9 min read · about 1 h 50 min with practice3 quick checks≈3% of the testCore: Core: tested on most papers
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This is the heaviest topic in the waves unit. It carries double-slit and grating calculations, two required practicals on AQA, a regular 6-mark extended response (on the practical or on the history of light), and conceptual traps about coherence and path difference. Master the path-difference argument and every formula follows from it.
By the end you’ll be able to
Explain coherence and the conditions for observable interference, using path difference and phase difference
Use w = λD/s for Young’s double slits and evaluate the practical, including laser safety
Describe single-slit diffraction patterns and how they change with slit width and wavelength
Apply d sin θ = nλ for diffraction gratings, find the maximum order and describe spectrometry applications
Explain historical significance: Young’s experiment as evidence for the wave nature of light
What the exam asks
Define coherence, path difference and phase difference, and state the conditions for observable interference.
Predict maxima and minima from path differences, for sound, microwaves and light.
Use w=sλD and describe Young’s double-slit experiment, including laser safety and the white-light pattern.
Describe the single-slit diffraction pattern and how it changes with slit width and wavelength.
Use , find the highest order, derive the equation (AQA) and describe applications.
vii.Check your understanding
3 questions on interference, diffraction and Young’s double slit. Every option is explained once you answer.
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Explain why Young’s experiment was evidence for the wave nature of light.
Board
Double slit
Grating
AQA
w=sλD (data sheet)
dsinθ=nλ, and its derivation
OCR A and Cambridge
λ=Dax, with a the slit separation and x the fringe separation
(OCR A: A level only)
Edexcel and IAL
no double-slit formula on the data list, so use path-difference reasoning
nλ=dsinθ (data list), core practical
OCR B
nλ=dsinθ with the small-angle approximation for a distant screen; superposition with phasors
nλ=dsinθ
Core ideas
Superposition, coherence and path difference
Principle of superposition: where two or more waves meet, the resultant displacement is the vector sum of the individual displacements.
Coherent sources have the same frequency and a constant phase difference, which need not be zero. Coherence makes the pattern stable. Two separate lamps are not coherent: their phase difference changes randomly millions of times a second, and the pattern averages out to even illumination.
Clear interference also needs similar amplitudes (so the minima are dark) and, for transverse waves, the same plane of polarisation.
Path difference=S2P−S1P. For sources in phase:
constructive interference (maximum) when the path difference =nλ
destructive interference (minimum) when the path difference =(n+21)λ
The phase difference caused by a path difference is Δϕ=2π×path difference/λ. If the sources are in antiphase, the conditions swap and the central line becomes a minimum.
Two-source interference with sound and microwaves
Two loudspeakers driven by one signal generator give alternate loud and quiet regions as you walk across in front of them. Microwaves passing through two gaps a few centimetres apart in a metal sheet give maxima and minima that a probe can detect. Interference is a property of all waves.
Young’s double-slit experiment
A coherent source (a laser, or historically a lamp behind a single slit) lights two narrow slits separated by s. Light diffracts at each slit, and the two diffracted waves overlap and interfere on a screen at distance D:
w=sλD(D≫s)
The fringes are equally spaced bright and dark bands, parallel to the slits.
Brightness falls away from the centre because of each slit’s single-slit diffraction envelope.
White light gives a white central fringe (every wavelength has zero path difference there), then coloured fringes with violet on the inside and red on the outside, because w∝λ. The pattern blurs after a few fringes.
Practical (AQA RP2, part 1): s is about 0.1–1 mm (read from the slide or measured with a travelling microscope), D is 1–3 m (tape measure), and w is found by measuring across many fringes, such as 10w, to cut the percentage uncertainty. A graph of w against D has gradient λ/s.
Why a laser? It is monochromatic (one wavelength, so sharp fringes with a single spacing), coherent, and intense and collimated (bright fringes even at large D).
Laser safety: never look into the beam or its reflections; use a low-power (class 2) laser; remove shiny surfaces and jewellery from the beam path; keep the beam horizontal and below eye level; never point it at anyone, and display a warning sign.
Single-slit diffraction
Diffraction is the spreading of a wave as it passes through a gap or around an obstacle. It is most noticeable when the gap is similar in size to the wavelength.
Monochromatic light through a single slit of width b gives:
a central maximum twice as wide as the other maxima, and much brighter;
side maxima that are equally spaced and much dimmer;
a first minimum at sinθ≈λ/b. This is useful for reasoning, but AQA and Cambridge only test the pattern qualitatively.
So:
a narrower slit gives a wider central maximum that is dimmer (less light gets through and it spreads further);
a longer wavelength (red rather than blue) gives a wider pattern;
white light gives a white central maximum with coloured fringes, blue on the inside and red on the outside.
The diffraction grating
A grating has many equally spaced slits, N per metre, so the slit spacing is d=1/N. With light at normal incidence, bright maxima appear where light from adjacent slits has a path difference of a whole number of wavelengths:
dsinθ=nλ
Derivation (AQA): draw two adjacent slits and the rays leaving them at angle θ towards a distant point. The right-angled triangle between the slits shows the path difference is dsinθ. Constructive interference needs this to equal nλ.
Highest order: since sinθ≤1, nmax is the whole-number part of d/λ. Always round down. The total number of maxima is 2nmax+1.
Compared with a double slit of the same d: the maxima are at the same angles but far sharper and brighter. With many slits, light cancels everywhere except very close to the directions where dsinθ=nλ, so the angles can be measured precisely.
White light: the zero order is white, and each higher order is a spectrum with violet at the smallest angle. The 2nd- and 3rd-order spectra overlap, because 2×700nm>3×400nm.
Applications: spectrometry, which identifies elements from their line spectra, finds the composition and red-shift of stars, and measures wavelengths precisely. X-ray diffraction by crystal lattices uses the same principle.
Young and the nature of light
In the 18th century Newton’s corpuscular theory, in which light is a stream of particles, was widely accepted, largely because of Newton’s reputation. Huygens had proposed a wave theory. Around 1801–1803 Young passed light through two slits and saw bright and dark fringes. Dark fringes mean that light added to light can produce darkness, which particles cannot explain but superposing waves predicts, together with the fringe spacing. The wave theory was confirmed when light was found to travel more slowly in water, as the wave model predicts and the particle model did not. In the 20th century the photoelectric effect restored a particle aspect, leading to wave–particle duality.
Worked examples
Exam technique
In every interference question, first write “path difference =⋯=…λ”, then decide maximum or minimum, then check whether the sources are in phase.
A coherence definition needs both “same frequency” and “constant phase difference”. “In phase” on its own loses the mark.
Convert lines per mm to d in metres straight away: d=10−3/Nmm.
In grating questions, check whether the angle given is between the two nth orders (2θ) or measured from the centre (θ).
A 6-mark question on Young’s slits or gratings usually has three strands: method, analysis (graph and gradient), and precautions including safety. Link them.
Common mistakes
Quick recap
Coherent sources have the same frequency and a constant phase difference.
For in-phase sources: a maximum when the path difference is nλ, a minimum at (n+21)λ.
Young’s slits: w=λD/s. White light gives a white central fringe and coloured fringes.
Single slit: the central maximum is twice the width of the others; a narrower slit or longer wavelength widens the pattern.
Grating: dsinθ=nλ; nmax is d/λ rounded down; the maxima are sharp and bright.
With white light, the 2nd- and 3rd-order spectra overlap.
Young’s fringes were decisive evidence for the wave theory of light over Newton’s corpuscles.