Reflection maximum of material

[salmayoussef]

Homework Statement

A coating of n1 = 1.33 material is to be added to n2 = 1.50 glass, in order to make it "irridescent."
a) What is the thinnest layer of material which will have a reflection maximum for normal-incidence light at BOTH 400 and 600 nm (vacuum) wavelength?
b) This thickness will have a reflection minimum at some wavelength between 400 and 600 nm. What is the wavelength of the reflection minimum?

Known:
n1 = 1.33 (coating)
n2 = 1.50 (glass)

3. The Attempt at a Solution
I drew a diagram, but I don't know how to begin to go about this problem. Can someone please guide me?
I also know there's a 180 phase change because n2 > n1.

 

[mfb]

You get interference between light that gets reflected at the first surface and light that gets reflected at the second surface. They need a special relationship to give the properties you want.