Question

A person is known to use a lens of power
(i) -7.5D for his distant vision
(ii) +3D for his near vision
Calculate the focal length of the lens used for correcting his (A) Distant vision and (B) Near vision problem

Answer 1

Given:

A person uses lens of power -7.5D for distant vision and +3D for near vision

To Find:

Focal length of both the lens

Solution:

Power of lens is defined as the ability of the lens to converge the rays of light falling on it.Mathematically it can  be defined as P=1/f where f is the focal length. The S.I. unit of power is Dioptre .

$P = \frac{1}{f}$

where  f should be in meters.

1) P = -7.5D

$f = \frac{1}{P} \\f = \frac{-100}{7.5} cm \\f = -13.33 cm$

2)P = +3D

$f=\frac{1}{P}\\ f = \frac{100}{3} = 33.33cm$

The person uses a concave lens of focal length - 13.33 cm for distant vision and uses a convex lens of focal length 33.33 cm for near vision.