Thin Lens Calculator

How it works

1. 1Enter the focal length f (positive for converging, negative for diverging) and the object distance dₒ, both in centimetres.
2. 2The calculator applies 1/f = 1/dₒ + 1/dᵢ, rearranged as dᵢ = (dₒ·f) ÷ (dₒ − f), to find the image distance.
3. 3Magnification m = −dᵢ ÷ dₒ is computed. Positive dᵢ = real image; negative = virtual. Negative m = inverted; positive = upright.

Use cases

• Designing camera lenses and projectors by predicting where the image forms.
• Solving optics homework on converging and diverging lenses.
• Understanding real vs virtual images from eyeglasses and magnifying glasses.

Frequently asked questions

What is the thin-lens equation?

1/f = 1/dₒ + 1/dᵢ, where f is focal length, dₒ object distance, and dᵢ image distance. Rearranged: dᵢ = (dₒ·f) ÷ (dₒ − f). With f = 10 cm and dₒ = 30 cm, dᵢ = 300 ÷ 20 = 15 cm.

What is the sign convention for focal length?

A converging (convex) lens has f > 0; a diverging (concave) lens has f < 0. Object distance dₒ is positive when the object is on the incoming-light side, the standard case.

How do I interpret the magnification?

m = −dᵢ ÷ dₒ. Negative m = inverted (real image, converging lens, dₒ > f); positive m = upright (virtual). |m| < 1 is smaller, |m| > 1 larger. The example (f = 10, dₒ = 30 → dᵢ = 15) gives m = −0.5: real, inverted, half size.