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 dioptre. What is the focal length of the lens required for correcting (i) distant vision and (ii) near vision?

Answer 1

(i) In order to correct distant vision, a person wears spectacles with concave lenses.

Given that the power of the concave lens is 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 = ${\displaystyle \frac{1}{p}}$

∴ f = ${\displaystyle \frac{1}{-5.5}}$

= −0.18 m

= −18 cm

Hence, the focal length of the concave lens required to correct the person's distant vision is −18 cm.

(ii) In order to correct near vision, a person wears spectacles with convex lenses.

Given 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 = ${\displaystyle \frac{1}{p}}$ 

f = ${\displaystyle \frac{1}{1.5}}$

= 0.67 m

= 67 cm

Hence, the focal length of the convex lens required to correct his near vision is 67 cm.