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---------------- Optics Primer - Locating the Entrance and Exit Pupils

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

The entrance and exit pupils are virtual images of the aperture as viewed from the object side and image side of the lens respectively.
They are virtual rather than real images because the rays that travel from the aperture outward diverge rather than converge.
Never-the-less we can use ray tracing to construct these virtual images.

Here are the entrance and exit pupil locations and sizes for our example lens:

The blue P is the entrance pupil and the red P' is the exit pupil.
On some diagram you may see them labeled as EP and XP or simply E and X respectively.

The pupil diameters are shown in the Optical Bench above the diagram and are 35.61mm and 54.68mm in this case.

A complete treatment of how pupils behave is beyond the scope of this article but I'll try to touch on the important points.

You might read elsewhere that the chief ray points at the entrance and exit pupils; this isn't entirely so.
This is only true when you view the lens straight on and as observation angle increases the pupils move.
For example, here's our lens and the chief ray at the angle of view:

It's clear that extending the chief ray to the optical axis doesn't point to the pupil locations.
The larger the angle of view of the lens, the larger the pupil shift effect (in fact the pupils actually move off of the optical axis).

On the subject of the chief ray, you might also read that it crosses the optical axis at the centers of the pupils as well as the aperture.
But for systems that produce an inverted image, like the photographic lenses we encounter, this is only true of the aperture and not the pupils.

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