Lenses and Dispersion

A converging lens brings parallel rays together at its principal focus; a diverging lens spreads them out. With ray diagrams you can find where an image forms and describe it: real or virtual, upright or inverted, enlarged or diminished. A prism splits white light into a spectrum because each colour refracts by a different amount.

Cambridge 5054 Paper 1Cambridge 5054 Paper 2Cambridge 0625 Papers 2, 4Cambridge 0625 Papers 1, 3≈ 35 minRevision 6 · updated 2026-11-01

Section 1 of 14

Learning objectives

Describe the effect of converging and diverging lenses, and define focal length.
Draw ray diagrams to find and describe images.
Calculate linear magnification.
Describe dispersion and the order of colours in the visible spectrum.

Pause and think

A magnifying glass held close to a page makes the words look bigger and the right way up. Held at arm's length, the view of the room is upside down. How can the same lens do both?

Section 2 of 14

Core idea

Start hereBurning paper with a magnifying glass

Hold a magnifying glass in sunlight and a bright dot appears where the rays meet. That point is the principal focus. Where a lens puts an image depends on how far the object is from that focus.

The big idea

Converging lens: parallel rays meet at $F$ . Two rays (parallel → through $F$ ; through the centre → straight) locate any image. White light disperses: violet bends most.

1. Ray diagrams

Converging lens: object beyond 2F gives a smaller, inverted, real image

Where the rays cross is the image: real (light really gets there), inverted and diminished. This is how a camera works.

Ray parallel to the axis → through $F$ beyond the lens.
Ray through the optical centre → undeviated.
Their meeting point is the image.

Where is the image?

Drawing diagram…

At exactly $2F$ the image is the same size; at $F$ no image forms.

Worked exampleMagnification

Object 2 cm tall, image 5 cm tall.

Goal: Magnification.
Strategy: Image ÷ object.

$m=\frac{\text{image height}}{\text{object height}}$
Definition.
$=\frac52=2.5$
No units.

Answer

2.5

✓ CheckLarger image: object between

F

and

2F

or inside

F

✓.

Common misconceptionVirtual images on screens Virtual images can't be projected: rays only appear to come from them.

2. Dispersion

A prism splits white light into a spectrum

Light bends towards the base of the prism at both faces. Each colour refracts by a slightly different amount: violet is deviated most, red least. This spreading is called dispersion: red, orange, yellow, green, blue, indigo, violet.

Violet slows most in glass, so bends most; red least.
At both faces the light bends towards the base of the prism.
Order: red, orange, yellow, green, blue, indigo, violet.

Pause and think

Which lens corrects short sight?

Summary

Two rays locate the image.
Real vs virtual.
Dispersion: violet bends most.

Focal length: Lens to principal focus.
Real image: Can be formed on a screen.

HistoryNewton's two prisms. In

1666

Isaac Newton split sunlight with a prism, then used a second prism to recombine the colours into white light. Others thought the prism was adding colour; Newton proved white light was already a mixture.

Fun factYour eye sees upside down. The lens in your eye forms a real, inverted image on your retina, so the world is projected upside down. Your brain flips it. In experiments, people wearing glasses that invert the view adapt within about a week and see normally.

Keep reading for free

Create a free account to read the rest of this lesson: key formulae, worked examples, explore the graph, common mistakes, exam tip, guided practice and more. Your answers are checked and your progress is saved.

Create free account Sign in