Thin Film Interference Question

[ChibiMolinero]

Homework Statement

White light is sent downward onto a horizontal thin film that is sandwiched between two materials. The indexes of refraction are 1.80 for the top material, 1.68 for the thin film, and 1.50 for the bottom material. The film thickness is 5.24*10^-7 m.

(a) Of the visible wavelengths (400 to 700 nm) that result in fully constructive interference at an observer above the film, which is the longer wavelength?

(b) Which is the shorter wavelength?

Homework Equations

2t = mλ/n - for constructive interference
2t = (m+.5)λ/n - for destructive interference

The Attempt at a Solution

I don't even know where to start. I'm not sure if the wave goes through air before hitting the top layer, or if that's even relevant? I don't know if they're looking for the wavelength in air? If I have to use the wavelength in the film to find the wavelength in the top layer to find the answer? Any help would be greatly appreciated.

 

[Delphi51]

Welcome to PF, Chibi.

The λ/n in the formula is the wavelength in the film, where λ alone is the wavelength in vacuum. Your answers will be values of λ.

The indices decrease as you go down through the 3 layers; this is opposite to the usual situation where the top layer is air. It seems to me this will cause a phase change that will change the formula. Might be worth looking into.