I was asked to determin the film thickness for an oil film (n=1.33) for a light beam (500 nm) to give total reflection. I could calculate refraction angle for air to oil, but have no idea as to how to approach this question.
This is an interference question. Light reflected from the front surface of the film interferes with light reflected from the back surface. For total reflection the 2 reflected waves must be in phase.
Points to consider
1) at the air/film surface a phase change of π (λ/2) occurs (there is no phase change at the film/air surface)
2) In the film the light travels a distance = 2 x thickness of the film and the wavelength changes.