Destructive Interference of Light in 165nm Bubble Film

[stickplot]

Homework Statement

Light waves of which wavelength will destructively interfere due to the thickness of the bubble film? The bubble film thickness is 165 nm, with an index of refraction of n = 1.3.

a= 430 nm
b= 650 nm
c= 860 nm
d= 285 nm
(different wavelengths)

Homework Equations

The Attempt at a Solution

for the interference to be destructive the wave passing through the bubble thickness is delayed by half a wavelength. The wavelength of the light decreases when it passes into the bubble film.
I know this but i just don't know how to apply it to a equation and the problem

 

[Carid]

The half wavelength path difference corresponds to a light ray traversing the bubble film and being reflected from the inner bubble surface. So the path difference is twice the bubble thickness modulated by the effect of the refractive index. How does the refractive index alter the effective path length? Well you can try either multiplying or dividing by the given value of 1.3 to get the right mathematical result by comparison with the multiple choices; more important is to try to understand physically why light behaves like this in a transparent medium.