K323 / 2027
Light overview

Lesson 4 of 5

Converging action and focal length

  • I can describe the action of a thin converging lens on a beam of light.Syllabus

    Syllabus K323, 12(h). Describe the action of a thin converging lens on a beam of light.

  • I can define the focal length of a converging lens.Syllabus

    Syllabus K323, 12(i). Define the focal length of a converging lens.

Make a guess. You are not marked.

Parallel rays of light from a very distant tree pass through a thin converging lens. Where do they meet?

  1. At the principal focus, one focal length from the lens.
  2. At twice the focal length, where an equal-sized image forms.
  3. At the centre of the lens, where the rays cross the axis.
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At the principal focus, one focal length from the lens.

Rays parallel to the principal axis are refracted to meet at the principal focus. Its distance from the lens is the focal length, which is how the focal length is measured.

A thin converging lens brings a beam parallel to its principal axis to a principal focus. Focal length is the distance from the lens's optical centre to that focus.

A beam contains many rays. Here the lens is thin, surrounded by air, and used with rays close enough to its principal axis for the simple lens model.

Identify the axis, centre and focus

Principal axis
The straight reference line through the centre of the lens and its principal foci.
Optical centre
The point at the centre of the thin lens through which a ray passes essentially undeviated in this model.
Principal focus F
The point where rays initially parallel to the principal axis meet after passing through a converging lens.
Focal length f
The distance from the optical centre to the principal focus. It is a length, measured in units such as cm or m.

A parallel beam meets at the principal focus

This thin converging lens has f = 8.0 cm in air. The focal length is measured from the optical centre, not from the object.

A converging lens focuses a beam parallel to its principal axisThree rays travel right, parallel to the horizontal principal axis, towards a thin converging lens. After the lens they converge at the right-hand principal focus, 8 cm from the optical centre. The central ray remains straight. Both focal points are marked the same 8 cm distance from the centre. A nearby object's diverging bundle need not meet at this focus.FFParallel beamPrincipalfocusOpticalcentre8 cm8 cmPrincipal axis
A beam parallel to the principal axis converges at F. The two principal foci are the same distance from the thin lens in the same surrounding medium.

Light arriving from the opposite direction has a corresponding focus on the other side. Mark f on each side when using a ray diagram.

Light from a nearby object point usually arrives as a diverging bundle, rather than a parallel beam. The lens changes that bundle's direction, but its image need not be at the principal focus. The image position depends on the incoming rays.

Estimate focal length with a distant object

  1. Choose a clear, sufficiently distant illuminated object. Rays from each small part of it reach the lens approximately parallel.
  2. Align the lens and a screen. Move the screen to find the sharpest image.
  3. Measure from the optical centre of the lens to the screen using a suitable ruler or optical-bench scale.
  4. Move the screen slightly to either side of best focus to judge the uncertainty in that position.

Two bench readings

Lens centre at 12.4 cm; focused screen at 20.5 cm

The separation is 20.5 - 12.4 = 8.1 cm, so the focal-length estimate is f ≈ 8.1 cm.

The 20.5 cm reading alone is not the focal length. It measures from the bench zero, while f measures from the optical centre.

Choose a scale covering the full separation with divisions fine enough for the focusing uncertainty. Read the lens centre's position rather than an edge of its holder, and keep lens and screen properly aligned. A finite target distance makes the incident beam only approximately parallel; using a nearer target gives an image distance that should not simply be labelled f.

F is defined using a parallel incident beam. A converging lens does not send every incoming ray to F, regardless of where that ray came from.

Check your understanding

A beam parallel to the principal axis is brought to a sharp focus at bench reading 31.6 cm. The thin converging lens centre is at 23.5 cm. What is its focal length?

  1. 8.1 cm, the distance from the lens centre to the focus.
  2. 31.6 cm, because this is where the focus is found.
  3. 55.1 cm, the sum of the two readings.
Show the answer

8.1 cm, the distance from the lens centre to the focus.

The parallel beam identifies the principal focus. Its distance from the optical centre is 31.6 - 23.5 = 8.1 cm. Both readings use the same bench scale.