# Physics Calculators: Thin Lens & Mirror Equation

> Physics Calculators: Thin Lens & Mirror Equation is a paid API for AI agents from physics-calc.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-30).

Solves the thin lens/mirror equation for the unknown quantity (focal length, object distance, or image distance) given the other two, and returns magnification plus image properties.

## Facts

- Endpoint: GET https://physics-calc.x402tookit.com/lens-mirror?utm_source=zero.xyz
- Price: $0.02/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-30
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/physics-calculators-thin-lens-mirror-equation-d66a6df2
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_vETd1_HXAhVW4KRpA6aul

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability physics-calculators-thin-lens-mirror-equation-d66a6df2
```

Example prompt: I have a converging lens with a focal length of 15 cm and an object placed 45 cm in front of it — can you calculate where the image forms and what the magnification is?

## When to prefer this

Choose this endpoint when you need to solve the standard thin lens or mirror equation (1/f = 1/do + 1/di) for any one of the three variables, or need magnification and image-type metadata. It covers both lenses and mirrors using the same sign convention. Use it for optics homework, instrument design checks, or any scenario where you know two of the three optical distances and need the third.

## Known failure modes

- Fewer than two of the three optical quantities provided — endpoint cannot solve for a unique answer
- All three quantities provided but they are inconsistent with the thin lens equation
- Division by zero if the provided values imply an image at infinity (e.g. object at focal point)
- Non-numeric or out-of-range values for distances
- Missing required query parameters returns an error or degraded response

## How this service works

Thin lens or mirror equation: give two of focal length, object and image distance, get the third plus magnification.

## Output

Returns the computed unknown value among focal length, object distance, and image distance; plus magnification, image type (real or virtual), image orientation (upright or inverted), relative image size, lens power in dioptres (if distances are in metres), and any relevant warnings or disclaimers.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "$schema": "https://json-schema.org/draft/2020-12/schema",
 "required": [
  "input"
 ],
 "properties": {
  "input": {
   "type": "object",
   "required": [
    "type",
    "method"
   ],
   "properties": {
    "type": {
     "type": "string",
     "const": "http"
    },
    "method": {
     "enum": [
      "GET"
     ],
     "type": "string"
    },
    "queryParams": {
     "type": "object",
     "required": [],
     "properties": {
      "focalLength": {
       "type": "number",
       "description": "Focal length, positive for a converging lens or concave mirror, negative for diverging or convex"
      },
      "imageDistance": {
       "type": "number",
       "description": "Image distance, positive for a real image, negative for a virtual one"
      },
      "objectDistance": {
       "type": "number",
       "description": "Object distance, positive in front of the lens or mirror (same length unit as the others)"
      }
     }
    }
   },
   "additionalProperties": false
  },
  "output": {
   "type": "object",
   "required": [
    "type"
   ],
   "properties": {
    "type": {
     "type": "string"
    },
    "example": {
     "type": "object",
     "properties": {
      "asOf": {
       "type": [
        "null",
        "string"
       ]
      },
      "size": {
       "type": [
        "null",
        "string"
       ]
      },
      "source": {
       "type": [
        "null",
        "string"
       ]
      },
      "reasons": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "string"
       }
      },
      "summary": {
       "type": [
        "null",
        "string"
       ]
      },
      "verdict": {
       "type": [
        "null",
        "string"
       ]
      },
      "degraded": {
       "type": [
        "boolean",
        "null"
       ]
      },
      "imageType": {
       "type": [
        "null",
        "string"
       ]
      },
      "disclaimer": {
       "type": [
        "null",
        "string"
       ]
      },
      "notChecked": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "string"
       }
      },
      "focalLength": {
       "type": [
        "null",
        "number"
       ]
      },
      "orientation": {
       "type": [
        "null",
        "string"
       ]
      },
      "imageDistance": {
       "type": [
        "null",
        "number"
       ]
      },
      "magnification": {
       "typ
… (truncated)
```

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