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 dioptres. What is the focal length of the required for correcting (i) distant vision, and (ii) near vision ?

Explanation

Power of the lens for correcting distant vision, `P_(1) = -5.5 D`
Power of the lens for correcting near vision, `P_(2) = +15 D`
Power of near vision is measured relative to the main part of the lens.
So, focal length of required lens,
`f=(1)/(P)`
`f=(1)/(1.5) =0.667 m`
Thus, focal length of near vision part will be
`f_(2)=(1)/(P_(2)) =(1)/((+6.5))=+15.4` cm
Focal length of the lens required for correcting, distant vision is -0.181 m and, near vision is 0.667 m.