Two convex lenses have focal lengths of 50 cm and 25 cm, respectively.

Two convex lenses have focal lengths of 50 cm and 25 cm, respectively. If these two lenses are placed in contact, then the net power of this combination will be equal to

+2 dioptre

+6 dioptre

-6 dioptre

+3 dioptre

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This question was previously asked in

UPSC NDA-2 – 2022

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The power of a lens (P) is the reciprocal of its focal length (f) in meters (P = 1/f). For a combination of thin lenses in contact, the total power (P_net) is the sum of the individual powers (P_net = P1 + P2 + …).
Given focal lengths: f1 = 50 cm = 0.5 m and f2 = 25 cm = 0.25 m. Both are convex lenses, so focal lengths are positive.
Power of the first lens: P1 = 1 / f1 = 1 / 0.5 m = +2 Dioptre (D).
Power of the second lens: P2 = 1 / f2 = 1 / 0.25 m = +4 Dioptre (D).
Net power of the combination: P_net = P1 + P2 = +2 D + +4 D = +6 D.

The power of a lens is a measure of its ability to converge or diverge light, and for lenses in contact, powers are additive.

The unit of power is the Dioptre (D), defined as the reciprocal of the focal length in meters. Convex lenses have positive power (converging), and concave lenses have negative power (diverging).

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