Thin Lens Equation

The thin lens equation links three distances in a lens system: how far the object is from the lens, where the image forms, and the lens’s focal length. It comes from the geometry of light rays refracted by an ideal thin lens, where ray paths through the lens are treated as if bending happens at a single plane. When any two of these quantities are known, the third can be calculated, which is why the formula is so useful in imaging and optics.

Use this when predicting where a sharp image will form for a camera, projector, or microscope objective, or when finding the focal length of a lens from measured object and image distances. It is most appropriate for thin lenses and paraxial rays, where the lens is small compared with the object and image distances.

• Mixing up object distance and image distance, especially when using different sign conventions
• Forgetting to use the same units for f, u, and v
• Treating the formula as exact for thick lenses or very close-up cases where the thin-lens approximation breaks down