Relation between Phase Difference and Path Difference

The phase difference is the difference in the phase angle of the two waves. Path difference is the difference in the path traversed by the two waves. The relation between phase difference and path difference is direct. They are directly proportional to each other.

Phase Difference and Path Difference

For any two waves with the same frequency, phase difference and path difference is related as –

\(\begin{array}{l}\Delta x=\frac{\lambda }{2\pi }\Delta \phi\end{array} \)

Where,

  • Δx is the path difference between the two waves.
  • ΔΦ is the phase difference between two waves.

Phase Difference and Path Difference Equation

The difference in the phase angle and difference in path length relation can be written in various ways-

Formula Unit
The relation between phase difference and path difference
\(\begin{array}{l}\frac{\Delta x}{\lambda }=\frac{\Delta \phi}{2\pi }\end{array} \)
No units
Phase Difference
\(\begin{array}{l}\Delta \phi=\frac{2\pi\Delta x}{\lambda }\end{array} \)
Radian or degree
Path Difference
\(\begin{array}{l}\Delta x=\frac{\lambda }{2\pi }\Delta \phi\end{array} \)
metre

Physics Related Topics:

Single Slit Diffraction
Polarisation by Scattering
Propagation Constant
Young’s Double Slit Experiment Derivation

 

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