0.33D; at C, 1/2 = +0.50D, at D, 1/1 = +1.00D and at E, 1/0.5 = +2.00D

click on image to enlarge

By convention, divergence is given in minus (-) vergence power and convergence is given in plus (+) vergence power.

• Convergent wavefronts are not found spontaneously in nature. They are the result of an alteration of a planar or divergent wavefront by a refractive or reflective medium.

• An object (O) is defined as a point or extended source that the pencil/beam of light comes from.

• The object’s distance from the object to the point of reference is designated as u.

• The object's vergence (U) is the distance from the object to the point of reference. U = 100/u (cm)

• The image (I) is defined as a point or extended source that the pencil/beam of rays go to.

• The image distance is measured from the point of reference to the image and is defined as v.

• The image’s vergence (V) is the distance from the image to the point of reference.

• V = 100/v (cm)

• When defining an optical system, it is conventional to set the incoming rays as object rays, the outgoing rays as image rays, and light travels from left to right.

Question: Define the term Diopter.

Answer: A diopter is a unit of accommodative amplitude; it describes the vergence of a waveform and describes the vergence at a specific distance from the source; and it is also defined as the power of the lens. A diopter is the reciprocal of the distance in meters.