Question

The near and far points of a person are at $50\text{cm}$ and $200\text{cm}$ respectively. He uses a contact lens to read a book placed at $25\text{cm}$. With this lens, he can clearly see up to a maximum distance of -

• A. $60\text{cm}$
• B. $40\text{cm}$
• C. $80\text{cm}$
• D. $70\text{cm}$

Answer 1

The correct option is B $40\text{cm}$

If the book is placed at $25\text{cm}$ from the lens, it should produce a virtual image at $50\text{cm}$ so that the person can see it clearly.

Thus, $u=-25\text{cm}$ and $v=-50\text{cm}$

Now,

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

$\Rightarrow \frac{1}{f}=\frac{1}{(-50)}-\frac{1}{(-25)}$

$\therefore f=50\text{cm}$

Let the maximum distance of object from the eye for a clear vision with this lens is $x$.

The lens should produce a virtual image at $200\text{cm}$ so that the person can see it clearly.

Thus, $u=-x\text{cm}$ and $v=-200\text{cm}$

Now,

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

$\Rightarrow \frac{1}{50}=\frac{1}{(-200)}-\frac{1}{(-x)}$

$\therefore x=40\text{cm}$

So, the person will be able to see up to a maximum distance of $40\text{cm}$ using this lens.

Hence, option $\left(B\right)$ is the correct answer.