Topic 4 of 5
Converging action and focal length
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.
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
- Choose a clear, sufficiently distant illuminated object. Rays from each small part of it reach the lens approximately parallel.
- Align the lens and a screen. Move the screen to find the sharpest image.
- Measure from the optical centre of the lens to the screen using a suitable ruler or optical-bench scale.
- 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.