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Power of a Lens and Combination of Thin Lenses

Power of a lens is the measure of its ability to converge or diverge light, numerically equal to the reciprocal of focal length in metres.

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Student-friendly explanation

A lens with shorter focal length bends light more strongly, so its power has greater magnitude. Convex lenses have positive power in air and concave lenses have negative power in air under the usual sign convention. When thin lenses are placed in contact, their powers add algebraically. This makes lens power useful in spectacles and optical instruments because combinations can be handled directly in dioptres.

How to write this in exams

  1. 1

    Start with the exact idea

    Power of a lens is the measure of its ability to converge or diverge light, numerically equal to the reciprocal of focal length in metres.

  2. 2

    Then show how to use it

    Convert each focal length to metre if power is not already given; find individual powers with signs; add powers algebraically; calculate equivalent focal length if asked; state whether the combination is converging or diverging.

  3. 3

    Add one concrete example

    A +2 D spectacle lens is converging with focal length 0.5 m. A -4 D lens is diverging with focal length -0.25 m.

  4. 4

    Avoid this incomplete answer

    For +3 D and -1 D, a common wrong answer is +4 D because signs are ignored and magnitudes are simply added.

Definition

Power of a lens is the measure of its ability to converge or diverge light, numerically equal to the reciprocal of focal length in metres.

Example

A +2 D spectacle lens is converging with focal length 0.5 m. A -4 D lens is diverging with focal length -0.25 m.

Rule to remember

Power: P = 1/f, where f is focal length in metre and P is in dioptre, D. Combination of thin lenses in contact: P = P1 + P2 + ... and 1/F = 1/f1 + 1/f2 + ... Use only for thin lenses in contact or negligible separation unless a separation formula is specifically given.

Memory hook

Power uses metres; combination uses signed addition.

Examples and method

Worked example

A +3 D lens and a -1 D lens are placed in contact. Combined power P = +3 + (-1) = +2 D. The equivalent focal length is F = 1/P = 1/2 m = 0.50 m. The combination acts as a converging lens of focal length 50 cm.

Method to apply

Convert each focal length to metre if power is not already given; find individual powers with signs; add powers algebraically; calculate equivalent focal length if asked; state whether the combination is converging or diverging.

Diagram support

A full ray diagram is not always required, but a simple representation can show a converging lens with positive power and a diverging lens with negative power. For combinations, lenses should be shown in contact along a common principal axis.

How CBSE asks it

It appears in short numericals on spectacle lenses, equivalent focal length of lenses in contact, and sign-based questions about convex and concave lenses.

Avoid common mistakes

Common confusion

Students often calculate power using focal length in centimetres. Power in dioptre requires focal length in metres.

Common wrong answer

For +3 D and -1 D, a common wrong answer is +4 D because signs are ignored and magnitudes are simply added.

Exam tip

Convert cm to m before using P = 1/f. Then keep the sign of focal length, because the sign tells whether the lens is converging or diverging.

Quick check

What is the power of a concave lens of focal length 50 cm?

A concave lens has negative focal length. Here f = -50 cm = -0.50 m, so P = 1/f = 1/(-0.50) = -2 D. The negative sign shows that it is a diverging lens.

Answer writing and exam use

1-mark answer

Power of a lens is the measure of its ability to converge or diverge light, numerically equal to the reciprocal of focal length in metres.

2-mark answer

Power of a lens is the measure of its ability to converge or diverge light, numerically equal to the reciprocal of focal length in metres. Power: P = 1/f, where f is focal length in metre and P is in dioptre, D. Combination of thin lenses in contact: P = P1 + P2 + ... and 1/F = 1/f1 + 1/f2 + ... Use only for thin lenses in contact or negligible separation unless a separation formula is specifically given. A +2 D spectacle lens is converging with focal length 0.5 m. A -4 D lens is diverging with focal length -0.25 m.

3-mark answer

A lens with shorter focal length bends light more strongly, so its power has greater magnitude. Convex lenses have positive power in air and concave lenses have negative power in air under the usual sign convention. When thin lenses are placed in contact, their powers add algebraically. This makes lens power useful in spectacles and optical instruments because combinations can be handled directly in dioptres. Power: P = 1/f, where f is focal length in metre and P is in dioptre, D. Combination of thin lenses in contact: P = P1 + P2 + ... and 1/F = 1/f1 + 1/f2 + ... Use only for thin lenses in contact or negligible separation unless a separation formula is specifically given. A +3 D lens and a -1 D lens are placed in contact. Combined power P = +3 + (-1) = +2 D. The equivalent focal length is F = 1/P = 1/2 m = 0.50 m. The combination acts as a converging lens of focal length 50 cm. It appears in short numericals on spectacle lenses, equivalent focal length of lenses in contact, and sign-based questions about convex and concave lenses. For +3 D and -1 D, a common wrong answer is +4 D because signs are ignored and magnitudes are simply added.
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