Thin Lens Equation Calculator
Solves the thin lens equation in any direction.
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The formula
1/f = 1/d₀ + 1/dᵢ m = −dᵢ ÷ d₀
A thin lens, with distances measured from its centre and rays close to the axis. This uses the real-is-positive convention: f is positive for converging, and dᵢ is positive for a real image on the far side. Some textbooks use a different convention, so check the signs against yours.
What to watch out for
Thick lenses and wide rays need more than this equation, which is why camera lenses use several elements.
Frequently Asked Questions
Where does a 10 cm lens image an object at 30 cm?
15 cm on the far side, inverted, at a magnification of -0.5.
What about an object inside the focal length?
At 5 cm, the image distance is -10 cm. The negative sign marks a virtual image, as in a magnifying glass, with a magnification of 2.