Which one among the following is the correct focal length of a combination of lenses of power 2.5 D and -2.0 D ?
- A.+0.5 m
- B.-0.5 m
- C.+2.0 m
- D.-2.0 m
Correct answer
Explanation
The correct answer is C, +2.0 m. For lenses in contact the powers add: 2.5 D + (−2.0 D) = +0.5 D, and the focal length is 1/0.5 = +2.0 metres.
The power of a lens is the reciprocal of its focal length in metres, P = 1/f, and its unit is the dioptre (D). A convex (converging) lens has positive power and a concave (diverging) lens has negative power. When thin lenses are placed in contact, the power of the combination is simply the algebraic sum of their powers. Here a converging lens of +2.5 D is combined with a diverging lens of −2.0 D, giving a net power of +0.5 D. A positive result means the combination acts as a converging lens with a focal length of +2 m.
A is wrong because +0.5 is the net power in dioptres, not the focal length in metres. B is wrong because it both confuses power with focal length and has the wrong sign. D is wrong because the net power is positive, so the focal length cannot be negative.
Exam tip: add powers, not focal lengths; then f (in metres) = 1/P.
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