A lens has a power of +2.0 Dioptre. Which one of the following statements about the lens is true ?
- A.The lens is concave and has a focal length of 0.5 metre
- B.The lens is convex and has a focal length of 2.0 metre
- C.The lens is convex and has a focal length of 0.5 metre
- D.The lens is concave and has a focal length of 2.0 metre
Correct answer
Explanation
The correct answer is C, convex with a focal length of 0.5 metre. A positive power means a converging (convex) lens, and f = 1/P = 1/2 = 0.5 m.
The power of a lens is the reciprocal of its focal length in metres: P = 1/f. Its SI unit is the dioptre (D), and 1 D is the power of a lens of focal length 1 m. By the sign convention, a convex lens has a positive focal length and positive power, while a concave lens has negative values. So a lens of +2.0 D is convex and its focal length is 1/2 m, which is 50 cm. Convex lenses of this kind are used in spectacles for long-sightedness (hypermetropia).
A is wrong: a concave lens would have negative power. B is wrong: the type is right but 2.0 m would give a power of only +0.5 D. D is wrong on both counts, the type and the focal length.
Exam tip: P = 1/f (f in metres); plus sign = convex, minus sign = concave.
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