How Thick is the Oil Layer for Strong Reflection of Green Light?

[Terraist]

Hi, I'm a high school physics student and I'm having a lot of trouble with thin film interference

Homework Statement

A thin layer of oil (noil=1.25) is floating on water (n=1.33). How thick is the oil in the region that strongly reflects green light (λ=556nm)?

Homework Equations

noil/nwater = λwater/λoil

t = mλ/2, where t is thickness of the film, m is order of interference maxima (i'm not sure about this one)

The Attempt at a Solution

1.25/1.33 = 556/λ
λ=592 nm

t=mλ/2
=(1)(592)/2
=296 nm

(ans in book 222 nm)

I'm not entirely sure of what I'm doing here. I'm trying to just find the right formula to plug the variables in and I don't grasp the principles behind it. If someone could shed some light on the subject and provide some tips on how to solve similar problems it would be greatly appreciated.

 

[flyers]

Everything is right except you're not supposed to use n oil and water but rather n air and oil, because the ray is coming from above in air and not from the water right?( I think this is a trick question or something) So your new wavelength would be 556/1.33 (n air is 1) = 444 and you should get the books answer.