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.
Along path BM in air, after reflection at the air – soap interface.
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 path
in air is the same length optically as the length
in film, so the path difference is
The film has a greater refractive index than air so a phase change of
occurs at B but none at E.
The total optical path difference is then
From the diagram,
If
so path difference
then destructive interference occurs.
If
then path difference
then constructive interference occurs.
