Phase Shift on Reflection

Think of a wave pulse on a rope. If the far end is tied to a wall (a "denser" fixed end), the reflected pulse comes back upside down, flipped. If the far end is loose and free, the pulse reflects right side up, no flip. Light does the same thing at a boundary. When light traveling through a lower-index material reflects off a higher-index material, it flips phase by half a wavelength. When light reflects off a lower-index material instead, it comes back with no flip at all. This single rule is the whole topic.

In a thin film, two reflections happen: one off the top surface, one off the bottom surface, and these two reflected waves recombine and interfere. Whether they add up bright or cancel dark depends on two things together: the extra distance the bottom ray travels (which depends on thickness and the angle), and whether either reflection carried a half-wavelength flip. You add up the flips and the path difference in terms of wavelength, then check whether the total pushes the two waves into phase or out of phase.

This is why thickness alone never tells you the answer, you need the flip count too. A film where both reflections flip, or neither does, behaves like an ordinary path-difference problem. A film where exactly one reflection flips acts opposite to what thickness alone would suggest. This sets up the next idea: writing a clean condition for constructive and destructive interference in thin films, where the flip becomes one term you add alongside the path length term.