5.4P Relate the power of a lens to its focal length and shape

The idea

The power of a lens measures how strongly it converges or diverges light. Power is the reciprocal of focal length: P = 1/f, with f measured in metres, so power is in dioptres (D), where 1 D = 1 m⁻¹. A short focal length gives a large power; a long focal length gives a small power. A converging (convex) lens has positive power, and a diverging (concave) lens has negative power. A fatter, more strongly curved lens bends light more and so has a shorter focal length and greater power.

For example: A lens of focal length 0.50 m has power 1 ÷ 0.50 m = 2.0 D, while a lens of focal length 0.25 m has power 4.0 D.

What earns the marks

• States that power is the reciprocal of focal length, P = 1/f, with f in metres and power in dioptres.
• Explains that a shorter focal length corresponds to a greater power.
• Relates a more strongly curved, fatter lens to a shorter focal length and therefore a greater power.
• Calculates power from focal length in metres, for example 1 ÷ 0.25 m = 4.0 D.

Common mistakes and how to put them right

• Uses focal length in centimetres without converting.

  Put it right by converting to metres before applying P = 1/f.

• Treats a longer focal length as greater power.

  Put it right by stating that power falls as focal length increases.

• Gives a converging lens a negative power.

  Put it right by assigning positive power to converging lenses and negative power to diverging lenses.

Exam tips

• Convert focal length to metres before dividing, and give power in dioptres.
• Use the inverse relationship to check whether a shorter focal length should give a larger power.
• State the sign of the power to show whether the lens converges or diverges.