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Thin Lens Calculator

Solve the thin lens equation.

Result

15.00 cm
-0.50×

How it is calculated

The thin lens equation is 1/f = 1/dₒ + 1/dᵢ, so the image distance is dᵢ = 1 / (1/f − 1/dₒ). Focal length f and object distance dₒ are both entered in the same unit; the results are labelled in cm, so use centimetres. Magnification is m = −dᵢ / dₒ. A positive dᵢ means a real image on the far side of the lens, and a negative value means a virtual image on the object's side. A negative m means the image is inverted. A negative f describes a diverging lens. If f or dₒ is zero, or if the object sits exactly at the focal point, there is no result because the image would be at infinity.

Worked example

A converging lens with f = 10 cm and an object 30 cm away. 1/f − 1/dₒ = 0.1 − 0.0333 = 0.0667, so dᵢ = 1 / 0.0667 = 15.00 cm, a real image. Magnification m = −15 / 30 = -0.50×, which means the image is inverted and half the size of the object.

Try this example →

Common mistakes

  • Mixing units, such as the focal length in millimetres and the distance in centimetres.
  • Placing the object at exactly the focal length: the rays leave parallel and no image forms, so the tool returns nothing.
  • Ignoring the sign: a negative image distance means a virtual image, not a mistake.
  • Entering a positive focal length for a diverging lens; it needs a negative value.
  • Using the formula for a thick lens or a lens system, where the thin lens assumption fails.

About this calculator

This calculator solves the thin lens equation, 1/f = 1/dₒ + 1/dᵢ, for image distance given a focal length and object distance, and also computes magnification as −dᵢ/dₒ, telling you whether the resulting image is enlarged, reduced, upright or inverted.

It's used in optics coursework, and by photographers and camera designers reasoning about focal length, lens focus distance and image size, as well as anyone working through problems involving magnifying glasses, projectors or simple telescopes.

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