Question

What is the focal length of a makeup mirror that has a power of$\mathbf{1}\mathbf{.}\mathbf{50}\mathbf{}\mathbf{D}$

Short answer

The focal length of the mirror is $\mathit{f}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{667}\mathbf{}\mathbf{m}$.

Step-by-step solution

Definition of power of the lens

The power of a lens is defined to be the inverse of its focal length.

Calculating the focal length of the mirror

Power of mirror is given as,

$\mathit{P}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{5}\mathbf{}\mathbf{D}$

So, the focal length can be calculated as:

$$\begin{gathered} \mathit{f}\mathbf{=}\frac{\mathbf{1}}{\mathbf{P}} \\ \mathit{f}\mathbf{=}\frac{\mathbf{1}}{\mathbf{1}\mathbf{.}\mathbf{5}\mathbf{}\mathbf{D}} \\ \mathbf{f}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{667}\mathbf{}\mathbf{m} \\ \mathbf{Therefore}\mathbf{,}\mathbf{}\mathbf{the}\mathbf{}\mathbf{focal}\mathbf{}\mathbf{length}\mathbf{}\mathbf{of}\mathbf{}\mathbf{the}\mathbf{}\mathbf{mirror}\mathbf{}\mathbf{is}\mathbf{}\mathbf{0}\mathbf{.}\mathbf{667}\mathbf{}\mathbf{m}\mathbf{}\mathbf{.} \end{gathered}$$