Question

The near point of hypermetropic eye is 75 cm from the eye. What is the power of the lens required to enable him to read clearly a book held at 25 cm from the eye?

• A. +3 D
• B. -2.5 D
• C. +2.66 D
• D. -2.66 D

Answer 1

The correct option is C +2.66 D

The near point of a normal human being is 25 cm. Therefore to correct a hypermetropic person capable of seeing from 75 cm only, we need a corrective lens which forms the image at 75 cm, of the object which is kept between 25 to 75 cm.

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

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

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