Notes
TIR collimator basics for LED downlights
October 14, 2026
A TIR collimator for an LED downlight gives the source two paths. Rays near the axis meet a lens and refract. Rays farther out meet the outer wall from inside the plastic and reflect when the hit is steep enough. The drawing is a meridional teaching model, not a production prescription. A custom 2D ray trace made the drawing and every number here. PMMA is index 1.49. Air is index 1.
Critical angle
Snell's law sets the critical angle at a PMMA-to-air face. The trace takes the arcsine of 1 divided by 1.49, which is 42.1552 degrees, or 42.2 degrees to one decimal place. On a flat face, a ray at 30 degrees transmits and leaves at 48.16 degrees. A ray at 40 degrees transmits and leaves at 73.29 degrees. A ray at 50 degrees is past the critical angle and reflects. Air into PMMA at 30 degrees bends to 19.61 degrees.
Teaching section
The source is a point at the origin. Lengths are millimeters. The air cavity radius is 2.4 mm, centered on the source, so the first hit is normal and the ray does not turn. The exit lens is a spherical cap of radius 3.55 mm, with its vertex 10.75 mm up and its rim 2.79 mm off axis. The flat exit lies at 9.4 mm, and the cap rises through that plane. The wall runs from (2.7, 0.85) mm to (6.16, 9.4) mm, 22.03 degrees off the axis. Incidence on that straight wall depends only on the launch angle.
What the fan does
Through 15 degrees the rays leave at the lens. The axial ray exits at 0 degrees, the 10 degree ray at 1.03 degrees, and the 15 degree ray at 4.79 degrees, so the sphere only collimates near the axis. The 20 degree ray misses the cap and the wall and leaves the flat exit at 30.64 degrees. From 40 to 50 degrees the wall reflects, with incidences 72.03, 67.03, and 62.03 degrees, and the rays leave at 6.06, 1.39, and 8.86 degrees. One straight cone does not equalize that band. At 70 degrees the wall incidence is 42.03, under 42.1552, and the ray leaks out at 25.98 degrees from the axis.
| Launch (deg) | Path | Wall incidence (deg) | Exit angle (deg) |
|---|---|---|---|
| 0 | Refracts at the lens | none | 0 |
| 10 | Refracts at the lens | none | 1.03 |
| 15 | Refracts at the lens | none | 4.79 |
| 20 | Misses the lens and the wall, refracts at the flat exit | none | 30.64 |
| 40 | Reflects at the wall, then leaves the flat exit | 72.03 | 6.06 |
| 45 | Reflects at the wall, then leaves the flat exit | 67.03 | 1.39 |
| 50 | Reflects at the wall, then leaves the flat exit | 62.03 | 8.86 |
| 70 | Refracts out through the wall | 42.03 | 25.98 |
What this section does not settle
A downlight still has an extended LED, often a cluster, plus Fresnel loss and a housing that can send light back into the optic. Those questions belong in a non-sequential model. Photopia, FRED, TracePro, and Zemax OpticStudio are the tools used for that work. This note is only the meridional split among refraction at the lens, reflection at the wall, and a ray that fails to reflect.