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Topic 3 · 3.2.3–3.2.4

Thin lenses and dispersion

Core and Extended · Papers 1–6

🎯What you need to be able to do

  • Describe the action of thin converging and diverging lenses on a parallel beam; define focal length, principal axis and principal focus.
  • Draw ray diagrams for a real image, and describe images as enlarged/same size/diminished, upright/inverted, real/virtual.
  • Draw ray diagrams for a virtual image; describe a magnifying glass and the correction of short and long sight EXTENDED.
  • Describe dispersion by a prism and the seven colours in order; recall that light of one frequency is monochromatic EXTENDED.

📚The physics

Lenses and a parallel beam

Left: rays parallel to the principal axis pass through a converging lens and meet at the principal focus F, one focal length from the lens. Right: parallel rays pass through a diverging lens and spread out as if coming from a principal focus F on the same side as the incoming light.
The focal length is the distance from the centre of the lens to the principal focus.
principal axis: the line through the centre of the lens at right angles to it
principal focus (focal point): the point where rays parallel to the principal axis converge after passing through a converging lens (or appear to diverge from, for a diverging lens)
focal length: the distance between the centre of the lens and the principal focus

Ray diagrams

Draw any two of these rays from the top of the object; where they meet is the top of the image:

  1. parallel to the principal axis, then through F on the far side;
  2. straight through the centre of the lens, undeviated;
  3. through F on the object side, then parallel to the principal axis.

A real image is formed where rays actually meet and can be projected on a screen. A virtual image is formed where diverging rays appear to come from when extended backwards; it cannot be projected. Describe any image as enlarged, same size or diminished; upright or inverted; real or virtual.

An object O placed closer to a converging lens than F. A ray parallel to the axis refracts through F; a ray through the centre continues straight. The rays diverge on the far side; traced back as dashed lines they meet behind the object, forming a larger, upright, virtual image I.
EXTENDED A magnifying glass: the object is inside the focal length.

Correcting sight EXTENDED

A short-sighted eye focuses light from a distant object in front of the retina. A diverging lens placed in front of the eye spreads the rays slightly so they focus on the retina. Long sight is the opposite: the image would form behind the retina, and a converging lens corrects it.
EXTENDED Short sight: diverging lens. Long sight: converging lens.

Dispersion

A ray of white light enters a triangular glass prism and splits into a spectrum: red, orange, yellow, green, blue, indigo and violet. Red is refracted least and violet most.
ROYGBIV: in order of decreasing wavelength and increasing frequency.

White light is a mixture of colours. A prism refracts each colour by a different amount, so they separate: this is dispersion. The seven colours, in order of increasing frequency (decreasing wavelength), are red, orange, yellow, green, blue, indigo, violet. EXTENDED Light of a single frequency is monochromatic.

✏️Worked example

(Modelled on 0625/42 June 2026 Q6.) (a) Complete the definition: the principal focus of a converging lens is the point … [2] (b) An object 3.0 cm tall stands 15 cm from a converging lens of focal length 10 cm. Draw a scale ray diagram to find the image. [3] (c) Describe the image. [2]

(a) … where rays parallel to the principal axis converge (meet) after passing through the lens.

A scale ray diagram. The object O, 3.0 cm tall, is 15 cm from a converging lens with foci 10 cm either side. Three rays from its top meet 30 cm beyond the lens, where an inverted image I 6.0 cm tall forms.

(b) Two rays (any two of the three shown) from the top of O meet 30 cm from the lens, 6.0 cm below the axis. Draw the image arrow from the axis to that point and label it I.

(c) Real, inverted, enlarged (magnified twice).

Check it. An object between F and 2F always gives a real, inverted, enlarged image beyond 2F: 30 cm is beyond 2F (20 cm). Projectors work this way.
Bending rays at both surfaces. For a thin lens, draw the change of direction once, at the centre line of the lens, and use a ruler.

📝Practise

In the style of the multiple-choice and theory papers. EXTENDED marks Supplement content.

1. (Multiple choice.) Which list gives three colours of the spectrum in order of decreasing frequency? A: red, green, violet. B: violet, green, red. C: green, red, violet. D: violet, red, green.
B. Violet has the highest frequency, red the lowest.
2. (Multiple choice.) EXTENDED A long-sighted student reads a book. Where does her eye form the image, and which lens corrects it? A: in front of the retina, converging. B: in front of the retina, diverging. C: behind the retina, converging. D: behind the retina, diverging. (Modelled on 0625/22 June 2026 Q21.)
C.
3. (Theory.) An object is 30 cm from a converging lens of focal length 10 cm. Describe the image formed. [3]
The object is beyond 2F, so the image is real, inverted and diminished, between F and 2F on the other side (15 cm from the lens).
4. (Theory.) State the difference between a real image and a virtual image. [2]
A real image is formed where rays actually meet and can be shown on a screen. A virtual image is where rays only appear to come from (traced back) and cannot be shown on a screen.
5. (Theory.) EXTENDED Explain how a converging lens can be used as a magnifying glass. [2]
Place the object closer to the lens than its principal focus (within the focal length). The lens forms an upright, enlarged, virtual image, seen by looking through the lens.
6. (Practical.) Describe how to measure the focal length of a converging lens quickly. [3]
Point the lens at a distant object (e.g. a window across the room) and move a screen behind it until a sharp image forms. Measure the distance from the lens to the screen: this is (approximately) the focal length, because rays from a distant object are almost parallel.
7. (Theory.) EXTENDED What is meant by monochromatic light? [1]
Visible light of a single frequency (one colour).

🔗Go deeper — other people’s work

These are external resources, not mine. If one stops working, tell me and everything above it on this page still stands.

  • PhET “Geometric Optics” — move an object and watch the image
  • The Physics Classroom — ray diagrams for converging lenses