### The Power of a Lens

- The power of a lens is defined as the reciprocal of the focal length in unit meter.
$$P=\frac{1}{f}$$
**Important Note**:*f*is in meter - The unit of power is diopter (D).
- The relationship of the power with the thickness and types of lens are shown in the diagram below.

Lens |
Power of the Lens |

Converging (Convex) | Positive |

Diverging (Concave) | Negative |

Thick, with short focal length. | High |

Thin, with long focal length. | Low |

Thinner – Lower Power – Longer Focal Length |

Thicker – Higher Power – Shorter Focal Length |

**Example**:

The power of a lens is labeled as +5D. What is the focal length of the lens (in cm)? Is this a concave lens or a convex lens?

**Answer**:

$$\begin{array}{l}P=\frac{1}{f}\\ (+5)=\frac{1}{f}\\ f=\frac{1}{5}=0.2m\text{=}20cm\end{array}$$

The power of the lens is positive. This is a convex lens.