Condition for constructive interference
Constructive interference occurs where the two waves arrive in phase, that is Δφ = 2nπ. For sources emitting in phase this means a path difference of nλ (n = 0, 1, 2, …), and the resultant amplitude is the sum of the two amplitudes.
Δφ = 2nπ ⇔ path difference = nλ (sources in phase, n = 0, 1, 2, …)What this actually means
Always answer in two steps: state what happens to phase, then state the path condition. A good answer reads the waves meet in phase, so constructive interference occurs and a maximum is detected.
The clause for sources in phase is doing real work. If the sources are antiphase, this same path difference of nλ gives destructive interference instead.
n = 0 is the central maximum, sitting on the perpendicular bisector of the two sources where both paths are equal. It is a maximum for every wavelength, which is why the central grating fringe is white.
Name the observable to match the wave type. Light gives a bright fringe, sound gives a loud sound, water gives a large-amplitude ripple, microwaves give a maximum reading on the detector or a strong signal.
Do not say the waves add to give double the amplitude unless the amplitudes really are equal. Safer phrasing: the resultant amplitude is the sum of the individual amplitudes, so the intensity is a maximum.
Quoting path difference = nλ without stating that the sources must be in phase, so the antiphase case is answered wrongly.
Prove it — watch it be true
- Drag the path-difference probe along the screen until the readout shows an integer number of wavelengths.
- Confirm the verdict panel reads BRIGHT and the intensity profile shows a peak at that position.
- Repeat for 2λ and 3λ and check each lands on a peak.