Since the index of refraction of the film is larger than that of air (n = 1) there is an additional phase shift for the reflection in the soap film.
The formula for constructive interference is
2L = (m+ 0.5)λ/n
Where,
L = thickness of the film
m = order number
λ = wavelength
n = index of refraction = 1.50
Rewriting in terms of λ:
λ = 3L/(m+ 0.5)
The information that λ = 800 nm and λ = 480 nm are consecutive maximum means that if λ = 800 nm refers to m, then λ = 480 nm refers to m + 1. Using the m dependence on λ, this implies that:
800 / (m + 1 + 0.5) = 480 / (m + 0.5)
800 (m + 0.5) = 480 (m + 1.5)
800 m + 400 = 480 m + 720
320 m = 320
m = 1
In other words for m = 1 and λ = 800 nm:
L = (m + 0.5)λ/3 = (1.5)*800/3 = 400 nm
