Question

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

Answer 1

For distant vision = −0.181 m, for near vision = 0.667 m 
The power P of a lens of focal length f is given by the relation. 
\(\text{Power (P)} = \frac{1}{f}\)

(i) Power of the lens used for correcting distant vision = −5.5 D 
Focal length of the required lens, \(f =\frac{1}{\text{P}}\)
\(f = \frac{1}{-5.5}\)
f = -0.181 m
The focal length of the lens for correcting distant vision is −0.181 m.

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(ii) Power of the lens used for correcting near vision = +1.5 D 
Focal length of the required lens, \(f =\frac{1}{\text{P}}\) 
\(f = \frac{1}{1.5}\) = +0.667 m
The focal length of the lens for correcting near vision is 0.667 m.