Question

The nearest distance of distinct vision for the grandpa who is suffering from long-sightedness is 75 cm. He wishes to read a book that is held at 25 cm from the eye.

What is the power of lens required?

• A. +2.6 D
• B. -2.6 D
• C. -5.3 D
• D. +5.3 D

Answer 1

The correct option is A +2.6 D

For correction of defect, the image of book kept 25 cm away should be formed 75 cm away.

Object distance, $u=-25cm$
Image distance, $v=-75cm$

Using lens formula,
$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$
$\frac{1}{f}=\frac{1}{-75}-\frac{1}{(-25)}$
$\frac{1}{f}=\frac{3-1}{75}$
$f=\frac{75}{2}cm=\frac{75}{200}m$

Power of lens:
$P=\frac{1}{f}$
$P=\frac{200}{75}$
$P=\frac{8}{3}=2.6D$