I am trying to work through a problem about thin film interference. In the problem a thin film ($n_1 = 1.5$) is deposited on a layer of silicon ($n_2 = 3$). I need to find the thickness of the film which will result in it having a purple colour when viewed at normal incidence.
My first thought would be to simply find the thickness ($d$) which would result in violet/purple constructive interference (I am assuming the incident light is white) using:
$$2n_1d = m\lambda$$
But instead I am supposed to try to find a thickness that results in constructive interference for both red light and blue light. I was under the (maybe wrong) impression that a particular thickness results in constructive interference for only a specific wavelength?
I assume there must be something I'm missing about the concept so I'd really appreciate it if someone explain it to me.