Snell's law & critical angle API

Applies Snell's law n1·sinθ1 = n2·sinθ2 to find the refraction angle, detects total internal reflection, and reports the critical angle when passing into a less-dense medium. Answers 'At what angle does light refract?', 'Is there total internal reflection here?'.

Price$0.04per request

MethodPOST

Route/v1/engineering/snell-refraction

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

opticssnellrefractioncritical-angletotal-internal-reflectionrefractive-indexwavesphysics

API URLhttps://x402.hexl.dev/v1/engineering/snell-refraction

Integration docs

Example request

{
  "index1": 1,
  "index2": 1.33,
  "incidentAngleDeg": 30
}

Example response

{
  "totalInternalReflection": false,
  "refractionAngleDeg": 22.0824,
  "criticalAngleDeg": null,
  "bending": "toward normal (into denser medium)",
  "interpretation": "Refracted ray at 22.082° from normal (n1=1 → n2=1.33)."
}

Input schema

{
  "type": "object",
  "required": [
    "index1",
    "index2",
    "incidentAngleDeg"
  ],
  "properties": {
    "index1": {
      "type": "number",
      "description": "Refractive index of incident medium",
      "examples": [
        1
      ]
    },
    "index2": {
      "type": "number",
      "description": "Refractive index of transmitting medium",
      "examples": [
        1.33
      ]
    },
    "incidentAngleDeg": {
      "type": "number",
      "description": "Angle of incidence from normal (0–90°)",
      "examples": [
        30
      ]
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}