AQA AQA 2018-style practice: In a Young's double-slit experiment, light passes through slits separated by 0.25 mm and forms fringes on a screen 1.8 m away. The fringe spacing is measured as 4.5 mm. Calculate the wavelength of the light.

Use the fringe equation w = λ Ds, rearranged to λ = wsD. Convert to SI units: w = 4.5 × 10^-3 m, s = 0.25 × 10^-3 m, D = 1.8 m. λ = (4.5 × 10^-3)(0.25 × 10^-3)1.8 = 6.3 × 10^-7 m, about 630 nm (red light). Markers reward the correct rearrangement, conversion to metres, and a sensible wavelength for visible light.

EnglandPhysicsSyllabus dot point

How do coherent waves interfere to produce bright and dark fringes, and what is needed to see a stable pattern?

The principle of superposition, path difference and phase difference, constructive and destructive interference, the conditions of coherence, Young's double-slit experiment, and the double-slit fringe equation.

A focused answer to AQA A-Level Physics 3.3.2.1 and 3.3.2.2, covering superposition, path and phase difference, constructive and destructive interference, coherence, Young's double-slit experiment and the fringe-spacing equation.

Generated by Claude Opus 4.810 min answerUpdated 2026-06-02

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What this dot point is asking
The principle of superposition
Path difference and phase difference
Coherence
Young's double-slit experiment
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What this dot point is asking

AQA specification points 3.3.2.1 and 3.3.2.2 want you to apply the principle of superposition, link path difference to phase difference, state the conditions for constructive and destructive interference, define coherence, describe Young's double-slit experiment, and use the fringe-spacing equation.

The principle of superposition

Superposition is the basis of all interference: where two crests coincide the displacement doubles, and where a crest meets a trough they cancel.

Path difference and phase difference

Path difference (the extra distance one wave travels) and phase difference are linked: a path difference of one whole wavelength corresponds to a phase difference of $2\pi$ radians (or $360^{\circ}$ ), so a path difference of half a wavelength is a phase difference of $\pi$ radians (antiphase).

Coherence

If the phase difference varied randomly, the bright and dark fringes would jump around and average out, leaving uniform brightness. This is why two separate lamps never produce visible interference fringes.

Young's double-slit experiment

Light from a single coherent source passes through two narrow, closely spaced slits. The slits act as two coherent sources, and the overlapping light produces a pattern of bright and dark fringes on a screen.

This experiment was historically the decisive evidence for the wave nature of light, because particles could not produce alternating bright and dark fringes.

Finding the wavelength from a double-slit pattern

In a Young's experiment, fringes are $w = 4.5 \text{ mm}$ apart, the screen is $D = 1.8 \text{ m}$ away and the slits are $s = 0.25 \text{ mm}$ apart. Find the wavelength.

step 1: Rearrange the fringe equation

From $w = \dfrac{\lambda D}{s}$ , the wavelength is $\lambda = \dfrac{ws}{D}$ .

step 2: Convert to SI units

$w = 4.5 \times 10^{-3} \text{ m}$ , $s = 0.25 \times 10^{-3} \text{ m}$ , $D = 1.8 \text{ m}$ .

step 3: Substitute

$\lambda = \dfrac{(4.5 \times 10^{-3})(0.25 \times 10^{-3})}{1.8}$ .

step 4: Evaluate

$\lambda = 6.3 \times 10^{-7} \text{ m}$ , about $630 \text{ nm}$ (red light).

Try this

Q1. State the condition on path difference for constructive interference. [1 mark]

Cue. Path difference $= n\lambda$ (a whole number of wavelengths).

Q2. Explain why a laser produces clear fringes in Young's experiment. [2 marks]

Cue. Laser light is coherent and monochromatic (constant phase difference, single wavelength), giving a stable, well-defined pattern.

Q3. State the phase difference, in radians, corresponding to a path difference of one wavelength. [1 mark]

Cue. $2\pi$ radians.

Exam-style practice questions

Practice questions written in the style of AQA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

AQA 20184 marksIn a Young's double-slit experiment, light passes through slits separated by

0.25 \text{ mm}

and forms fringes on a screen

1.8 \text{ m}

away. The fringe spacing is measured as

4.5 \text{ mm}

. Calculate the wavelength of the light.

Show worked answer →

Use the fringe equation $w = \dfrac{\lambda D}{s}$ , rearranged to $\lambda = \dfrac{ws}{D}$ .

Convert to SI units: $w = 4.5 \times 10^{-3} \text{ m}$ , $s = 0.25 \times 10^{-3} \text{ m}$ , $D = 1.8 \text{ m}$ .

$\lambda = \dfrac{(4.5 \times 10^{-3})(0.25 \times 10^{-3})}{1.8} = 6.3 \times 10^{-7} \text{ m}$ , about $630 \text{ nm}$ (red light).

Markers reward the correct rearrangement, conversion to metres, and a sensible wavelength for visible light.

AQA 20214 marksExplain what is meant by coherent sources, and state why coherence is necessary to observe a stable interference pattern in Young's double-slit experiment.

Show worked answer →

Two sources are coherent if they emit waves of the same frequency with a constant phase difference.

In Young's experiment the bright and dark fringes occur at fixed positions because the path differences at each point correspond to a fixed phase relationship. If the sources were not coherent, the phase difference would change randomly with time, so the positions of constructive and destructive interference would shift and the fringes would wash out, leaving uniform illumination.

Using a single source split into two slits (or a laser) ensures the two beams keep a constant phase difference.

Markers reward the definition of coherence (same frequency, constant phase difference) and explaining that a changing phase difference would wash out the fringes.

Related dot points

Sources & how we know this

AQA A-level Physics (7408) specification — AQA (2017)