Oil film thickness for total reflection 500nm

[messick11]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

 

[technician]

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.

Hope this gets you started !

 

[messick11]

Thank you VERY much. I never thought of it as an interference problem!

 

[technician]

Its a pleasure. Did you get 94nm (λ/4 for the wave in the oil)?