Lens Maker's / Thin Lens

This formula connects the three key distances in a thin lens setup: the focal length, the object distance, and the image distance. It comes from the geometry of how a converging or diverging lens bends rays so they meet, or appear to meet, at an image point. The signs matter because real and virtual images lie on opposite sides of the lens, so the equation is really a compact way to track lens direction and image formation.

Use it when you know two of the three lens quantities and need the third, especially in ray-diagram problems or simple optics calculations. It is most useful for thin lenses in school physics, camera/eyeglass-style lens questions, and image-position predictions.

• Using the wrong sign for u or v when the image is virtual or the object is on the opposite side of the lens
• Mixing up focal length with object distance and substituting the wrong quantity into f
• Forgetting to keep units consistent, such as combining cm and m in the same calculation