Solve the thin lens equation 1/f = 1/d₀ + 1/dᵢ (also the mirror equation) for focal length, object distance or image distance. The calculator also gives magnification, image height, whether the image is real or virtual and upright or inverted, and the lens power in dioptres.
Thin lens and mirror equations
Worked example
An object 30 cm from a converging lens with f = 10 cm: 1/dᵢ = 1/10 − 1/30 = 2/30, so dᵢ = 15 cm. Magnification = −15/30 = −0.5: a real, inverted image half the size, like a camera. Move the object inside the focal length (say 5 cm) and dᵢ = −10 cm: a virtual, upright image magnified 2×, like a magnifying glass.
Image rules for a converging lens
- Object beyond 2f → real, inverted, smaller (camera, eye).
- Object at 2f → real, inverted, same size.
- Between f and 2f → real, inverted, larger (projector).
- Inside f → virtual, upright, larger (magnifying glass).
Frequently asked questions
What is the thin lens equation?
1/f = 1/d₀ + 1/dᵢ, linking focal length, object distance and image distance. The same equation works for curved mirrors.
How do I calculate magnification?
m = −dᵢ / d₀, or image height ÷ object height. A negative value means the image is inverted.
What sign should focal length have?
Positive for converging (convex) lenses and concave mirrors, negative for diverging (concave) lenses and convex mirrors.
What does a negative image distance mean?
The image is virtual: it forms on the same side as the object and can’t be projected on a screen, as in a magnifying glass or a bathroom mirror.
Related tools
Free educational tool by HawkInc. Results are calculated in your browser and rounded for display; check critical work by hand or with a second method.