# Relation Between Phase Difference And Path Difference

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

Image

Figure: Two waves traveling with the same frequency but with a phase difference of ??/2 and path difference of ??/4.

## Phase Difference And Path Difference

For any two waves with the same frequency, Phase Difference and Path Difference are related as-

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

Where,

• ?? is the wavelength of the wave.
• ??x is the path difference between the two waves.
• ???? 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 Relation between phase difference and path difference $\frac{\Delta x}{\lambda }=\frac{\Delta \phi}{2\pi }$ No units Phase Difference $\Delta \phi=\frac{2\pi\Delta x}{\lambda }$ Radian or degree Path Difference $\Delta x=\frac{\lambda }{2\pi }\Delta \phi$ meter

Hope you understood the relation and conversion of Phase Difference and Path Difference of the wave.

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#### Practise This Question

Two point charges +q and -q are held fixed at (-d, 0) and (d, 0) respectively of a (X,Y) coordinate system. Then