Path difference and phase

Intermediate

Phase difference equals 2π times path difference over λ.

Key relationΔφ = 2πΔx/λ

A path difference Δx corresponds to a phase difference 2πΔx/λ. Constructive when Δx = nλ, destructive when Δx = (n + ½)λ.

Worked example

Δx = 1.5λ gives destructive.

Common mistake

Include any phase change on reflection.

In more detail

The phase difference between two waves is 2π times their path difference divided by the wavelength. Interference depends on this phase difference.

Designing antenna arrays to direct radio signals.
Measuring small distances by interference patterns in optical instruments.
Optical interference experiments use the path difference between two beams to predict where bright and dark fringes appear.

How do I get the phase from path?

Multiply the path difference by 2π over the wavelength.

Does the phase depend on speed?

Indirectly, because wavelength depends on speed for a given frequency.

How do I get from path difference to phase?

Multiply the path difference by 2π over the wavelength, which gives the phase difference between the two waves.