C
CraftExam
medium difficulty9 min

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.

In one line: Power uses metres; combination uses signed addition.

Concept Practice Coming Soon

Understand it

  • 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.

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.

Formula and rule

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.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

A +3 D lens and a -1 D lens are placed in contact.

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

Method you can reuse

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.

Visual tip

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.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

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

Think first, then show answer
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.

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.

Don't mix this up

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

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.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

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.
  1. 1

    Enough for 1 mark

    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

    Add for 2 marks

    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.

  3. 3

    Add for 3 marks

    A lens with shorter focal length bends light more strongly, so its power has greater magnitude.

Practice

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