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 - Science

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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?

Solution 1

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.

Solution 2

In order to correct distant vision, a person wears spectacles with concave lenses.
Given that the power of the concave lens required to correct the distant vision of the person, P = -5.5 D.
The focal length of the concave lens required for correcting the defect is given by  f=1/p

∴f=1/-5.5=-0.1818m=-18.18cm

Hence, the focal length of the concave lens required to correct the person's distant vision is -18.18 cm.

(b) In order to correct near vision, a person wears spectacles with convex lenses.
Given that the power of the convex lens, P = +1.5 D.
The focal length of the convex lens required for correcting this defect is given by

f=1/p

f=1/(+1.5)=0.666m=+66.6cm

Hence, the focal length of the convex lens required to correct his near vision is +66.6 cm.

Concept: Power of a Lens
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