Constructive/Destructive Interference in a Thin Oil Film

[Quattad]

Hi PhysicsForums,

Here's a thin film interference question I'm having problems with.

An oil film (n=1.50) floats on a water body (n=1.33) in an air environment. Normal incident white light is reflected by the oil film. But in the spectrum of reflected light, 500nm and 700nm light are missing.

(a) Find the minimal non-zero thickness of the film.
(b) If an oil film is on sapphire (n=1.78) instead of water and the 500nm and 700nm wavelengths of light are still missing, find the two smallest possible thicknesses of the film.Please find attached for my workings.

For part (a), if two wavelengths are missing due to destructive interference of the reflected rays, shouldn't there be two possible thicknesses of the film as well?
For part (b), I'm not too sure whether to use 500nm or 700nm to find out the two minimum thicknesses.

Any possible insight will be greatly appreciated!

 

[DrClaude]

My workings so far are in the following link https://drive.google.com/file/d/0B8ersklrGbQlcnAza3l1VW1hTjg/view

Please post them here, not in a file on an external server.