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?

The ability of the lens of the eye to adjust its focal length to clearly focus rays coming from distant as well from near objects on the retina is known as the power of accommodation of the eye. The power (P) of a lens of focal length f is given by the relation

Power (P) = 1/f

(i) the focal length of the lens required for correcting distant vision

Power of the lens (used for correcting distant vision) = – 5.5 D

Focal length of the lens (f) = 1/P

f = 1/-5.5

f = -0.181 m

The focal length of the lens (for correcting distant vision) is – 0.181 m.

(ii) the focal length of the lens required for correcting near vision

Power of the lens (used for correcting near vision) = +1.5 D

The 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.

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