Build the model
Send collimated light from left to right in air at 550 nm. Place the convex first vertex at z = 0, with radius +50 mm and center thickness 5 mm. The second surface is flat. Use constant index 1.5 and a 10 mm entrance pupil. Place the front of a 3 mm parallel plate at z = 15 mm. Set the plate index to 1.0 for the air reference and 1.5 for the glass run.
Trace three pupil heights
For each pupil height, extend the outgoing ray to its intersection with the optical axis. The table gives positions measured from the first vertex. The near-axis intercept moves about 1.00 mm away from the lens, consistent with the paraxial shift t(1 − 1/n).
| Fraction of pupil radius | Air reference, z (mm) | Glass plate, z (mm) |
|---|---|---|
| 0.01 | 101.66664 | 102.66664 |
| 0.50 | 101.59428 | 102.59463 |
| 0.90 | 101.43175 | 102.43288 |
Read the marginal ray
Without the plate, the ray at 90% pupil radius crosses the axis about 0.235 mm before the ray at 1%. A single focus position therefore does not describe the whole pupil. These are calculated monochromatic ray intersections for the stated model.