#spectroscopy

Optical-prism geometry as an API, computed locally and deterministically. The deviation endpoint computes the minimum deviation angle of a light ray passing through a prism of apex angle A and refractive index n, δ_min = 2·arcsin(n·sin(A/2)) − A, together with the symmetric angle of incidence and the internal refraction angle A/2 on each face — an equilateral prism (A = 60°) of crown glass (n = 1.5) deviates light by about 37.2°. The refractive-index endpoint inverts the spectrometer formula n = sin((A + δ_min)/2) / sin(A/2), the standard way a refractive index is measured from a prism’s apex angle and its measured minimum deviation. The dispersion endpoint computes the angular dispersion between two wavelengths from their refractive indices and the apex angle, and, given the three Fraunhofer indices n_F, n_C and n_D, the dispersive power ω = (n_F − n_C)/(n_D − 1) and the Abbe number V = 1/ω that quantify how strongly a glass spreads colours — crown glass has ω ≈ 0.017 and V ≈ 59. All angles are in degrees. Everything is computed locally and deterministically, so it is instant and private. Ideal for optics, spectroscopy, refractometry, photonics and physics-education app developers, lens-and-prism design tools, and lab software. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is prism geometry; for a single flat-surface refraction use a Snell’s-law API and for thin lenses a lens API.

api.oanor.com/prism-api

Quantum and atomic-physics maths as an API, computed locally and deterministically. The photoelectric endpoint applies Einstein's photoelectric equation, KE = hf − φ — from the incident light's wavelength or frequency and a metal's work function it gives the photon energy, whether electrons are emitted, their maximum kinetic energy, the threshold frequency and wavelength (f₀ = φ/h), the maximum electron speed and the stopping voltage. The bohr endpoint computes the Bohr-model energy level Eₙ = −13.606·Z²/n² eV and orbital radius rₙ = 0.529·n²/Z Å of a hydrogen-like atom, the ionisation energy, and — given a second level — the wavelength of the emitted or absorbed photon. The rydberg endpoint computes a spectral line's wavelength from the Rydberg formula, 1/λ = R·Z²·(1/n₁² − 1/n₂²), and names its series (Lyman, Balmer, Paschen …) and spectral region. Everything is computed locally and deterministically, so it is instant and private. Ideal for physics-education, spectroscopy, astronomy and science app developers, atomic-physics and spectral tools, and STEM teaching. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is quantum and atomic physics; for electromagnetic wavelength and photon energy use a wavelength API and for special relativity a relativity API.

api.oanor.com/quantum-api

Beer–Lambert spectroscopy maths as an API, computed locally and deterministically. The beer-lambert endpoint applies the law A = ε·c·l, where absorbance equals the molar absorptivity times the concentration times the optical path length: give any three of the four and it solves for the fourth (the path length defaults to the standard 1 cm cuvette when omitted), and it always reports the matching transmittance and percent transmittance. The transmittance endpoint converts between absorbance and transmittance in both directions, A = −log₁₀(T) and T = 10^(−A), and accepts a fraction or a percentage. The calibration endpoint reads a concentration off a linear calibration curve, A = slope·c + intercept, solving for the concentration from a measured absorbance or for the expected absorbance from a concentration. Units are whatever you supply consistently — for molar absorptivity in M⁻¹cm⁻¹, a path length in cm and absorbance dimensionless, the concentration comes out in molar. Everything is computed locally and deterministically, so it is instant and private. Ideal for analytical-chemistry and lab tools, spectrophotometer and assay apps, biotech and education software, and quality-control calculators. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is Beer–Lambert spectroscopy; for solution dilution and molarity use a dilution API and for chemical compound data use a chemistry API.

api.oanor.com/beerlambert-api