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?
Answer
We know that,
Power of a lens = 1/Focal Length
Therefore,
Focal Length = 1/ Power of the lens
Note : Here power is in m
(i) distant vision
For distant vision,
Power of the lens = −5.5 D
Focal length(m) = 1/ Power of the lens
= 1/ (−5.5)
= −10/55
= −2/11
= -0.1818 m
= −0.1818 × 100 cm
= −18.18 cm
= −18.2 cm
Focal length of the lens required for correction for distant vision is −18.2 cm .
Since the focal length is negative, the lens used is concave lens.
(ii) near vision
For near vision,
Power of the lens = 1.5 D
Focal length(m) = 1/ Power of the lens
= 1/ (1.5)
= 10/15
= 2/3
= 0.667 m
= 0.667 × 100 cm
= 66.7 cm
Focal length of the lens required for correction for near vision is 66.7 cm .
Since the focal length is positive, the lens used is convex lens.