A person with a defective eye-vision is unable to see the objects nearer than 1.5 m. He wants to read books…
A person with a defective eye-vision is unable to see the objects nearer than 1.5 m. He wants to read books at a distance of 30 cm. Find the nature, focal length and power of the lens he needs in his spectacles.
Solution
The defect is **hypermetropia**.
His near point is at $1.5\ \text{m}$, so the image must form at $v = -150\ \text{cm}$, while the book is at $u = -30\ \text{cm}$.
$\dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{-150} - \dfrac{1}{-30} = -\dfrac{1}{150} + \dfrac{5}{150} = \dfrac{4}{150}$
$f = \dfrac{150}{4} = +37.5\ \text{cm}$
$P = \dfrac{100}{f\ (\text{cm})} = \dfrac{100}{37.5} = +2.67\ \text{D}$
He needs a **convex lens** of focal length $37.5\ \text{cm}$ and power $+2.67\ \text{D}$.