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?
Answers
1. For correcting distant vision we need concave lens, so focal length is going to be negative,
P = - 5.5
We know that power, P = 1/f
-5.5 = 1/f, f = -1/5.5 = - 0.18 m
Focal length of lens is - 0.18 m or -18cm for correcting distant vision.
2. For correcting near vision he will have to use convex lens, hence, focal length is positive.
P = 1/f, P = + 1.5 D
f = 1/P
f = 1/1.5 = 0.666.. m
Focal length required is 0.666m or 66.6 cm for correcting near vision
Explanation:
The power P of a lens of focal length f is given by the relationP= 1/f
(i) Power of the lens used for correcting distant vision = - 5.5 D
Focal length of the required lens, f= 1/Pf= 1/-5.5 = -0.181 m
The focal length of the lens for correcting distant vision is - 0.181 m.
(ii) Power of the lens used for correcting near vision = +1.5 D
Focal length of the required lens, f= 1/P
f= 1/1.5 = +0.667 m
The focal length of the lens for correcting near vision is 0.667 m.