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Interference & Coherence (CIE A Level Physics)

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Interference & coherence

Interference

  • Interference occurs when waves overlap and their resultant displacement is the sum of the displacement of each wave
  • This result is based on the principle of superposition and the resultant waves may be smaller or larger than either of the two individual waves
  • Interference of two waves can either be:
    • In phase, causing constructive interference. The peaks and troughs line up on both waves. The resultant wave has double the amplitude
    • In anti-phase, causing destructive interference. The peaks on one wave line up with the troughs of the other. The resultant wave has no amplitude

Constructive and destructive interference

Constructive and destructive, downloadable AS & A Level Physics revision notes

Waves in superposition can undergo constructive or destructive interference

Conditions for constructive and destructive interference

  • In general, for waves emitted by two coherent sources very close together:
  • The condition for constructive interference is:

path difference = n lambda

  • The condition for destructive interference is:

path difference = open parentheses n space plus thin space 1 half close parentheses lambda

  • Where:
    • λ = wavelength of the waves in metres (m)
    • n = 0, 1, 2, 3... (any other integer)

 Coherence

  • At points where the two waves are neither in phase nor in antiphase, the resultant amplitude is somewhere in between the two extremes
  • Waves are coherent if they have the same frequency and constant phase difference

Coherent vs. incoherent waves

Coherent v non coherent, downloadable AS & A Level Physics revision notes

Coherent v non-coherent wave. The abrupt change in phase creates an inconsistent phase difference

 

  • Coherence is vital in order to produce an observable interference pattern
  • Laser light is an example of a coherent light source, whereas filament lamps produce incoherent light waves

Worked example

The diagram shows the interferences of coherent waves from two point sources.

we-interference

Which row in the table correctly identifies the type of interference at points X, Y and Z.

  X Y Z
A Constructive Destructive Constructive
B Constructive Constructive Destructive
C Destructive Constructive Destructive
D Destructive Constructive Constructive

Answer: B

  • At point X:
    • Both peaks of the waves are overlapping. This is constructive interference and rules out options C and D

  • At point Y:
    • Both troughs are overlapping so constructive interference occurs there

  • At point Z:
    • A peak of one of the waves meets the trough of the other. This is destructive interference (Row B) 

Examiner Tip

Think of ‘constructive’ interference as ‘building’ the wave and ‘destructive’ interference as ‘destroying’ the wave.

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Ashika

Author: Ashika

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Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.