Power of a Lens

A lens with a short focal length bends light through a bigger angle than one with a long focal length — it's 'more powerful' at converging or diverging light. This is captured directly in the power of a lens: P = 1/f, where f is in metres.

The unit of power is the dioptre (D). A lens with a focal length of exactly 1 metre has a power of 1 D. By convention, a convex lens has positive power, and a concave lens has negative power — this is exactly why an eyeglass prescription like '+2.0 D' tells you it's a convex lens (for hypermetropia), while '−2.5 D' tells you it's concave (for myopia).

When lenses are combined together in contact (as in cameras, microscopes, or an optician's testing frame), their powers simply add up algebraically: P = P₁ + P₂ + P₃ + .... This is far more convenient than adding focal lengths directly, which is why opticians always prescribe power rather than focal length.