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Thin Lens Calculator

Calculate image distance and magnification from focal length and object distance using the thin-lens sign convention.

Uses a common convention: positive f for converging lenses, negative f for diverging, and positive dₒ for a real object.

How to use

The thin-lens equation links focal length, object distance and image distance. The signs of image distance and magnification help classify the image.

  1. Enter signed focal length f.
  2. Enter positive dₒ for a real object.
  3. Calculate dᵢ.
  4. Review m and image type.

How it is calculated

1/f=1/dₒ+1/dᵢ; m=−dᵢ/dₒ

Example

A converging lens with f=10 cm and object at 30 cm gives dᵢ=15 cm and m=−0.5: a real inverted image.

Important notes

Optics sign conventions vary by textbook; use the convention stated here consistently when comparing answers.

Frequently asked questions

What does negative dᵢ mean?

A virtual image in this convention.

What does negative m mean?

An inverted image.

What happens at dₒ=f?

The ideal image distance tends to infinity, so no finite result is returned.