Question

Which of the following statements is true?

• A. A convex lens has 4 dioptre power having a focal length $0.25\mathrm{m}$.
• B. A convex lens has $–4$ dioptre power having a focal length $0.25\mathrm{m}$.
• C. A concave lens has $4$ dioptre power having a focal length $0.25\mathrm{m}$
• D. A concave lens has $–4$ dioptre power having a focal length $0.25\mathrm{m}$

Answer 1

The correct option is A

A convex lens has 4 dioptre power having a focal length $0.25\mathrm{m}$.

Explanation for the correct option:

1. The power of the lens is the ability of a lens to converge or diverge the rays of light falling on it.
2. Dioptre of power of a lens is described as the unit of measurement of the optical power of a lens or curved mirror equivalent to the reciprocal of focal length $\left(f\right)$. The focal length is measured in meters $\left(\mathrm{m}\right)$.
3. One dioptre is the power of the lens whose focal length is $1\mathrm{m}$.
4. Mathematically, the power of the lens can be expressed as, $P=\frac{1}{f}$,Where $f$ denotes focal length.
5. Substitute $0.25$ for $f$ in power formula given as,

$$\begin{gathered} P=\frac{1}{0.25} \\ =4\mathrm{D} \end{gathered}$$

A positive focal length value indicates a convex lens.

Hence, option (A) is correct.