Pupil-viewer explorer

This interactive explorer uses a JavaScript module. Open it through a local web server to change the lens geometry. Figure 1.6 remains the static reference for the two apparent images of one physical stop.

A physical aperture stop lies between two thin lenses. The preceding lens forms the entrance-pupil image seen from object space, and the following lens forms the exit-pupil image seen from image space. Dashed colored paths are side-specific stop-image constructions, not ordinary propagating system rays.
One real stop can have two side-dependent apparent pupil images.

Interactive explorer

Explore: where are the entrance and exit pupils?

Hold one physical aperture stop at z = 0 between two clear thin lenses. Choose a viewing side, then use a ray construction to locate that side’s apparent image of the same fixed stop.

Predict first

If the physical stop lies closer to a positive lens than that lens’s focal length, will its apparent pupil lie beyond the lens toward the viewer or back on the stop side? Switch viewpoints: the entrance and exit pupils are different images of the same real opening.

View the fixed stop from

Fixed schematic axes: laboratory positions span −520 to +520 mm and transverse heights span ±36 mm. Axial and transverse scales intentionally differ. The lenses are assumed clear and nonlimiting; the gray opening is the only physical aperture stop in this model.

Set the fixed stop and lenses

Before the stop

After the stop

Selected apparent pupil

Laboratory coordinate, z
Diameter
Lateral magnification, M
Image from the active lens, q

Construction rule

For the selected side only, measure s positive from the stop toward the viewer. The active lens is at s = d.

q = fd/(d − f)

M = f/(f − d)

Dpupil = |M|Dstop

Dashed paths are side-specific stop-image constructions. They are not the system’s ordinary left-to-right propagating rays.