ASPhysicsEdexcelRevision Notes5. Waves & Particle Nature of LightInterference & Stationary WavesPhase & Path Difference

Phase & Path Difference (Edexcel AS Physics): Revision Note

Exam code: 8PH0

Written by: Lindsay Gilmour

Reviewed by: Caroline Carroll

Updated on 8 October 2026

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Understand this topic with deeper explanations and understanding checks.

Phase & Path Difference

Waves are said to be coherent if they have:
- The same frequency
- A constant phase difference

Phase Difference

Two points on a wave, or on different waves, are in phase when they are at the same point in their wave cycle
The angle between their wave cycles is the phase difference

A circle with a radius rotating anticlockwise, marked at 0°, 45°, 90°, 180°, 270° and 360°, next to one cycle of a sine wave. Dashed lines show that each position of the radius matches a point on the wave at the same phase angle, from 0° to 360°.

Path Difference

The type of interference occurring at a given point (i.e. constructive or destructive) depends on the path difference of the overlapping waves
Path difference is defined as:

The difference in distance travelled by two waves from their sources to the point where they meet

Path difference is generally expressed in multiples of wavelength

Waves from two sources, S₁ and S₂, travel to two points. At P₂ the path difference is λ, giving constructive interference; at P₁ the path difference is λ/2, giving destructive interference.

At point P₂ the waves have a path difference of a whole number of wavelengths resulting in constructive interference. At point P₁ the waves have a path difference of an odd number of half wavelengths resulting in destructive interference

In the diagram above, the number of wavelengths between:
- S₁ ➜ P₁ = 6λ
- S₂ ➜ P₁ = 6.5λ
- S₁ ➜ P₂ = 7λ
- S₂ ➜ P₂ = 6λ
The path difference at point P₁ is 6.5λ – 6λ = λ / 2
The path difference at point P₂ is 7λ – 6λ = λ
In general:
- For two coherent sources in phase, the condition for constructive interference is a path difference of nλ
- For two coherent sources in phase, the condition for destructive interference is a path difference of (n + ½)λ
- In this case, n is an integer i.e. 0, 1, 2, 3...

Hence:
- Destructive interference occurs at point P₁
- Constructive interference occurs at point P₂

Circular wavefronts spread out from two sources, S₁ and S₂, with thick lines for crests and thin lines for troughs. Point P is 4λ from S₁ and 6λ from S₂.

At point P the waves have a path difference of a whole number of wavelengths resulting in constructive interference

Another way to represent waves spreading out from two sources is shown in the diagram above
At point P, the number of crests from:
- Source S₁ = 4λ
- Source S₂ = 6λ
The path difference at P is 6λ – 4λ = 2λ
This is a whole number of wavelengths, hence constructive interference occurs at point P

Worked Example

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

Diagram of six coherent waves from two point sources, travelling to a vertical line at points X, Y and Z. At X two peaks meet; at Y two troughs meet; at Z a peak meets a trough.

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
- Path difference = 5.5λ – 4.5λ = λ
- This is constructive interference and rules out options C and D
At point Y:
- Both troughs are overlapping
- Path difference = 3.5λ – 3.5λ = 0
- Therefore constructive interference occurs
At point Z:
- A peak of one of the waves meets the trough of the other
- Path difference = 4λ – 3.5λ = λ / 2
- This is destructive interference

Examiner Tips and Tricks

Phase difference and path difference are easy to confuse because the names sound similar. However, they are very different concepts.

Phase difference tells us how far apart the waves are when comparing their phases (you can think of this as their peaks and troughs).

Path difference is how much further along one wave is than another. Think of it as how much further along the path it has travelled.

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