How Is Destructive Interference Achieved in a Liquid Film on Glass?

[Penguin98]

Mentor note: Thread moved from Adv. Physics Homework
1. Homework Statement
Light is incident normally from air onto a liquid film that is on a glass plate. The liquid film is 174 nm thick, and the liquid has index of refraction 1.60. The glass has index of refraction n = 1.50. Calculate the longest visible wavelength (as measured in air) of the light for which there will be totally destructive interference between the rays reflected from the top and bottom surfaces of the film. (Assume that the visible spectrum lies between 400 and 700 nm.)

Homework Equations

n-film<n-glass, thus, it is non-reflective coating
equation to use: t=lamda/4*n
t = 174nm
lamda = wavelength (which I need to find)
n = ? (some kind of ratio, one of the n values provided?)

But having trouble figuring out value of n. Any help or where to go after this will be appreciated!

 

[kuruman]

You need to write an equation for destructive interference involving two rays, one reflected off the top of the film (air-liquid interface) and one off the bottom (liquid-glass interface) as the problem suggests. What is the condition for total destructive interference in terms of the path length difference? Don't forget that the wavelength of the light traveling in the liquid is shorter than in air.

 

[Penguin98]

I already figured this one out, thanks though!