Question

A person can see clearly only up to a distance of $30\text{cm}$. He wants to read a book placed at a distane of $50\text{cm}$ from his eyes. What is the power of the lens he requires for his spectacles?

• A. $-1.0D$
• B. $-1.33D$
• C. $-1.67D$
• D. $-2.0D$

Answer 1

The correct option is B $-1.33D$

The person is myopic. This defect is corrected by using a concave lens. Putting $u=-50\text{cm}$ and $v=-30\text{cm}$ in the lens formula
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$\frac{1}{-30}-\frac{1}{-50}=\frac{1}{f}$
$\frac{-1}{30}+\frac{1}{50}=\frac{1}{f}$
$\frac{-50+30}{30\times 50}=\frac{1}{f}$
$f=-75\text{cm}$.
Therefore, the power of the lens $\frac{1}{f}=\frac{1}{0.75}=-1.33D$,
​​​​​​​which is choice (b).