The formula
1/f = 1/o + 1/i
| Symbol | Quantity | Unit |
|---|---|---|
| f | Focal length | cm |
| o | Object distance | cm |
| i | Image distance | cm |
What it means
The reciprocal of the focal length equals the sum of the reciprocals of the object and image distances. Working in reciprocals looks awkward and is what makes the relationship so simple.
How to work it out by hand
- Take the reciprocal of the focal length
- Subtract the reciprocal of the object distance
- Take the reciprocal of the result for the image distance
What is worth knowing
The sign conventions carry the physics and are where the mistakes live: a positive focal length is a converging lens and a negative one diverges, while a negative image distance means the image is virtual — on the same side as the object, like the one in a magnifying glass. Optometrists work in dioptres, which is simply the reciprocal of the focal length in metres, so a +2 dioptre lens has a 50 cm focal length. That is also why prescriptions add so conveniently: reciprocals of focal lengths sum directly.