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 — C, the lens is convex and has a focal length of 0·5 metre. Power P equals 1/f (with f in metres), so f = 1/P = 1/2·0 = 0·5 metre. A positive power of +2·0 D means a converging lens, that is a convex lens. Both conditions, convex and f = 0·5 m, are satisfied only by option (c).
- (a)The lens is concave and has a focal length of 0·5 metre — The focal length is right, but a positive power means the lens is convex (converging), not concave.
- (b)The lens is convex and has a focal length of 2·0 metre — The lens is convex, but f = 1/P = 1/2·0 = 0·5 m, not 2·0 m.
- (d)The lens is concave and has a focal length of 2·0 metre — Both parts are wrong: positive power means convex, and f = 0·5 m, not 2·0 m.
The power of a lens, measured in dioptres (D), is the reciprocal of its focal length in metres: P = 1/f. The sign of the power tells the type of lens — a convex (converging) lens has positive power, and a concave (diverging) lens has negative power. One dioptre is the power of a lens of focal length one metre.
Two things must be checked together: the sign of the power fixes the lens type, and the magnitude fixes the focal length. Here +2·0 D gives a convex lens of focal length 0·5 m, so only one option can be fully correct.
- Power in dioptres equals 1/f with f in metres, so here f = 1/2·0 = 0·5 m.
- A convex (converging) lens has positive power; a concave (diverging) lens has negative power.
- One dioptre is the power of a lens whose focal length is one metre.
- For lenses placed in contact, powers add: P = P1 + P2.
Positive power means a convex lens, and f = 1/P = 0·5 m.
- Forgetting that f must be in metres when using P = 1/f.
- Assigning a positive power to a concave lens.
Given the power, identify the lens type and focal length (or the reverse); watch the sign for convex versus concave.
No directly related past PYQ was found.
- practice — not a real PYQ
The power of a convex lens of focal length 25 cm is
- (a)+2 D
- (b)+4 D
- (c)-4 D
- (d)+0.25 D
Answer(b) +4 D — P = 1/f = 1/0.25 m = +4 D.
- practice — not a real PYQ
A lens of power -2·5 D is
- (a)a convex lens of focal length 0.4 m
- (b)a concave lens of focal length 0.4 m
- (c)a convex lens of focal length 2.5 m
- (d)a concave lens of focal length 2.5 m
Answer(b) a concave lens of focal length 0.4 m — negative power means concave, and f = 1/2.5 = 0.4 m.