Thin lens / mirror equation API

Solves the thin-lens/spherical-mirror equation 1/f = 1/do + 1/di for whichever of focal length, object or image distance is missing, plus magnification and real/virtual + upright/inverted classification with sign conventions handled. Answers 'Where does a lens form the image?', 'Is the image real, inverted, and magnified?'.

Price$0.04per request

MethodPOST

Route/v1/engineering/thin-lens

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

opticslensmirrorthin-lensfocal-lengthmagnificationimagingphysics

API URLhttps://x402.hexl.dev/v1/engineering/thin-lens

Integration docs

Example request

{
  "focalLengthM": 0.1,
  "objectDistanceM": 0.3
}

Example response

{
  "focalLengthM": 0.1,
  "objectDistanceM": 0.3,
  "imageDistanceM": 0.15,
  "magnification": -0.5,
  "imageType": "real",
  "orientation": "inverted",
  "relativeSize": "reduced",
  "interpretation": "Image is real, inverted, reduced (|m| = 0.5)."
}

Input schema

{
  "type": "object",
  "properties": {
    "focalLengthM": {
      "type": "number",
      "description": "Focal length in metres (>0 converging, <0 diverging)",
      "examples": [
        0.1
      ]
    },
    "objectDistanceM": {
      "type": "number",
      "description": "Object distance in metres",
      "examples": [
        0.3
      ]
    },
    "imageDistanceM": {
      "type": "number",
      "description": "Image distance in metres",
      "examples": [
        0.15
      ]
    }
  },
  "description": "Provide exactly two of the three distances."
}

Output schema

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