Thin Lens Calculator
Calculate thin lens instantly in your browser — the published formula, worked locally with no data sent anywhere.
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What this tool does
Calculate thin lens instantly in your browser — the published formula, worked locally with no data sent anywhere. Sign convention: distances in front of the lens (real side) are positive for images; converging lenses have positive f. The lens is treated as thin and paraxial (rays near the axis).
How to use the Thin Lens Calculator
- Enter or select focal length (cm, + converging / − diverging).
- Enter or select object distance (cm).
- Read the calculated result; change any measurement to compare alternatives.
Formula
thin-lens equation: 1/f = 1/dₒ + 1/dᵢ, so image distance dᵢ = 1 / (1/f − 1/dₒ); lateral magnification m = −dᵢ/dₒ (negative = inverted).
- fl
- Focal length (cm, + converging / − diverging)
- dob
- Object distance (cm)
Sign convention: distances in front of the lens (real side) are positive for images; converging lenses have positive f. The lens is treated as thin and paraxial (rays near the axis).
Worked example
For thin lens calculator, the following measurements illustrate the exact method: Focal length (cm, + converging / − diverging): 10; Object distance (cm): 30.
Inputs
- Focal length (cm, + converging / − diverging)10
- Object distance (cm)30
Result
- Image distance (cm)15
- Magnification (×)-0.5
- Image typeReal (forms on a screen, opposite side of the lens)
- OrientationInverted
- SizeReduced
Results explained
- Image distance (cm)
- Image distance (cm) from the formula above. Sign convention: distances in front of the lens (real side) are positive for images; converging lenses have positive f. The lens is treated as thin and paraxial (rays near the axis).
- Magnification (×)
- Magnification (×) from the formula above. Sign convention: distances in front of the lens (real side) are positive for images; converging lenses have positive f. The lens is treated as thin and paraxial (rays near the axis).
- Image type
- Image type from the formula above. Sign convention: distances in front of the lens (real side) are positive for images; converging lenses have positive f. The lens is treated as thin and paraxial (rays near the axis).
- Orientation
- Orientation from the formula above. Sign convention: distances in front of the lens (real side) are positive for images; converging lenses have positive f. The lens is treated as thin and paraxial (rays near the axis).
- Size
- Size from the formula above. Sign convention: distances in front of the lens (real side) are positive for images; converging lenses have positive f. The lens is treated as thin and paraxial (rays near the axis).
Frequently asked questions
thin-lens equation: 1/f = 1/dₒ + 1/dᵢ, so image distance dᵢ = 1 / (1/f − 1/dₒ); lateral magnification m = −dᵢ/dₒ (negative = inverted).
Sign convention: distances in front of the lens (real side) are positive for images; converging lenses have positive f. The lens is treated as thin and paraxial (rays near the axis).
Every field is labelled with its unit — enter values in exactly the labelled unit and read the result in the labelled output unit. Fields with a unit symbol also support the site-wide imperial/metric switch, which converts before the formula runs.
It uses double-precision arithmetic and the published constants and formulas named on this page. The last displayed digit may be rounded, and real conditions can differ from the idealized model described in the assumptions.
Yes. Every calculation runs entirely in your browser; nothing you enter is uploaded, stored or shared.