Question

The near-point of a hypermetropic eye is $75\text{cm}$ from the eye. What is the power of the lens required to enable the person to read a book held at $25\text{cm}$ from the eye?

• A. $-2.66\text{D}$
• B. $+2.66\text{D}$
• C. $+3\text{D}$
• D. $-2.5\text{D}$

Answer 1

The correct option is B $+2.66\text{D}$

The near point of a normal human being is $25\text{cm}$. Therefore, to correct a hypermetropic person capable of seeing things only $75\text{cm}$ away from the eyes, we need a corrective lens that forms the image at $75\text{cm}$ of the object which is kept between $25$ to $75\text{cm}$.

Focal length of convex lens to be used can be found by the lens formula:
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
where $f$ is the focal length and $u,v$ are the object and image distance respectively.
Here $u=-25\text{cm}=-\frac{1}{4}\text{m}v=-75\text{cm}=\frac{-3}{4}\text{m}$

$\Rightarrow \frac{1}{f}=\frac{1}{\left(\frac{-3}{4}\right)}-\frac{1}{\left(\frac{-1}{4}\right)}$

$=\frac{-4}{3}-\frac{(-4)}{1}=\frac{8}{3}$

We know that,
$\text{Power, P}=\frac{1}{f}=\frac{8}{3}=2.66\text{D}$
So the person needs a convex lens of power $+2.66\text{D}$.