optics op• Data kinds: measurement → measurement
• Call: import fullseye as fs; fs.ledger.snell_angle(theta_i_deg, eta1=1.0, eta2=1.5) (to call the implementation directly, import match3d; match3d.snell_angle(theta_i_deg, eta1=1.0, eta2=1.5); from the registry, ops3d.get("snell_angle"))
Angle of incidence (deg) → angle of refraction (deg). n1 sinθi = n2 sinθt. Beyond the critical angle it is NaN (total internal reflection).
Returns θt = arcsin((eta1/eta2)·sin θi) in degrees (float). theta_i_deg is a real scalar (arrays and None raise ValueError). The sign is preserved (a negative angle of incidence gives a negative refraction angle). If |(eta1/eta2) sin θi| > 1, nan (total internal reflection; occurs only when eta1 > eta2). The critical angle is degrees(arcsin(eta2/eta1)). If eta1 == eta2, the angle of incidence unchanged. To bend as vectors use refract (for batches glassmirror.refract_rays; refract returns None for the whole batch if even 1 ray has TIR); for reflectance use fresnel_reflectance(cos(radians(θi))). There is no entry point that bends an array of angles at once —— when thinking in terms of speed rather than refractive index, as in acoustics, pass eta = 1/c (n ∝ 1/c).
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• snell_refraction — py -3.11 examples_3d/snell_refraction.py
measurement as input)vol_gaussian_psf · fuse_to_voxel · fresnel_reflectance
optics)reflect · refract · fresnel_reflectance · normal_from_reflection
*Provenance: match3d.py — 3D operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.