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Power of a Lens

Simple Explanation

A lens's power measures how strongly it bends (converges or diverges) light, defined as the reciprocal of its focal length. Power is measured in dioptres (D) — a more powerful lens has a shorter focal length.

Why Do We Need It?

Lens power is the practical unit used by opticians when prescribing eyeglasses and contact lenses, and is essential for combining multiple lenses in optical instruments.

Formula

Power of a Lens

P = 1/f

A lens's power measures how strongly it converges (or diverges) light — a shorter focal length means a more powerful lens.

P
— Power of the lens, in dioptres (D), where 1 D = 1 m⁻¹
f
— Focal length of the lens, in metres (positive for converging, negative for diverging)

When to use it: Use to find the optical power of a lens (as prescribed for glasses, for instance) from its focal length, or vice versa.

Worked Example

Finding a lens's power

A converging lens has a focal length of 0.25 m. Find its power.

    Why Does This Work?

    A shorter focal length means light converges to a focus point closer to the lens, which requires stronger (more dramatic) bending of the light rays — defining power as the reciprocal of focal length directly captures this: smaller f gives larger P, matching the intuition that a 'more powerful' lens bends light more strongly.

    Real-Life Example

    Eyeglass prescriptions

    An eyeglass prescription specifies lens power in dioptres, such as -2.5 D for short-sightedness.

    Opticians use dioptres directly because lens powers ADD when lenses are combined (unlike focal lengths, which do not simply add) — this makes dioptres the practical unit for prescribing and combining corrective lenses.

    Practice

    A lens has a focal length of 0.5 m. Find its power.

    Easy
    D

    Common mistake

    Forgetting to convert focal length to METRES before calculating power — dioptres are specifically defined using focal length in metres; using centimetres directly gives a result off by a factor of 100.

    Quick Review

    • P = 1/f: power is the reciprocal of focal length, in dioptres (D) when f is in metres.
    • A shorter focal length means a more powerful (stronger-bending) lens.
    • Lens powers add when lenses are combined, making dioptres practical for prescriptions.
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