Question

Your camera’s zoom lens has an adjustable focal length ranging from $\mathbf{80}\mathbf{.}\mathbf{0}$to $\mathbf{200}$mm. What is its range of powers?

Short answer

The camera lens has an adjustable focal length with range $80\mathrm{mm}-200\mathrm{mm}$ has a range of power $5.00\mathrm{D}-12.5\mathrm{D}$.

Step-by-step solution

Concept Introduction

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 nature of the lens and mirror (concave or convex), the focal length varies with the sign (positive or negative).

Information Provided

• Focal Length of the lens: $80\mathrm{mm}-200\mathrm{mm}$.

Calculation for a range of powers

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

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

That is, the minimum focal length corresponds to the maximum power, and vice-versa, keeping in mind that the focal length must be substituted in meters in order to obtain the proper unit of dioptre for power.

The minimum power is –

role="math" localid="1654064610343" $$\begin{gathered} {\mathit{P}}_{\mathbf{m}\mathbf{i}\mathbf{n}}\mathbf{=}\frac{\mathbf{1}}{{\mathbf{f}}_{\mathbf{m}\mathbf{a}\mathbf{x}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{1}}{\mathbf{200}\mathbf{\times }{\mathbf{10}}^{\mathbf{‐}\mathbf{3}}\mathbf{}\mathbf{m}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{5}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{D} \end{gathered}$$

The maximum power is –

$$\begin{gathered} {\mathit{P}}_{\mathbf{m}\mathbf{a}\mathbf{x}}\mathbf{=}\frac{\mathbf{1}}{{\mathbf{f}}_{\mathbf{m}\mathbf{i}\mathbf{n}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{1}}{\mathbf{80}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{‐}\mathbf{3}}\mathbf{}\mathbf{m}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{12}\mathbf{.}\mathbf{5}\mathbf{}\mathbf{D} \end{gathered}$$

Therefore, the values for power are ${\mathit{P}}_{\mathbf{m}\mathbf{i}\mathbf{n}}\mathbf{=}\mathbf{5}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{D}$ and ${\mathit{P}}_{\mathbf{m}\mathbf{a}\mathbf{x}}\mathbf{=}\mathbf{12}\mathbf{.}\mathbf{5}\mathbf{}\mathbf{D}$.