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?
Answers
The power of lens to correct the distant vision is P1 which is given as -5.5 D.
The power of lens to correct the near vision is P2 which is +1.5 D.
The focal length to correct a distance vision is 1/P1 which is -18.73 cm.
The power of near-vision is calculated as P = P1 + P2.
The value of P2 is +6.5 D.
The focal length of near-vision is 1/P2 which is + 15.4 cm.
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.