How this calculator works
The thin-lens approximation treats refraction as occurring in one plane. A real object has positive distance. A converging lens has positive focal length and a diverging lens has negative focal length. Real images opposite the object are positive, while virtual images on the object side are negative. At the focal point the image is at infinity, so no finite image distance is returned. The paraxial model neglects aberrations.
Formula
1/f = 1/do + 1/di; m = -di/do. di = f do/(do - f).
Worked example
A 300 mm object distance with +100 mm focal length gives a +150 mm image distance and magnification -0.5. The image is real, inverted and half as tall.
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Frequently asked questions
What do negative image distances mean?
The image is virtual: rays appear to come from its location rather than meeting there.
Why is an object at the focal point rejected?
The outgoing rays are parallel and the image distance is infinite.
What does the sign of magnification tell me?
A negative value indicates an inverted image, while a positive value indicates an upright image.