When a small amount of petrol is poured onto some water, interference fringes can be see. Light is reflected from the upper and lower surfaces of the film. When the phase difference between the reflected waves is a whole number of wavelengths, fringes are observed.
Suppose the thickness of the film is
Light is reflected from the upper and lower surfaces of the petrol film. When light is reflected from a material with a greater refractive index a phase change of 180 degrees occurs. This occurs at the air oil interface but not at the oil water interface.
If the angle of incidence is
for the air oil interface, by Snell's law, the angle of refraction is given by
The extra distance the light must travel through the oil is
over and above the light that is reflected from the air oil interface.
The path difference is
and for constructive interference (taking phase changes into account),