How Does Angle of Incidence Affect Color Reflection in Soap Films?

[adc22]

A thin soap film (n=1.318) suspended in air has a uniform thickness. When white light strikes the film at normal incidence, violet light (412 nm) is constructively reflected. At what angle of incidence will green light (564 nm) be most strongly reflected? Assume that the film as the minimum thickness that can produce these reflections.


Snell's Law?
delta = (4*pi*d*nsoap / wavelength) + pi

I am at a real loss here because I just don't know what I should be thinking. I get the difference between constructive and destructive interference, but I have not had to blend wavelengths and indices of refraction using Snell's Law.

Please advise

 

[rl.bhat]

You can rewrite the formula as
2ndcos(beta) = ( m - 1/2 ) lambda. Here beta is the angle of refraction. For brightest reflection m should be 1
Using the values for violet light, find the thickness of the soap film.
Using this thickness find the angle of refraction for green light. Then using Snell's law find the angle of incidence of the green light.