Thick spherical lens

OpticalSetup intersects each ray with the two drawn plane or exact circular-arc faces, applies vector Snell refraction at each boundary, tracks the ray while it is inside the glass, and supports total internal reflection. Focal length and back focal distance are derived paraxial summaries of that geometry at the 587.6 nm d line; the tracer never aims rays at either reported point. Spherical and chromatic aberration therefore emerge from the traced surfaces and wavelength-dependent index rather than being drawn as an effect.

In the default left-to-right orientation, positive radius means the centre of curvature lies toward local +x. A biconvex singlet is therefore R₁ > 0 and R₂ < 0; R = 0 makes that face plane. The Shape readout names the resulting profile so the sign convention can be checked directly.

The selectable N-BK7, fused-silica, N-SF5, and N-SF11 models use each glass's published d-line index and Abbe number^[4]. If a requested radius is too small for the clear aperture, or the centre thickness would make the faces cross, the inspector shows the exact constructible geometry the tracer uses instead of hiding the adjustment.

Two glass bodies must not touch. The tracer ignores any intersection closer than 0.05 mm along a ray, so a pair of coincident interfaces loses one of them and the ray wrongly exits into air. Building a cemented doublet by pushing two singlets together therefore gives an answer that is not obviously broken, just wrong — measured on a crown+flint pair, the focus lands 4 mm short with one interface silently skipped. Leave at least 0.06 mm between them and both interfaces come back; the inspector warns when anything is closer. That gap costs about 0.1% of the back focal distance, and a real cemented group is a 10–20 µm layer of not-quite-glass anyway. Nested or fully overlapping bodies are a separate unsupported case — boundaries are never merged.