Question

A person wears glasses of power $-2.5\text{D}$. What is the far point of this person, without the glasses?

• A. $90\text{cm}$
• B. $25\text{cm}$
• C. $35\text{cm}$
• D. $40\text{cm}$

Answer 1

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

Given:

Power of the glasses, $P=-2.5\text{D}$

Since, the power of the glasses is negative, it is a concave lens and concave lens is used to correct myopia.

Focal length of the lens,

$f=\frac{1}{P}=\frac{1}{-2.5}=-0.4\text{m}=-40\text{cm}$

For correcting myopia, the image of the object placed at infinity must form at the far point of that person.

Let the far point of the person is $x$.

So,

$u=-\infty$, $v=-x$ and $f=-40\text{cm}$

Now,

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

$\Rightarrow \frac{1}{(-40)}=\frac{1}{(-x)}-\frac{1}{(-\infty )}$

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

Therefore, the far point of this person, without the glasses, is $40\text{cm}$.

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