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--------------------------------------------------------- By Bill Claff

Now that we have the focal
points and the focal length we can determine the location of the principal
points:

It is conventional to use the letter H from the German Hauptpunkt. The
principal points are located one focal length from the focal points.

They don't have any physical significance but are important in a variety of
formulas.

The lines through the principal points indicate the principal planes. These
aren't truly planes but curved surfaces but we generally simply indicate them
as planes.

The points shown are where the curves cross the optical axis.

There is also a pair of nodal points which I don't bother to indicate because
in air the nodal points and the principal points coincide.

Here is the actual location of
the principal surfaces:

The planes are constrained by their respective marginal rays.

These three pairs of points; focal, principal, and nodal; constitute the cardinal points of Gaussian optics.

The distance between H and H'
turns out to be important, particularly at closer focusing distances.

I call this the inter-nodal distance and use the letter 'i' in my formulas.

This is also called the hiatus and is also commonly shown as HH'.

Note that the inter-nodal distance can be negative, zero, or positive. In the case of this lens it is about -12.2mm