Thin Lens Calculator
Find image distance and signed magnification for a thin lens and a real object. Distinguish real, virtual and focal-plane cases with a lens layout.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Use the thin-lens equation with a positive distance for a real object. A positive image distance is on the opposite side of the lens and forms a real image. A negative image distance is on the object side and forms a virtual image. Signed magnification determines orientation.
1/f=1/u+1/v; v=fu/(u−f); magnification m=−v/u
Worked example
With f=10 cm and u=30 cm, v=15 cm and m=−0.5: a real, inverted image at half the object height. For u=5 cm, v=−10 cm and m=2: a virtual, upright image. At u=f, emergent rays are parallel and the image is at infinity.
Assumptions and input details
Paraxial thin-lens model in one surrounding medium; use a real object and u>0. Converging focal length is positive and diverging focal length is negative. Nonzero lengths are limited to 1e−12–1e12 meters in magnitude. At u=f there is no finite image distance or finite magnification. Very close inputs can be sensitive to measurement and rounding. Horizontal layout positions use signed distances; arrow heights are schematic. Lens thickness, aberrations and full camera focusing mechanisms are not modeled.
References: OpenStax thin lenses and sign convention
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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