Edexcel A Level (IAL) Physics-2.8 Phase & Path Difference- Study Notes- New Syllabus

Relationship Between Phase Difference and Path Difference

The phase difference between two waves tells us how far “out of step” they are in a cycle. The path difference tells us how much further one wave has travelled compared to the other. These two quantities are directly related.

 Key Relationship

The phase difference \( \phi \) (in radians) is related to the path difference \( \Delta x \) by:

$ \phi = \frac{2\pi}{\lambda}\,\Delta x $

• \( \phi \) = phase difference (radians)
• \( \Delta x \) = path difference (m)
• \( \lambda \) = wavelength (m)

Meaning:

• One full wavelength → \( \Delta x = \lambda \) → \( \phi = 2\pi \).
• Half wavelength → \( \Delta x = \lambda/2 \) → \( \phi = \pi \).
• Quarter wavelength → \( \Delta x = \lambda/4 \) → \( \phi = \pi/2 \).

For Constructive and Destructive Interference

Constructive interference (waves in phase):

$ \Delta x = n\lambda,\quad \phi = 2\pi n $

Destructive interference (waves \( 180^\circ \) out of phase):

$ \Delta x = (n+\tfrac12)\lambda,\quad \phi = (2n+1)\pi $

Rearranged Form

Sometimes we know the phase difference and need the path difference:

$ \Delta x = \frac{\phi\,\lambda}{2\pi} $

Key Notes

• Phase difference is dimensionless (measured in radians).
• Phase difference determines interference pattern brightness/visibility.
• Waves must be coherent for stable phase differences.