Mirror & Lens Equation Calculator

How it is calculated

The tool solves 1/di = 1/f − 1/do for the image distance, then m = −di / do. Here f is the focal length, do the object distance and di the image distance, all in one length unit (the unit cancels in the magnification).

Sign convention used: object distance must be positive; focal length is positive for a converging lens or concave mirror and negative for a diverging lens or convex mirror. A positive di is a real image, a negative di a virtual one. A negative m means inverted. Results show four decimals. No result is given when the object distance is zero or negative, the focal length is zero, or the object sits exactly at the focal point, where the image would be at infinity.

Common mistakes

• Entering a negative focal length for an ordinary magnifying glass or concave mirror. Those are positive; only diverging lenses and convex mirrors take a negative f.
• Placing the object exactly at the focal length and expecting a number. The image is at infinity there, so the tool gives no result.
• Reading a negative magnification as 'smaller'. The minus sign only means inverted; the size is the absolute value, so −2 is twice as large and upside down.
• Mixing units, such as f in centimetres and the object distance in metres. Use the same unit for both, and the image distance comes back in that unit.
• Treating a negative image distance as an error. It is a valid answer meaning a virtual image on the same side as the object.