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 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.