Power of a lens

The idea

The power P of a lens expresses its degree of convergence or divergence and is the reciprocal of its focal length, P = 1/f; the shorter the focal length, the more the lens bends light rays.

Strong and weak lenses

Two convex lenses can bend light by different amounts. One brings parallel rays to a point close to it. The other brings them to a point far away.

Which lens bends the rays more?

• The one with the shorter focal length
• The one with the longer focal length
• Both bend them equally

Short and long f

Move the focal length slider to 20 cm, then to 100 cm. Watch how much the red rays are bent.

Bending and focal length

With f = 20 cm the rays were bent through large angles and met close to the lens. With f = 100 cm they were bent little. A concave lens of very short focal length spreads the rays more than one of longer focal length.

The power of a lens expresses its degree of convergence or divergence of light rays. It is the reciprocal of its focal length: P = 1/f. The shorter the focal length, the more the lens bends the rays.

Notes

Power P = 1/f: the reciprocal of the focal length. The shorter the focal length, the more the lens bends light.

Check yourself

What does the power of a lens tell us?

The power P of a lens of focal length f is

Lens A has a focal length of 20 cm and lens B has a focal length of 50 cm. Both are convex. Which statement is correct?

A lens has power P = 1/f. Its focal length is made shorter. What happens to the power?

• How much the lens converges or diverges light rays — correct. Yes!
• How bright the image is. Brightness is not what power measures. Power expresses the degree of convergence or divergence of rays.
• How thick the glass is. The book defines power through the focal length, not through the thickness.
• P = f. Power is the reciprocal of the focal length, not the focal length itself.
• P = 1/f — correct. Yes!
• P = 1/f², the square of the reciprocal. The power is the reciprocal of the focal length, P = 1/f, with no square.
• Lens B bends light rays more, because its focal length is larger. A convex lens of short focal length bends rays through larger angles, so A bends them more.
• They bend light equally, since both are convex. The bending depends on the focal length. The one with the shorter focal length bends more.
• Lens A bends light rays more than lens B — correct. Yes!
• It becomes larger, since 1/f grows when f gets smaller — correct. Yes!
• It becomes smaller. Power is 1/f, so it grows when f becomes shorter.
• It stays the same. Power is the reciprocal of the focal length, so a different f gives a different power.