Lens Equation Calculator
Where a lens forms an image and how large it is — from the focal length and the object distance, with whether the image is real or virtual.
The thin lens equation is 1÷f = 1÷u + 1÷v, where f is the focal length, u the object distance and v the image distance.
How the lens equation calculator works
The thin lens equation is 1÷f = 1÷u + 1÷v, where f is the focal length, u the object distance and v the image distance. Magnification is −v÷u, and the sign carries the meaning: a negative magnification means the image is inverted, a negative image distance means it forms on the same side as the object and is virtual — you can see it through the lens but cannot project it onto a screen.
The interesting case is an object inside the focal length. A converging lens then produces an upright, magnified, virtual image, which is exactly what a magnifying glass does.
Formula: 1/f = 1/u + 1/v; magnification = −v ÷ u
Worked examples
| Inputs | Image distance | Note |
|---|---|---|
| A 10 cm lens, object at 30 cm | 15 cm | image at 15 cm, inverted and half size |
| A magnifying glass — object inside the focus | -10 cm | virtual, upright, twice the size |
| A diverging lens | -10 cm | always virtual and reduced |
FAQFrequently asked questions
What is the thin lens equation?
1÷f = 1÷u + 1÷v, relating focal length, object distance and image distance.
What does a negative image distance mean?
The image is virtual — it forms on the same side as the object and cannot be projected onto a screen, only viewed through the lens.
Why is magnification negative?
A negative magnification means the image is inverted. Positive means upright.
How does a magnifying glass work?
The object sits inside the focal length, which produces an upright, enlarged, virtual image.
What is lens power in dioptres?
The reciprocal of the focal length in meters — a 50 cm lens is 2 dioptres. Spectacle prescriptions use it.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Institute of Standards and Technology — the US measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.