Question

A person needs a lens of power, − 5.5 dioptres for correcting his distant vision. For correcting his near vision, he needs a lens of power, +1.5 dioptres. What is the focal length of the lens required for correcting (i) distant vision, and (ii) near vision?

Answer 1

In order to correct distant vision, a person wears spectacles with concave lenses.
Given that the power of the concave lens required to correct the distant vision of the person, P = -5.5 D.
The focal length of the concave lens required for correcting the defect is given by $f=\frac{1}{p}$.
∴ $f=\frac{1}{-5.5}=-0.1818m=-18.18cm$
Hence, the focal length of the concave lens required to correct the person's distant vision is -18.18 cm.

(b) In order to correct near vision, a person wears spectacles with convex lenses.
Given that the power of the convex lens, P = +1.5 D.
The focal length of the convex lens required for correcting this defect is given by $f=\frac{1}{p}$.
∴ $f=\frac{1}{+1.5}=+0.666m=+66.6cm$
Hence, the focal length of the convex lens required to correct his near vision is +66.6 cm.