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Waves and Particle Nature of Light

Lens power and the thin lens equation

  • 2 things to know
  • Papers 2 and 3

Overview

Recall questions on power in dioptres, the sign of a diverging lens, why the powers of thin lenses in contact add, and the real-is-positive convention.

What you need to know

Answer each one before you reveal it.

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Numbers

What is the equation for the power of a lens, its unit, and the sign of a diverging lens's power?

Numbers

What is the real-is-positive sign convention, and where is the image of an object 0.30 m from a converging lens of focal length 0.20 m, and from a diverging lens of focal length −0.20 m?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    State the equation for the power of a lens and give its unit:

    Model answer

    The power of a lens is P = 1/f with the focal length in metres, and the unit is the dioptre (D).

  2. 2

    A converging lens has a focal length of 25 cm. What is its power?

    Model answer

    The power is P = 1/0.25 = +4.0 D.

  3. 3

    What is the sign of the power of a diverging lens, and why?

    Model answer

    It is negative, because the focal length of a diverging lens is negative under the real-is-positive convention.

  4. 4

    How is the power of several thin lenses placed in contact found?

    Model answer

    The powers simply add, so the combined power is P = P₁ + P₂ + P₃ and so on for each lens.

  5. 5

    Why do the powers of thin lenses in contact add?

    Model answer

    Each lens changes the convergence of the beam by an amount equal to its own power, and with thin lenses in contact these changes act at essentially the same place, so they combine directly.

  6. 6

    A +5.0 D lens is placed in contact with a −2.0 D lens. What is the focal length of the combination?

    Model answer

    The combined power is +5.0 − 2.0 = +3.0 D, so the focal length is 1/3.0 = 0.33 m and the combination converges.

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