Thin lens equation calculator
Enter the focal length (positive for converging, negative for diverging) and the object distance to see where the image forms, its size and orientation.
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How to use it
- Enter focal length (negative for diverging) and object distance.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
1 / f = 1 / dₒ + 1 / dᵢ, so dᵢ = 1 / (1 / f − 1 / dₒ), and magnification m = −dᵢ / dₒ.
Example
Inputs: Focal length (negative for diverging) = 10 cm, Object distance = 30 cm. Result: Image distance: 15 cm; Magnification: -0.5 ×; Image type: Real (behind the lens).
Limits and caveats
- It assumes a thin lens and rays near the axis, with no aberrations or lens thickness.
- It uses the common sign convention: a positive image distance means a real image on the far side of the lens.
Questions about this tool
When is a converging lens image virtual?
When the object is closer to the lens than its focal point, as with a magnifying glass.
Does it work for concave mirrors?
Yes. The same equation applies to spherical mirrors, with focal length equal to half the radius of curvature.
What does a negative magnification mean?
The image is upside down relative to the object.