We will start deriving the vertex distance
compensation formula with the following points:
-
Dl is the power of the lens needed to give the focal length f that
is the sum of the vertex distance and the length of the eye globe.
-
We are going to make d, the distance the lens is moved, negative in the
drawing above. For example, if we are moving the lens from 10 mm to 12
mm, we would say that d = -2mm, so that f - d = 10 - (-2) = 12 mm.
-
Dc is the power needed to give a focal length of f minus d, the distance
that the lens is moved, in meters.
-
We convert all distances (d in particular) to meters, since that is what
is used in the focal length formula.
-
We know that Dl = 1/f, and
-
we know that Dc = 1/(f - d).
So,
1
Dc = ------------
f - d
We can divide numerator and denominator by f, and get
1/f
Dc = -------------
1 - d/f
Substituting into this fraction we have
Dl
Dc = ------------
1 - dDl
The proof for De is similar.
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