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 ?

Explanation

(i) For distant vision, given : Power of the lens , `P_(1) = -5.5 D`. Focal length, `f = (1)/(P_(1)) = (1)/(-5.5) = 0.1873m = -18.73 cm`
(ii) For near vision, power is measured relative to the main part of the lens. Therefore,
`P_(1) + P_(2) = P` or `-5.5 + P_(2) = + 1.5` or `P_(2) = +7D`
Focal length, `f = (1)/(P_(2)) = (1)/(+6.5)`