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Here it is mentioned that for dielectric mirrors (mirrors designed to reflect a specific wavelength of light) "there is a 180-degree difference in phase shift at a low-to-high index boundary, compared to a high-to-low index boundary, which means that these reflections are also in phase" and therefore the reflections will interfere constructively. How is this the case - I thought that a 180˚ difference in phase shift meant the waves were actually antiphase and should interfere destructively?

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Here is the full sentence from that Wikipedia article:

The reflections from the low-index layers have exactly half a wavelength in path length difference, but there is a 180-degree difference in phase shift at a low-to-high index boundary, compared to a high-to-low index boundary, which means that these reflections are also in phase.

Observe that there are two effects going on:

  1. The path length difference is one-half wavelength (180 degrees)

  2. The phase shift at the boundary is different by 180 degrees.

These two effects add to produce a 360 degree (full wave) shift. That is why the reflections are in phase.

This can all be visualized as:

enter image description here

Each layer is a quarter-wavelength. That means that a round-trip through the layer is a half-wavelength (180 degrees). This phase shift added to the different phase shift due to reflection at the high-to-low and low-to-high index boundaries explains why the reflections are in phase.

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