The physical principles of thin film interence

The simple form of thin film interference consist of a three layer stack;opaque metal layer coated with a transparent dielectric layer then a semi transparent layer on the top.
When a monochromatic beam of light is incident upon the first semi-transparent layer,its amplitude will split or divided by partial reflection.
The reflected wave will propagate towards the observer whilst the second transmitted beam will travel an optical path length of 2ndcos,where n is the reflective index of the transparent material.