{"uid":"cap_vETd1_HXAhVW4KRpA6aul","slug":"physics-calculators-thin-lens-mirror-equation-d66a6df2","name":"Physics Calculators: Thin Lens & Mirror Equation","description":"Thin lens or mirror equation: give two of focal length, object and image distance, get the third plus magnification.","url":"https://physics-calc.x402tookit.com/lens-mirror?utm_source=zero.xyz","method":"GET","headers":{},"bodySchema":{"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":{"type":["null","number"]},"objectDistance":{"type":["null","number"]},"powerDioptresIfMetres":{"type":["null","number"]}}}}}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.02","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.02/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_5l4oIv30Nakj7tGqqyVJZ","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.02","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"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.","exampleAgentPrompt":"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?","exampleUseCases":[{"title":"Optics homework: find image distance","prompt":"For a concave mirror with a focal length of 20 cm and an object 60 cm in front of it, where does the image form and is it real or virtual?"},{"title":"Determine unknown focal length from experiment","prompt":"I set up a lens experiment and measured the object distance as 40 cm and the image distance as 60 cm — can you work out the focal length and the magnification?"},{"title":"Check if image is virtual for a diverging lens","prompt":"I have a diverging lens with focal length −25 cm and an object 50 cm away. What is the image distance, is the image real or virtual, and what's the magnification?"}],"resultDescription":"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.","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-30T00:35:49.420Z","isFirstParty":false,"canonicalSlug":"physics-calculators-thin-lens-mirror-equation-d66a6df2"}