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

Focal length for distant vision = -0.181 m, focal length for near vision = 0.667 m.
The power (P) of a lens is related to its focal length (f) by the formula:
\(\text{Power (P)} = \frac{1}{f}\)

(i) To correct distant vision, the lens power is -5.5 D.
The focal length of this lens is calculated as:
\(f =\frac{1}{\text{P}}\)
\(f = \frac{1}{-5.5}\)
f = -0.181 m.
Thus, the focal length for correcting distant vision is -0.181 m.

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(ii) To correct near vision, the lens power is +1.5 D.
The focal length of this lens is calculated as:
\(f =\frac{1}{\text{P}}\) 
\(f = \frac{1}{1.5}\) = +0.667 m.
Therefore, the focal length for correcting near vision is 0.667 m.