Question

A person can see clearly objects only when they lie between $40\text{cm}$ and $250\text{cm}$ respectively. The minimum power of the lens he/she should use while reading at $25\text{cm}$ is

• A. $2\text{D}$
• B. $4\text{D}$
• C. $4.5\text{D}$
• D. $1.5\text{D}$

Answer 1

The correct option is D $1.5\text{D}$

If an object is placed at $25\text{cm}$ from the correcting lens it should produce the virtual image at $40\text{cm}$.

Thus, $u=-25\text{cm},v=-40\text{cm}$

Using lens formula,

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

Substituting the given data we get,

$\frac{1}{f}=\frac{-1}{40}+\frac{1}{25}$

$\Rightarrow f=\frac{200}{3}\text{cm}\text{or}\frac{2}{3}\text{m}$

$\therefore$ Power of lens $P=\frac{1}{f}$

$\Rightarrow P=\frac{3}{2}=1.5\text{D}$

Hence, option (d) is the correct answer.