Lens Magnification Calculator
Find the magnification of a lens and the image size from the object and image distances.
How it works
m = −dᵢ ÷ dₒ = hᵢ ÷ hₒ · image height hᵢ = m · hₒ
Linear magnification compares image size to object size and equals minus the ratio of image distance to object distance. The sign carries the geometry: a negative magnification means a real, inverted image (as a camera or projector forms), while a positive value means an upright, virtual image (as a magnifying glass gives). A magnitude above 1 enlarges the object; below 1 shrinks it.
Worked example
An object sits 0.30 m from a lens that forms its image 0.60 m away. m = −0.60/0.30 = −2. A 5 cm-tall object therefore produces an image −2 × 5 = −10 cm tall — twice as large and inverted.
Sources: Magnification — Wikipedia
Frequently asked questions
What does a negative magnification mean?
The image is inverted (upside down) relative to the object, which happens for the real images formed by a converging lens when the object is beyond the focal point. A positive magnification means the image is upright.
How is this different from the thin-lens equation?
The thin-lens equation (1/f = 1/dₒ + 1/dᵢ) relates the distances to the focal length; magnification then compares the sizes. Use the thin-lens calculator to find dᵢ first if you only know the focal length.
What sign convention is used?
Distances measured on the outgoing-light side are positive. A positive image distance is a real image on the far side of the lens; the magnification m = −dᵢ/dₒ then comes out negative for those real images.
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This calculator is for educational purposes. Double-check important results before acting on them.