interface op• Data kinds: none → measurement (an op determined by its arguments alone — it takes no image or data input)
• Call: import fullseye as fs; fs.ledger.critical_angle_deg(n1=1.5, n2=1.0) -> 'float' (to call the implementation directly, import glassmirror; glassmirror.critical_angle_deg(n1=1.5, n2=1.0) -> 'float'; from the registry, opsoptics.get("critical_angle_deg"))
Critical angle of total internal reflection [deg] = asin(n2/n1). Raises ValueError unless n1 > n2 (it does not exist otherwise).
It only occurs when light leaves glass into air. The design value of total-internal-reflection faces in optical fibres and prisms.
Formula: degrees(asin(n2 / n1)). If the angle of incidence (angle from the normal) is at or above this, no refracted light exists and total internal reflection occurs. Examples: N-BK7 equivalent n1 = 1.5 → air n2 = 1.0 gives 41.8 degrees, water n1 = 1.333 → air gives 48.6 degrees.
• n1: refractive index of the side the light leaves (denser medium), n2: refractive index of the side it enters (less dense medium). Both positive finite scalars (converted with float(), so arrays are not accepted).
• n1 <= n2 has no critical angle, so ValueError (no fudging with NaN or 90 degrees).
• Returns: float [deg], (0, 90).
• No wavelength dependence. To evaluate including dispersion, pass an n1 obtained from the glass's Sellmeier equation (prism_min_deviation_deg does that internally).
For the behaviour when a cos_i at or beyond the critical angle is passed to fresnel_dielectric, see that function. The Brewster angle (the angle where the reflection of p polarization becomes 0) is brewster_angle_deg.
Every optics op validates its input before computing (nothing slips through silently):
• Units are baked into the argument name — _mm / _um / _deg / _mrad. Confusing mm with µm does not crash; it yields a plausible-looking wrong answer, so the name prevents it. Nothing here guesses the unit from the magnitude.
• Strings raise ValueError — float('50') succeeds, so an unparsed configuration value would slip through as a length (measured: thin_lens('50', '200') returned a plausible 66.667 mm). bool is refused too, as the implicit promotion True == 1.
• complex / masked arrays raise ValueError (real-valued slots only; silently dropping the imaginary part or peeling off the mask is refused). NaN/Inf raises ValueError on every input.
• Division by zero and its relatives are refused by name: focal length 0, radius of curvature 0, refractive index <= 0, a fully opaque aperture (all zeros, so the normalisation is 0/0), a PSF whose sum is <= 0, a Stokes vector with S0 = 0, and an object sitting at the front focal point (the image is at infinity).
• Only two ops return a non-finite value, and both state it as a contract: depth_of_field returns far_mm = inf beyond the hyperfocal distance (that is what the hyperfocal distance means), and gaussian_beam returns wavefront_radius_mm = inf at the waist (the radius of curvature of a plane wavefront). Both also return a finite companion (far_is_infinite / curvature_per_mm). Any other silent NaN/Inf is detected internally and raises ValueError — "float64 overflowed" and "the answer is infinite" are different claims, so the first is never returned wearing the face of the second.
• Size caps: generated grids are capped by optics.MAX_GRID (4096); supplied fields/PSFs/apertures by optics.MAX_FIELD_ELEMENTS (2^24); ABCD element chains by optics.MAX_SYSTEM_ELEMENTS (1024); Zernike by MAX_ZERNIKE_TERMS (512) / MAX_ZERNIKE_ORDER (40) / MAX_ZERNIKE_BASIS (2^25). This closes, fail-closed, the paths where a small argument triggers a huge internal allocation (measured: n_max=40 × 4096² needs 108 GB).
• Physically impossible states are refused too: a Stokes vector with degree of polarisation > 1, negative transmittance, negative intensity, and invalid Zernike indices such as n-|m| odd.
• 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.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• glass_and_mirror_optics — py -3.11 examples/glass_and_mirror_optics.py
measurement as input)—
interface)fresnel_dielectric · fresnel_conductor · brewster_angle_deg
*Provenance: glassmirror.py — OPTICS 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.