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Which one among the following is the correct focal length of a combina

June 1, 2025 by rawan239

Which one among the following is the correct focal length of a combination of lenses of power 2·5 D and –2·0 D ?

+0·5 m

–0·5 m

+2·0 m

–2·0 m

This question was previously asked in

UPSC NDA-2 – 2024

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For thin lenses in contact, the total power of the combination (P_total) is the algebraic sum of the individual powers (P₁, P₂). Given P₁ = 2.5 D and P₂ = -2.0 D, the total power is P_total = P₁ + P₂ = 2.5 D + (-2.0 D) = 0.5 D. The focal length (f) of a lens or lens combination is the reciprocal of its power (P), with power in dioptres (D) and focal length in meters (m). So, f_total = 1 / P_total = 1 / 0.5 D = 1 / (0.5 m⁻¹) = 2 m. The focal length is positive, indicating a converging lens combination.

Power of a lens (P) is the reciprocal of its focal length (f) in meters (P = 1/f). The power of a combination of thin lenses in contact is the sum of their individual powers. Positive power indicates a converging lens, and negative power indicates a diverging lens.

The unit of power is the dioptre (D), which is equal to m⁻¹. A combination of a converging lens (+P) and a diverging lens (-P’) can result in a net converging or diverging combination depending on the relative magnitudes of their powers.

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