Question

A man can see the object clearly, between the distance range $15\text{cm}$ to $30\text{cm}$. He uses a lens to see faraway objects. Due to this lens, his near point will be -

• A. $20\text{cm}$
• B. $30\text{cm}$
• C. $15\text{cm}$
• D. $35\text{cm}$

Answer 1

The correct option is B $30\text{cm}$

The man can see faraway objects $i.e.$ objects at infinity only when the lens forms the image of these objects at his far point, $i.e.30\text{cm}$.

So,

$u=-\infty$ and $v=-30\text{cm}$

Now,

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

$\Rightarrow \frac{1}{f}=\frac{1}{(-30)}-\frac{1}{(-\infty )}$

$\therefore f=-30\text{cm}$

For new near point due to this lens,

$f=-30\text{cm}$ and $v=-15\text{cm}$

So, using,

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

$\Rightarrow \frac{1}{(-30)}=\frac{1}{(-15)}-\frac{1}{u}$

$\therefore u=-30\text{cm}$

So, the near point, after using the lens, will become $30\text{cm}$.

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