Two convex lenses with power 2 dioptre are kept in contact with each other. The focal length of the combined lens system is
- A.0.10 m
- B.2 m
- C.4 m
- D.0.25 m
Correct answer
Explanation
The correct answer is D, 0.25 m. Powers of lenses in contact simply add, so the combination has a power of 2 + 2 = 4 dioptre, and its focal length is 1/4 m, that is 0.25 m.
The power of a lens is the reciprocal of its focal length in metres, P = 1/f, and is measured in dioptres (D). A convex lens has positive power, a concave lens negative power. For thin lenses placed in contact, the total power is P = P1 + P2, which is why opticians add the powers of lenses when testing eyes. Here each lens alone has a focal length of 0.5 m; together they bend light more strongly and focus it at half that distance.
A is wrong because 0.10 m would need a power of 10 D. B is wrong because 2 m corresponds to a power of only 0.5 D. C is wrong because 4 m mistakes the total power, 4 D, for the focal length; the focal length is its reciprocal.
Exam tip: P = 1/f (f in metres); in contact, P = P1 + P2.
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