A concave lens has focal length −25 cm. Find its power.

Solution & explanation

1. Power uses focal length in metres, including its negative sign.

2. Convert centimetres to metres.

   $$f=-\frac{25}{100}=-0.25$$

3. Write lens power.

   $$P=\frac{1}{f}$$

4. Insert the signed focal length.

   $$P=\frac{1}{-0.25}$$

5. Take the reciprocal.

   $$P=-4$$

6. The unit m⁻¹ is the dioptre, D; negative power indicates a diverging lens.

P = −4 D