Biomedical Engineering Reference
In-Depth Information
3
The Vergence Relationship
As we learned in the previous chapter, ray diagrams can be used to determine the
location and size of an image. Drawing diagrams, however, can be time-consuming
and inconvenient, so we generally use the
vergence relationship
, sometimes
referred to as the
paraxial relationship
, to locate images and determine mag-
nification.
1
Before we introduce this relationship and show you how to use it,
however, we need to talk a bit more about vergence and linear sign conventions.
After these short detours, we'll jump into the vergence relationship and see how
useful it can be.
MORE ON VERGENCE
We learned some important things about vergence in Chapter 1, but not the
whole story. Let's review and expand upon this. Recall that the vergence of light
rays emitted from an object that is located in air is the reciprocal of the distance
(in meters) to the object. We'll designate this distance as
l
. The absolute value of
the object vergence is given by
1.00
l
L
=
For the object in Figure 3-1A, the vergence is
1.00
0.33 m
L
=
1. This relationship applies only to paraxial rays—those light rays that are in relatively close proximity
to the optical axis of the surface. For these rays, the angle of incidence,
θ
(in radians), approximates
sin
. Most basic optical problems can be solved by assuming that the rays are paraxial. See
Appendix E for a derivation of the paraxial equation.
θ
29
