A doctor has prescribed a corrective lens of power + 2.0 D to a woman. Which lens will she require?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Convex lens of focal length 50 cm.
The power of a lens is the reciprocal of its focal length in metres, \(P=\frac{1}{f}\). A positive power means a convex (converging) lens; a negative power means a concave lens.
\(\displaystyle f=\frac{1}{P}=\frac{1}{+2.0}=+0.5\,\mathrm{m}\)
\(0.5\,\mathrm{m}=50\,\mathrm{cm}\), and the plus sign makes the lens convex
Why the other options are incorrect
Option (1) Concave lens of focal length 50 cm. — Incorrect. The focal length is right, but a concave lens has a negative power.
Option (2) Convex lens of focal length 0.5 cm. — Incorrect. The focal length is 0.5 m, not 0.5 cm; 0.5 cm would be a power of +200 D.
Option (4) Concave lens of focal length 0.5 cm. — Incorrect. Both the type of lens and the unit are wrong.