In the film thin interference illustration I've attached, I've proposed two cases. The black, yellow and blue EM waves denote the incident wave, incident's reflected wave off yellow region, incident's reflected wave off blue region. The white, yellow and blue regions denotes a medium with a refractive index of n=1.5, 1.2 and 1.0 respectively.
In case 1's yellow region, the yellow/blue reflected lights oscillate with the same phase as where the incident light hits the yellow/blue region. Therefore, there is no phase difference between the yellow and blue reflected lights.
In case 2's blue region, the yellow/blue reflected lights DOES NOT oscillate with the same phase as where the incident light hits the yellow/blue region. Instead, the reflected lights start off its wave cycle at phase=0. Therefore, there is a phase difference between the yellow and blue reflected lights (or between the yellow/blue reflected lights and the incident light).
May I ask which case is the correct representation of how EM waves behave when they hit a region of different refractive index? (I chose n=1.5, 1.2, 1.0 to simplify the phenomenon and ignore π shifts)
By analogy with a pulse reflected off a free end, I believe it should be case 1 that is correct.
However, if case 1 is correct, then it wouldn't explain the significance of considering path differences in thin film interference i.e. 2d=(mλ)/n for constructive interference or 2d=(mλ)/(2n) for destructive interference. Since no matter how thick the thin film is, or how much distance has been travelled, the reflected lights will be in phase.
Therefore, I believe case 2 should be correct in order to explain the significance of considering path differences in thin film interference.