#optics

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

Angular-size astronomy and optics maths as an API, computed locally and deterministically. The angular-size endpoint computes the angular diameter an object subtends, δ = 2·arctan(d/(2D)), from its physical size and its distance, returning the angle in radians, degrees, arcminutes and arcseconds, along with the small-angle approximation δ ≈ d/D — the Sun and Moon are each about half a degree (31 arcminutes) across. The distance endpoint inverts the relation, D = d/(2·tan(δ/2)), to give an object's distance from its known true size and its measured angular size, the basis of the standard-ruler distance method. The object-size endpoint computes an object's physical diameter, d = 2·D·tan(δ/2), from its distance and angular size. Size and distance use any one consistent unit, and angles may be given in radians, degrees, arcminutes or arcseconds. Everything is computed locally and deterministically, so it is instant and private. Ideal for astronomy, telescope, astrophotography, surveying and optics app developers, field-of-view and rangefinding tools, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is angular size; for stellar magnitude and parallax distance use a star-magnitude API and for sidereal time a sidereal API.

api.oanor.com/angularsize-api

Optical-fibre photonics maths as an API, computed locally and deterministically. The numerical-aperture endpoint computes a step-index fibre's numerical aperture NA = √(n1² − n2²) from the core and cladding refractive indices, the acceptance angle θa = arcsin(NA) — the half-angle of the cone of light the fibre can capture — the full acceptance cone and the relative index difference Δ = (n1 − n2)/n1. The v-number endpoint computes the normalized frequency V = 2π·a·NA/λ from the core radius, the numerical aperture (or the indices) and the wavelength, classifies the fibre as single-mode when V is below the 2.405 cutoff or multimode above it, and gives the cutoff wavelength for single-mode operation. The modes endpoint estimates the number of guided modes — about V²/2 for a step-index fibre and V²/4 for a graded-index one — and confirms single-mode operation below the cutoff. Core radius and wavelength are in metres (1310 nm = 1.31×10⁻⁶ m) and refractive indices are dimensionless. Everything is computed locally and deterministically, so it is instant and private. Ideal for telecom, photonics, datacenter, sensor and laser app developers, fibre-link and waveguide-design tools, and optics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is optical-fibre guiding; for thin lenses and mirrors use a lens API and for refraction at a surface a Snell API.

api.oanor.com/fiber-api

Gaussian-beam laser-optics maths as an API, computed locally and deterministically. The beam endpoint propagates a Gaussian beam from its wavelength and waist radius: the Rayleigh range z_R = π·w₀²/λ and depth of focus, the divergence half- and full-angle θ = λ/(π·w₀), and — for a given distance — the beam radius and diameter w(z) = w₀·√(1+(z/z_R)²); an optional M² beam-quality factor scales it for real beams. The focus endpoint computes the diffraction-limited focused spot of a lens, w_f = λ·f/(π·w_in), with the depth of focus and the f-number, so you can size the spot a lens will deliver. The irradiance endpoint turns a beam power and spot size into the beam area and the average and on-axis peak irradiance (power density) in W/m² and W/cm². Wavelengths are in nanometres, sizes in millimetres or micrometres, distances in metres and power in watts. Everything is computed locally and deterministically, so it is instant and private. Ideal for photonics, laser-engineering, materials-processing and optics app developers, beam-delivery and laser-safety tools, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is Gaussian-beam laser optics; for refraction use a Snell API and for thin-lens imaging a lens API.

api.oanor.com/laser-api

Optical resolution by the Rayleigh criterion as an API, computed locally and deterministically. The angular endpoint gives the smallest angle two points can be apart and still be told apart through a circular aperture, θ = 1.22·λ/D — the diffraction limit set by the wavelength and the aperture diameter — in radians, degrees, arcminutes and arcseconds (a 100 mm telescope resolves about 1.4 arcseconds in green light), and solves the aperture needed for a target resolution. The distance endpoint turns that angle into a real separation at a distance, s = θ·L = 1.22·λ·L/D — how far apart two objects must be to be resolved at a given range. The microscope endpoint computes resolving power from the numerical aperture: the Rayleigh limit d = 0.61·λ/NA and the Abbe limit d = λ/(2·NA), with NA = n·sin(θ) from a refractive index and half-angle, and the maximum useful magnification. Wavelength defaults to 550 nm (visible) and can be set in metres, nanometres or micrometres. Everything is computed locally and deterministically, so it is instant and private. Ideal for astronomy, telescope and binocular tools, microscopy and imaging-system design, camera and optics apps, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is the diffraction-limited resolving power; for thin-lens imaging use a lens API and for slit and grating diffraction use a diffraction API.

api.oanor.com/resolution-api

Thin-lens and mirror imaging optics as an API, computed locally and deterministically. The lens endpoint applies the thin-lens equation, 1/f = 1/do + 1/di, and solves for whichever of the focal length, object distance or image distance you leave out, then returns the magnification m = −di/do and the full description of the image — real or virtual, upright or inverted, enlarged, reduced or the same size — and whether the lens is converging (convex, f > 0) or diverging (concave, f < 0). The mirror endpoint does the same for a spherical mirror, taking the focal length or the radius of curvature (f = R/2), classifying it as concave or convex and describing the image. The power endpoint converts between focal length in metres and optical power in diopters, D = 1/f, and combines several thin lenses placed in contact by adding their powers, D_total = ΣD, returning the combined focal length. Distances use whatever consistent unit you supply. Everything is computed locally and deterministically, so it is instant and private. Ideal for physics and optics-education tools, lens and optical-system design, eyewear and vision apps, and photography learning. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is geometric-optics imaging; for Snell's-law refraction angles use a Snell API and for camera depth of field and field of view use a photography API.

api.oanor.com/lens-api

Snell's-law refraction optics as an API, computed locally and deterministically. The refraction endpoint applies Snell's law, n1·sin(θ1) = n2·sin(θ2): from the refractive indices of two media (given directly or by material — vacuum, air, water, glass, diamond and more) and the angle of incidence it returns the angle of refraction, or solves for the incidence angle from a refraction angle; when light passes into a less dense medium beyond the critical angle it reports total internal reflection instead of a refracted ray. The critical-angle endpoint gives the threshold for total internal reflection, θc = asin(n2/n1) for n1 > n2 — the principle behind optical fibres — defaulting the exit medium to air. The speed endpoint gives the speed of light in a medium, v = c/n, as a fraction of c, and — with a vacuum wavelength — the shorter wavelength inside the medium (the frequency is unchanged). Angles are in degrees, wavelengths in nanometres. Everything is computed locally and deterministically, so it is instant and private. Ideal for optics and photonics tools, fibre-optic and lens-design apps, photography and physics education, and AR/VR and rendering software. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is Snell's-law refraction; for camera depth of field and field of view use a photography API.

api.oanor.com/snell-api

Camera and optics maths as an API. The depth-of-field endpoint computes the near and far limits of sharp focus, the total depth of field and the hyperfocal distance from a focal length, aperture and focus distance, using the circle of confusion for your sensor format — full-frame, APS-C, Micro Four Thirds, 1-inch, medium format, Super 35 and more, or your own value. The field-of-view endpoint gives the horizontal, vertical and diagonal angle of view for a focal length on a given sensor, plus the crop factor and the 35 mm-equivalent focal length. The exposure endpoint computes the exposure value (EV) from aperture, shutter speed and ISO, and can also solve for the shutter speed or aperture that hits a target EV. Everything is computed locally and deterministically, so it is instant and private. Ideal for photography and videography apps, camera and lens tools, focus-stacking and landscape planning, and teaching exposure and optics. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 4 endpoints. This computes camera optics; for reading EXIF metadata from photo files use an EXIF API.

api.oanor.com/photography-api