OCR A Level Physics A: Superposition, interference and the double slit (H556) – Revision Notes

These notes condense section 4.4.3 (Superposition) of the OCR Advanced GCE in Physics A specification (H556), Version 3.0 (March 2026), for first assessment in 2017. For full explanations and worked examples, read the study guide, then test yourself with the practice questions. The course hub, checklist and free 10-minute diagnostics help you plan. The specification says that d sin θ = nλ and diffraction gratings are assessed at A level only.

Definitions to recall word for word

Term	Definition
Principle of superposition	Where waves overlap, the net displacement is the signed sum of what each wave would give alone
Interference	Superposition of waves giving reinforcement in some places and cancellation in others
Coherent sources	Sources with a constant phase difference (so the same frequency)
Path difference	Difference in the distances travelled by two waves to the same point
Phase difference	How far one wave is ahead of the other in its cycle, in degrees or radians
Constructive interference	Waves meet in phase; resultant amplitude is larger
Destructive interference	Waves meet in antiphase; resultant amplitude is smaller (zero for equal amplitudes)

Equations

Equation	Meaning	Notes
phase difference = 2π × path difference / λ	radians	Use 360° in place of 2π for degrees
constructive: path difference = nλ	n = 0, 1, 2, …	For sources in phase
destructive: path difference = (n + ½)λ	n = 0, 1, 2, …	For sources in phase
λ = ax/D	a: gap between the slits; x: spacing of fringes; D: distance to screen	Needs a ≪ D
d sin θ = nλ	d grating spacing, n order	A level only
d = 1/N	N lines per metre	Convert from lines per mm first

Method in steps: graphical superposition

1. Draw both waves on the same axes and scale.
2. Choose points at regular intervals along the axis.
3. Read both displacements at each point, with signs.
4. Add them and plot the sum.
5. Join with a smooth curve. Equal-amplitude waves in phase double the amplitude. In antiphase they cancel everywhere.

Partial case: amplitudes 3.0 cm and 2.0 cm with 90° phase difference give a resultant amplitude of about 3.6 cm, between the 1.0 cm (antiphase) and 5.0 cm (in phase) limits.

Method in steps: is a point loud, quiet, bright or dark?

1. Find the two distances from the sources and subtract to get the path difference.
2. Divide the path difference by λ.
3. Whole number: constructive (sources in phase). Half-integer: destructive.
4. For phase difference, multiply the ratio by 2π (or 360°).
5. If one source is reversed (antiphase), swap the conclusions.

Worked reminder. Two sources in phase, λ = 0.50 m. A point is 4.20 m from one and 5.45 m from the other. Path difference = 1.25 m = 2.5λ, so destructive. Phase difference = 5π rad (900°).

Experiments with sound, microwaves and light (PAG5)

Wave	Set-up	What you observe	Key measurement
Sound	Two loudspeakers on one signal generator, microphone and oscilloscope	Loud and quiet regions along a line	Positions of adjacent maxima, speaker separation, distance to the line
Microwaves	Transmitter, metal plates with two gaps, probe receiver	Meter reading rises and falls	Positions of maxima, gap separation, distance to the detector line
Light	Laser or filtered lamp, double slit, screen	Bright and dark fringes	Distance across many fringes, D, a

Good practice: one common source for coherence, measure across several spacings and divide, repeat positions, interpolate between ruler markings, and take laser safety precautions. Treat a reading as uncertain by about half the smallest division and compare percentage uncertainties.

Young’s double slit

• Each slit diffracts the light, so the two beams overlap on the screen.
• The slits are coherent because they are lit by the same wavefront.
• Bright fringe: path difference nλ. Dark fringe: (n + ½)λ.
• Fringes are equally spaced for small angles.
• White light: central fringe white, other fringes coloured spectra.
• It gave a classical confirmation of the wave nature of light.
• Newton and Huygens held different ideas about light, so be ready to say what the experiment showed.

Change	Effect on fringe spacing x
Increase λ (red instead of blue)	Increases
Increase D	Increases
Increase a	Decreases
Halve a and double D	Multiplies x by 4

Validity of λ = ax/D. It comes from sin θ ≈ tan θ ≈ θ. It works for light because a is tiny compared with D. For microwaves with a = 12.0 cm and D = 1.50 m the formula is about 3% out, so state a ≪ D when you use it.

Model explanations to learn

Why is there a bright fringe at P? The slits are coherent because they are lit by the same wavefront. Light from the two slits reaches P with a path difference of a whole number of wavelengths. The waves arrive in phase, so they superpose constructively and the resultant amplitude is a maximum.

Why is there a dark fringe at Q? The path difference is an odd number of half wavelengths. The waves arrive in antiphase, so the displacements are equal and opposite, and the resultant amplitude is a minimum.

Why does the pattern vanish with two separate lamps? Their phase difference varies randomly and quickly, so maxima and minima keep moving and average out to uniform brightness.

Worked reminder with microwaves. Microwaves of wavelength 2.0 cm pass through gaps 8.0 cm apart, and the detector is 2.00 m away. x = λD/a = (0.020 × 2.00) / 0.080 = 0.50 m. Here sin θ = 0.25, so a/D is small enough for the formula to be a fair approximation, but the exact result differs by a few percent.

Diffraction grating (A level only)

• d = 1/N. For 200 lines per mm, N = 2.00 × 10⁵ m⁻¹ and d = 5.0 × 10⁻⁶ m.
• Maxima: d sin θ = nλ. The zeroth order is straight on.
• Highest order: largest whole number below d/λ. Never round up.
• Use sin θ, not tan θ or θ, because grating angles are large.
• To measure θ in practice, use tan θ = y/L from a screen at distance L, then find sin θ.
• Maxima are sharp, so the angle is measured more precisely than a double-slit fringe position.
• White light gives spectra, violet nearest the centre.

Must-know distinctions

• Coherent versus in phase. Coherent means a constant phase difference. In phase is one particular value, zero.
• Path difference versus phase difference. One is a distance, the other an angle.
• x versus the distance to the nth fringe. x is the spacing between neighbouring fringes.
• a versus d. a is the double-slit separation, d the grating spacing. Both are centre-to-centre.

Quick self-test

1. State the principle of superposition in your own words.
2. Two waves of amplitudes 5.0 cm and 2.0 cm meet in antiphase. What is the resultant amplitude?
3. Two in-phase sources are 0.90 m further from one than the other, and λ = 0.60 m. State the interference and the phase difference in degrees.
4. Two sources emit in antiphase. What happens at a point equidistant from both?
5. Define coherence and say why two torch bulbs do not give fringes.
6. A double slit with a = 0.20 mm and D = 1.60 m is lit with 600 nm light. Find x.
7. How does x change if a is halved and D doubled?
8. A grating has 200 lines per mm. Find d.
9. For 640 nm light on that grating, find the highest order and the angle of the second order.
10. Why measure across many fringes?

Answers

1. The net displacement is the signed sum of the displacements of the separate waves.
2. 3.0 cm (5.0 − 2.0).
3. Ratio 0.90 / 0.60 = 1.5, so destructive. Phase difference = 1.5 × 360° = 540°.
4. Equal paths give no path difference, but antiphase sources start half a cycle apart, so destructive interference.
5. A constant phase difference. Separate bulbs emit in random short bursts, so the phase difference changes constantly.
6. x = λD/a = (600 × 10⁻⁹ × 1.60) / (0.20 × 10⁻³) = 4.8 mm.
7. x ∝ D/a, so it becomes 4 times larger.
8. d = 1 / (2.00 × 10⁵) = 5.0 μm (5.0 × 10⁻⁶ m).
9. d/λ = 7.8, so highest order 7. sin θ = 2 × 640 × 10⁻⁹ / 5.0 × 10⁻⁶ = 0.256, so θ = 14.8°.
10. The percentage uncertainty in x is smaller for a long distance than for one small spacing.

Where marks are usually lost

• Writing “waves add” without saying displacements add as vectors, with sign.
• Saying coherent sources “have the same phase”. The wording is a constant phase difference.
• Stating the conditions as nλ and (n + ½)λ without saying they are path differences.
• Giving a path difference in wavelengths and forgetting to convert it to a phase difference.
• Using a in mm and λ in nm in the same calculation.
• Measuring one fringe spacing instead of many.
• Using small-angle approximations on a grating.
• Writing lines per mm as d, or rounding the highest order up.
• Forgetting that a ≪ D is needed for λ = ax/D.

Official syllabus

OCR, Advanced GCE in Physics A (H556) specification, Version 3.0 (March 2026), for first assessment in 2017, section 4.4.3 Superposition.