8.3 Interference

2026 Syllabus Objectives

By the end of this topic, you should be able to:

  1. Understand the terms interference and coherence
  2. Show an understanding of experiments that demonstrate two-source interference using water waves, sound, light, and microwaves
  3. Understand the conditions required for two-source interference fringes to be observed
  4. Recall and use λ = ax / D for double-slit interference using light

1. Interference and Coherence

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What is Interference?

When two or more waves meet at the same point, they overlap and combine to produce a new resultant wave. This is called interference. The resultant wave's displacement is found using the Principle of Superposition — you simply add up the displacements of each individual wave at that point.

The resulting wave can be larger or smaller than either of the original waves depending on how they combine.

Types of Interference

Constructive Interference

This happens when two waves meet in phase — meaning their peaks (crests) line up with peaks, and their troughs line up with troughs.

  • The waves add together, producing a resultant wave with greater amplitude
  • If both waves have the same amplitude A, the resultant has amplitude 2A
  • This produces a maximum — the loudest sound, or the brightest light

💡 Think of "constructive" as building the wave up — making it bigger.

Destructive Interference

This happens when two waves meet in anti-phase (completely out of phase) — meaning the peak of one wave lines up exactly with the trough of the other.

  • The waves cancel each other out, producing a resultant wave with zero amplitude (if the two waves have equal amplitude)
  • This produces a minimum — silence, or a dark fringe
  • If the waves have unequal amplitudes, they only partially cancel, producing a smaller wave (partial destructive interference)

💡 Think of "destructive" as destroying the wave — making it smaller or zero.

Path Difference

Path difference is the difference in the distances that two waves travel from their sources to a specific point.

If one wave travels 14 cm to reach point P, and another wave travels 10 cm to reach the same point, the path difference is:

Path difference = 14 − 10 = 4 cm

The path difference determines whether interference at a point is constructive or destructive:

Type of InterferenceCondition (sources in phase)
Constructive (maximum)Path difference = nλ (a whole number of wavelengths)
Destructive (minimum)Path difference = (n + ½)λ (a whole number + half a wavelength)

Where:

  • λ = wavelength of the wave (in metres, m)
  • n = 0, 1, 2, 3… (any whole number / integer)

Example: Two sources in phase produce waves with λ = 2 cm. A point P is 14 cm from source 1 and 10 cm from source 2.

  • Path difference = 14 − 10 = 4 cm
  • 4 = n × 2 → n = 2 (a whole number)
  • ∴ Constructive interference occurs at P

Another example: if distances were 15 cm and 10 cm:

  • Path difference = 15 − 10 = 5 cm
  • 5 = n × 2 → n = 2.5 (not a whole number — it's a half-integer)
  • ∴ Destructive interference occurs at that point

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