Lensmaker's equation API

Computes focal length and dioptric power of a thin lens from its refractive index and two surface radii via 1/f = (n/n_med − 1)(1/R1 − 1/R2), with optional surrounding-medium index. Answers 'What focal length results from these radii?', 'How many dioptres is this lens?'.

Price$0.04per request

MethodPOST

Route/v1/engineering/lensmaker

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

opticslensmakerlensdioptrefocal-lengthrefractive-indexcurvaturephysics

API URLhttps://x402.hexl.dev/v1/engineering/lensmaker

Integration docs

Example request

{
  "refractiveIndex": 1.5,
  "radius1M": 0.2,
  "radius2M": -0.2
}

Example response

{
  "focalLengthM": 0.2,
  "powerDioptres": 5,
  "relativeIndex": 1.5,
  "lensType": "converging",
  "interpretation": "Converging lens, f = 0.2 m, power = 5 D."
}

Input schema

{
  "type": "object",
  "required": [
    "refractiveIndex",
    "radius1M",
    "radius2M"
  ],
  "properties": {
    "refractiveIndex": {
      "type": "number",
      "description": "Lens material refractive index",
      "examples": [
        1.5
      ]
    },
    "radius1M": {
      "type": "number",
      "description": "First surface radius of curvature (m)",
      "examples": [
        0.2
      ]
    },
    "radius2M": {
      "type": "number",
      "description": "Second surface radius of curvature (m)",
      "examples": [
        -0.2
      ]
    },
    "mediumIndex": {
      "type": "number",
      "description": "Surrounding medium index (default 1)",
      "examples": [
        1
      ]
    }
  }
}

Output schema

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