The power of a lens of focal length 10 cm is
- A.0.1 dioptre
- B.1 dioptre
- C.10 dioptre
- D.100 dioptre
Correct answer
Explanation
The correct answer is C, 10 dioptre. Power is the reciprocal of focal length in metres, and 10 cm is 0.1 m, so P = 1 ÷ 0.1 = 10 D.
The power of a lens measures how strongly it converges or diverges light. It is defined as P = 1/f, with the focal length f in metres, and its SI unit is the dioptre (D). A shorter focal length means a more powerful lens. By convention a convex (converging) lens has positive power and a concave (diverging) lens has negative power, so a convex lens of focal length 10 cm has a power of +10 D. When thin lenses are placed in contact, their powers simply add, which is why opticians prescribe spectacles in dioptres.
A is wrong: 0.1 D would need a focal length of 10 m.
B is wrong: 1 D corresponds to a focal length of 1 m.
D is wrong: 100 D would need a focal length of only 1 cm, ten times shorter than this lens.
Exam tip: P = 1/f (f in metres) = 100/f (f in cm); convex positive, concave negative.
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