Why Does Oil on Water Create Rainbow Colors?

[sckeen1988]

A scientist notices that an oil slick floating on water when viewed from above has many different rainbow colors reflecting off of the surface. She aims a spectrometer at a particular spot, and measures the wavelength to be 750 nanometers (in air). The index of refraction of water is 1.33

The index of refraction of the oil is 1.20. What is the minimum thickness t of the oil slick at that spot?

I've thought about this for a little while and can't really think of how to get started. Really just looking for either a starting equation or an idea on how to approach the problem if anyone has any suggestions.

 

[Xisune]

Since the index of refraction of oil is less than water in this case, what must the path difference be for constructive interference?