What is the focal length of $\mathbf{1}\mathbf{.}\mathbf{75}\mathbf{}\mathbf{D}$reading glasses found on the rack in a pharmacy?

The focal length is the distance between a convex lens or a concave mirror and the focal point of a lens or mirror. It is the point at which two parallel light beams meet or converge. Depending on the lens and mirror (concave or convex), the focal length varies with the sign (positive or negative).

• Power of reading glasses: $\mathbf{1}\mathbf{.}\mathbf{75}\mathbf{}\mathbf{D}$

The power in dioptres of lenses is inversely proportional to the focal length of the; where the power is given by,

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

Hence, knowing the power of the reading glasses, then directly substitute in the above equation to find the focal length of the lens. Keeping in mind that since the power is given in unit of dioptre, then substituting in the above equation the obtained unit for the focal length will be in unit of meter.

Hence, on substituting the value –

$$\begin{gathered} \mathit{f}\mathbf{=}\frac{\mathbf{1}}{\mathbf{P}} \\ \mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{1}}{\mathbf{1}\mathbf{.}\mathbf{75}\mathbf{}\mathbf{D}} \\ \mathbf{}\mathbf{}\mathbf{=}\mathbf{0571}\mathbf{}\mathbf{m} \\ \mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{571}\mathbf{\times }\mathbf{1000}\mathbf{}\mathbf{mm} \\ =571\mathrm{mm} \end{gathered}$$

Therefore, the value of focal length is $\mathit{f}\mathbf{=}\mathbf{571}\mathbf{}\mathbf{mm}$.