Hi there,
I am unsure of how to calculate the path difference in questions relating to constructive and destructive interference.
I understand that when two waves are exactly in phase with each other, constructive interference occurs, so I labeled the intersecting points as areas where constructive interference occurs. But the answer scheme states that at the points where the waves are in phase, the path difference is $nλ$, while at the points where destructive interference occurs, the path difference is $(n − 1/2)\lambda$.
Where do these equations come from?
Best Answer
Re. "Where do these equations come from?"
Note that $sin(\theta + n\lambda)$ = $sin(\theta)$ so a phase shift of $n\lambda$ leaves the two waves in phase so they reinforce.
Whereas $sin(\theta + (n-1/2)\lambda)$ = $-sin(\theta)$ so a phase shift of $(n-1/2)\lambda$ leaves the two waves 180 degrees out of phase so the cancel.