Enter any 2 of focal length, object distance and image distance.
About this tool
Thin Lens & Mirror Equation Calculator is a free, in-browser optics tool. Pick lens or mirror mode, enter any two of focal length f, object distance dₒ and image distance dᵢ, and it solves for the third, then reports the magnification and describes the image. Everything is computed locally in your browser.
It applies the thin lens / mirror equation 1/f = 1/dₒ + 1/dᵢ, rearranged as f = dₒ·dᵢ/(dₒ + dᵢ), dᵢ = f·dₒ/(dₒ − f) or dₒ = f·dᵢ/(dᵢ − f). The magnification is m = −dᵢ/dₒ, and the image height is hᵢ = m·hₒ. For a mirror it also reports the radius of curvature R = 2f.
Using the standard sign convention, a positive image distance means a real, inverted image and a negative one means a virtual, upright image; |m| > 1 is enlarged and |m| < 1 is reduced. Enter distances in centimetres (any consistent length unit works) and read off the classification instantly.
Frequently asked questions
What equation is used?
The thin lens / mirror equation 1/f = 1/dₒ + 1/dᵢ. Given two of the three quantities the tool algebraically solves for the missing one, then computes magnification m = −dᵢ/dₒ.
What sign convention does it follow?
The standard convention: a positive image distance dᵢ gives a real, inverted image; a negative dᵢ gives a virtual, upright image. A positive focal length is a converging lens or concave mirror, a negative one is diverging or convex.
How is the image classified as enlarged or reduced?
By the absolute magnification |m| = |dᵢ/dₒ|. If |m| is greater than 1 the image is enlarged, if less than 1 it is reduced, and exactly 1 means it is the same size as the object.
How is the mirror radius of curvature found?
For a spherical mirror the focal length is half the radius, so R = 2f. The tool shows this in mirror mode. All optics math runs locally; nothing is uploaded.
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