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# ---------------------- Optics Primer - Locating the Principal Points

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

We locate points on what is called the principal plane by finding the intersection of the ray from infinity and the ray as traced back from the focal point:

In the above diagram I added thick blue and red lines to illustrate.
The principal planes are indicated by H and H'. It is conventional to use the letter H from the German Hauptpunkt for the principal points.

It's obvious that the intersections don't fall on the planes as indicated; that's because although we call them planes they are in fact curved.
Here is what those surfaces look like:

They don't have any physical significance but are important in a variety of formulas.
Most importantly the distance between F and H, and the distance between F' and H', is the focal length.
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.

The principal 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