Path difference (definition)
● VERBATIM — examined word-for-wordPath difference is the difference in the distances travelled by two waves from their respective sources to the point where they meet.
Δ = |S₂P − S₁P|What this actually means
It is a length, so it carries a unit (m, or often expressed as a multiple of λ). Two sources, one meeting point, subtract the two distances.
Path difference is what makes the phase difference at a point different from the phase difference at the sources. Two sources that start perfectly in phase can still arrive antiphase somewhere on the screen purely because one wave travelled half a wavelength further.
In geometry questions the distances are usually a Pythagoras job. Draw the triangle, find both distances to 3 or 4 significant figures, then subtract. Rounding too early kills the answer because you are taking a small difference of two large numbers.
Expressing the answer in wavelengths is the fastest route to the verdict. Δ = 2.0 m with λ = 1.0 m is Δ = 2λ, so constructive if the sources are in phase.
For a single source plus a reflector, the two paths are the direct path and the reflected path from the same source. The same rules apply, provided you are told there is no phase change on reflection.
Adding the two distances, or measuring both from the same source, instead of subtracting the two source-to-point distances.
Prove it — watch it be true
- Drag the path-difference probe to a point off the central axis.
- Read the two source distances and confirm the displayed path difference is their subtraction.
- Move the probe until the path difference reads exactly 1.00λ and check the verdict flips to BRIGHT.