Vertex distance is the distance between the eye (front of the cornea) and the corrective lens. In most cases, it is considered zero for contact lenses. In case of glasses this distance is typically around \(12 mm\). The basic phenomenon that makes this measure important is the fact that changing the distance between the corrective lens and the eye changes the power of the lens.

The vertex distance formula tells that the corrective power of a lens with power \(F\) at \(d\) distance is

\(F_c = \frac{F}{1-dF}\)

This formula tells us how the vertex distance changes the required lens power. In case of low power lenses the effect is is very small. Consider a \(F = -4D \) lens with a \(12mm\) vertex distance. The corrective power becomes -3.82D. In most cases this small change is negligible.

### How well vertex distance needs to be measured?

#### Problem I.

*Assume there is a glass correction with -7D. Further assume that one uses an average vertex distance (\(12mm\)) instead of the actual \(17mm\). How big correction mistake is made?*

#### Solution

Since this patient needs \(F = -7D \) correction, and we use \(12mm\) vertex distance, the lens are made with power: \(F = \frac{F_c}{1-dF_c} = -7.64D\)

Such a lens makes \(F_c = -6.76D\) correction at \(17mm\) which is the actual distance.

#### Discussion

One can see that even with high power lens using an average vertex distance as a correction factor, does not make a big mistake.

If we change this problem slightly by estimating the vertex distance to be 14mm, the corrective lens power becomes \(F_c = -7.76D\) which gives \(F_c = -6.86D\) at \(17mm\) which is almost inside clinical tolerance (0.125D).

This maths shows that measuring the vertex distance with \(3mm\) accuracy is sufficiently accurate in a vast majority of the cases, while in lower diopter cases an average value gives sufficiently good power estimation.

In conclusion one can say that measuring the vertex distance is important in case high power lens is used, but even in those cases a \(3mm\) accurate estimate gives good corrected lens parameter values.