Question

A person has near point at $100\text{cm}$. What power of lens is needed to read at $20\text{cm}.$ If he/she uses spectacles, having glasses $2\text{cm}$ separated from eyes?

• A. $4.55\text{D}$
• B. $4\text{D}$
• C. $4.92\text{D}$
• D. $5\text{D}$

Answer 1

The correct option is A $4.55\text{D}$

Given,

Near point $=100\text{cm}$

Since, spectacles are used which are $2\text{cm}$ away from the eyes.
So, object distance would be $u=20-2=18\text{cm}$

To read, the image should form at near-point of the eye.

$\therefore v=-100\text{cm}$

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

$\Rightarrow \frac{1}{f}=\frac{-1}{100}+\frac{1}{18}=\frac{82}{1800}$

$\therefore f=\frac{1800}{82}\text{cm}=\frac{18}{82}\text{m}$

Power, $P=\frac{1}{f}=\frac{82}{18}=4.55\text{D}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(A\right)$ is the correct answer.

Why this question ? Caution : Distance of object or image is calculated from lens (spectacles).