Question

A person can see clearly objects only when they lie between $50\text{cm}$ and $250\text{cm}$ respectively. The person uses a lens of power $2\text{D}$ , while reading at $25\text{cm}$. With this lens, find the maximum distance clearly visible for the person?

• A. $30\text{cm}$
• B. $25\text{cm}$
• C. $42\text{cm}$
• D. $35\text{cm}$

Answer 1

The correct option is C $42\text{cm}$

Suppose the maximum distance of clear vision is $d$ and person can see a maximum distance of $250\text{cm}$. Then the object at a distance is imaged by the lens at $250\text{cm}$.

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

Given $P=+2\text{D}$

$\because f=\frac{1}{P}$ we get,
$f=\frac{1}{2}\Rightarrow f=50\text{cm}$

i.e

$-\frac{1}{250}-\frac{1}{d}=\frac{1}{50}$

$\Rightarrow \frac{1}{d}=\frac{-1}{250}-\frac{1}{50}$

$\Rightarrow \frac{1}{d}=\frac{-6}{250}$

$\Rightarrow d=\frac{250}{6}\approx 42\text{cm}$

Hence, option (c) is the correct answer.