Conditioins for Interference Patterns in a Film

A parallel sided film can produce an interference pattern as a result of the reflections that take place at both surfaces.

From point B there are two possible paths to the air air the top.

    1. Along path BM in air, after reflection at the air – soap interface.

    2. Along BNEP in the film, undergoing refraction, refraction, reflection respectively at successive interfaces.

These ray will interfere and the nature of the interference – constructive or destructive – will depend on the optical path difference. The pathin air is the same length optically as the lengthin film, so the path difference is

The film has a greater refractive index than air so a phase change ofoccurs at B but none at E.

The total optical path difference is then

From the diagram,

Ifso path differencethen destructive interference occurs.

Ifthen path differencethen constructive interference occurs.

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