Question

A person wears glasses of power $-2.5\text{D}$. Is the person far sighted or near sighted? What is the far point of the person without the lenses?

• A. Farsighted, $40\text{cm}$
• B. Far sighted, $25\text{cm}$
• C. Near sighted, $25\text{cm}$
• D. Near sighted, $40\text{cm}$

Answer 1

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

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

Since, the power of the glassed is negative, so it is a concave lens.

Concave lens is used to correct nearsightedness.

Let the far point of person be $x$.

Focal length of the lens,

$f=\frac{1}{P}=\frac{-1}{2.5}=\frac{-10}{25}\text{m}=-40\text{cm}$

When the glass is used in near sightedness, then the image of an object kept at very far away distance forms at far point.

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

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

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

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

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