λ = light ray's wavelength : 380 nm to 760 nm for visible light (white rays).
μ_film = 1.33
thickness of film = d = 320 nm
θ1 = 0° = angle of incidence at the top layer of film
μ_air = 1
θ2 = angle of refraction into the soap film = angle of reflection at the film-air interface.
μ_air Sin θ1 = μ_film Sin θ2 --- (1)
There is a phase shift of 180 deg. when light rays are reflected at the top surface of the film, as μ_air < μ_film. There is no phase shift when rays are reflected at the film-to-air interface. The OPD (optical path difference) is:
2 μ_film d Cos θ2 = (m - 1/2) λ for constructive interference. --(2)
2 μ_film d Cos θ2 = m λ for destructive interference. -- (3)
here m = an integer.
As θ1 = 0°, θ2 = 0°.
2 * 1.33 * 320 nm = Optical path difference OPD
= 661.12 nm
In equations (2) and (3), the RHS is λ/2, λ, 3λ/2 ... We have the range of white light wavelengths mentioned above.
661.12 = λ for red color satisfies equation (3). So red color is destroyed.
661.12 = 1.5 λ for λ = 440.7 nm satisfies equation (4), ie., violet color is constructively added.